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Systematic Review

Biomechanical Insights into the Variation of Maxillary Arch Dimension with Clear Aligners: A Finite Element Analysis-Based Scoping Review

by
Alessandra Putrino
1,*,
Gaia Bompiani
1,
Francesco Aristei
1,
Valerio Fornari
2,
Ludovico Massafra
2,
Roberto Uomo
1 and
Angela Galeotti
1,3,*
1
Dentistry Unit, Management Innovations, Diagnostics and Clinical Pathways, Bambino Gesù Children’s Hospital, IRCCS, 00165 Rome, Italy
2
Nuvola Research & Development Division, Gruppo Europeo di Ortodonzia, 00030 San Cesareo, Italy
3
UN-EU International Research Project on Human Health–Oral Health Section, 1200 Geneva, Switzerland
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2025, 15(17), 9514; https://doi.org/10.3390/app15179514
Submission received: 27 July 2025 / Revised: 22 August 2025 / Accepted: 27 August 2025 / Published: 29 August 2025
(This article belongs to the Special Issue Advances in Orthodontic Treatment, 2nd Edition)
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Versions Notes

Abstract

Featured Application

Finite element analysis offers a powerful tool for the design and customization of orthodontic devices, especially clear aligners, allowing treatment to be customized to the individual needs of patients and improving the prediction of therapeutic effects.

Abstract

Clear aligners (CAs) have emerged as a widely accepted alternative to conventional fixed orthodontic appliances due to their aesthetic appeal, comfort, and removability. Despite their increasing use, the precise biomechanical behavior of CAs—particularly in relation to maxillary arch expansion and torque control—remains incompletely understood. This scoping review aims to synthesize and critically examine the recent body of evidence derived from finite element analysis (FEA) studies investigating the performance of clear aligners in managing transverse discrepancies and controlling tooth movement. It considered studies published up to April 2025. All included FEA studies assumed dental and bone tissues as linearly elastic, homogeneous, and isotropic, unless otherwise specified. Five in silico studies were included, all employing three-dimensional FEA models to assess the influence of various clinical and design parameters, such as aligner thickness, movement sequence, attachment configuration, and torque compensation. The findings consistently show that movement protocols involving alternating activation patterns and specific attachment designs can significantly improve the efficiency of maxillary expansion, while reducing undesired tipping or anchorage loss. Additionally, greater aligner thicknesses were generally associated with increased force delivery and more pronounced tooth displacement. Although FEA provides a powerful tool for visualizing stress distribution and predicting mechanical responses under controlled conditions, the lack of standardized force application and limited clinical validation remain important limitations. These findings underscore the potential of optimized aligner protocols to enhance treatment outcomes, but they also highlight the need for complementary in vivo studies to confirm their clinical relevance and guide evidence-based practice.

1. Introduction

Orthodontic treatment has evolved significantly with the introduction of clear aligners (CAs), offering a less invasive and more aesthetic alternative to traditional fixed multi brackets therapies [1,2,3,4]. One of the primary challenges in clear aligner therapy is achieving predictable and controlled tooth movement in the management of complex orthodontic cases [5], particularly those requiring corrective modifications of upper arch dimension, expansion, distalization, deep bite, open bite, cross-bite, crowding, or mandibular advancement [6,7,8,9,10,11,12]. Recent studies have demonstrated their ability to produce significant transverse changes in the upper arch [6,8] and to provide predictable outcomes in distalization and sagittal correction with mandibular advancement appliances [7,12]. Evidence also supports their efficacy in vertical discrepancies, such as deep bite [10] and anterior open bite [11], as well as in transverse problems like anterior crossbite [9]. Specifically, unlike conventional rapid palatal expanders, CAs rely on biomechanical principles to induce gradual tooth displacement, necessitating precise control of force application [13]. Current knowledge on CAs shows that they provide a slow expansion comparable to a quad helix expander but with a better preservation of both the height and thickness of the alveolar bone [14]. Even if expansion with these devices in mixed dentition is effective, the greatest increase in maxillary width can be detected at the level of upper first and second deciduous molars followed by canines, whereas the upper permanent first molars show a greater expansion in the intermolar mesial width due to a rotation that occurs around their palatal roots [6]. However, the outcomes are not always clear, and it is still considered difficult for clinicians to predict these dental movements [6,15]. The opportunity to integrate clinical experience with the latest generation computational analyses derived from biomedical engineering research and experimentation has meant that in vitro studies and pilot studies, supporting clinical evidence on larger samples and on this specific field of research, have been, at least in this area, greatly overwhelmed by finite element analysis (FEA) studies. FEA has emerged as a valuable tool in understanding the orthodontic biomechanics since 2013 [16,17,18] and specifically mechanical behavior of CAs and their impact on dental structures in more recent studies [19,20,21]. Recent research has explored various factors influencing aligner efficiency, including the role of aligner thickness, movement patterns, attachment configurations, and expansion rebound effects [22,23,24,25,26,27,28]. Case-based and in vitro studies demonstrated that differences in material composition and thickness significantly affect the magnitude and distribution of orthodontic forces delivered by aligners [22,23]. Finite element analyses further highlighted that both aligner thickness and the type of tooth movement influence the biomechanics of arch expansion and distalization, thereby affecting clinical predictability [24]. Systematic reviews also confirmed that variability in aligner design and biomechanics contributes to differences in treatment effectiveness across malocclusion types [25]. In addition, the configuration and surface wear of attachments were shown to play a critical role in controlling tooth movement, with optimized attachment designs improving the predictability of specific movements such as canine distalization and overbite reduction [26,27]. Finally, advances in material sciences, including the development of biomimetic and smart polymers as well as additive manufacturing technologies, are expected to further refine aligner performance and customization [28]. By analyzing stress distribution and force transmission in three-dimensional models, researchers aim to optimize aligner design and improve treatment outcomes, filling the lack of predictability that affects movements with ambiguous results, such as expansion with clear aligners. The objective of this scoping review is therefore to systematically examine current FEA-based research on clear aligners, with a focus on the variation of maxillary arch dimensions, the influence of different expansion protocols, torque control mechanisms, and the impact of material properties on aligner performance. The underlying hypothesis is that FEA provides reproducible and clinically relevant insights into the biomechanical behavior of CAs, which may ultimately enhance treatment predictability and patient satisfaction.

2. Materials and Methods

2.1. Type of Study

This scoping review was developed based on the PRISMA-ScR (Preferred Reporting Items for Systematic reviews and Meta-Analyses extension for Scoping Reviews) guidelines [29]. This scoping review project was registered on 10th April 2025 as an OSF-Standard Pre-Data Collection Registration (DOI 10.17605/OSF.IO/XGMU7) on OSF Registries (Open Science Framework, Center for Open Science©, 2011–2025). The research took place on 27 and 28 April 2025. The search was conducted using the following MeSH terms and free terms in combination with the Boolean operators “AND” and “OR”: clear aligners, palatal expansion, finite element analysis, tooth movement.

2.2. Review Question

The research question “What is the available evidence on the use of finite element analysis (FEA) in studies investigating clear aligners for maxillary arch expansion?” was formulated according to the acronym PCC, as follows: (1) population: finite element models simulating dental arches or tissues (also derived from real digital casts); (2) concept: use of finite element analysis (FEA) to simulate mechanical behavior and stress distribution; (3) context: application of clear aligners for maxillary arch expansion.

2.3. Inclusion and Exclusion Criteria

This review included articles belonged to the finite element analysis study design related arch maxillary expansion, which can be consulted in both the abstract and in the full text reading and written in English. No limits on the year of publication were placed. Other types of studies or previous reviews on the subject and articles not written in English were discarded.

2.4. Search Strategy and Study Selection

The review of the literature on the variation of the maxillary arch dimension with CAs using “Finite Element Analysis” was carried out by consulting the main scientific literature databases (PubMed, Scopus, LILACS, Cochrane) and two registers (Clinical Trial.gov, Open Science Framework). The initial results of the various databases, whose duplicates were eliminated thanks to the Zotero software (Zotero 5.0 for Windows, Corporation for Digital Scholarship, Vienna, VA, USA), were then selected on the basis of the availability of the abstracts and the verification that the contents, then deepened by the full-text reading, met the pre-established eligibility criteria until obtaining the final number of resources to be included in the results, subjected only to descriptive statistical analysis based on absolute frequencies.

2.5. Study Selection and Data Collection

Since the identification of studies and data collection were performed by two experienced orthodontists (A.P. and R.U.), all phases were carried out autonomously, and only at the end were the results combined and compared. A good agreement was observed in the inclusion process with Cohen’s Kappa equal to 0.90 and 0.88, respectively. Any possible discordant opinions or studies subject to dubious classification were overcome through a shared review of the specific content and full-text readings of the results excluded from the primary examination of the abstract. A third operator (A.G.), also a specialist in orthodontics, supervised the review process. The contents of any FEA studies included were collected in an electronic sheet and charted according to the authors and year of publication, country, objective of the study, study protocol, results, and conclusions (Table 1).

2.6. Risk of Bias

Even if this scoping review aims to map existing literature and does not intend to assess the effectiveness of interventions, so that a formal risk of bias assessment is not mandatory following the manual published by the Joanna Briggs Institute [34], a tool recently proposed (based on 6 domains and 22 questions) and specifically developed for the risk of bias assessment in finite element analysis in dentistry, called ROBFEAD (Risk of Bias and Feasibility for Finite Element Analysis) [35], has been used in its original version. It was performed by two reviewers (A.P. and F.A.) independently with a high degree of agreement (Cohen’s Kappa equal to 0.98). A third reviewer (R.U.) was consulted in case of disagreement in the risk of bias analysis.

3. Results

A total of 250 articles were initially identified; of these, 27 were included for abstract reading after the removal of duplicates (n = 71) and of records marked as ineligible by automation (n = 152). In this context, “automation” referred to the automatic functions of the electronic databases, including duplicate detection, filtering by document type (conference abstracts, editorials, and letters), and language restrictions (non-English records). Then, 20 studies were excluded and the remaining 7 were sought for retrieval. The reports assessed for eligibility were six, but one report was then excluded because it did not clearly address the maxillary arch expansion topic. Five studies were finally considered, because they fulfilled all the inclusion criteria, as follows: (1) being related to maxillary arch expansion with clear aligners; (2) finite element analysis study design; (3) full text reading available; (4) written in English. The findings were presented in detail and listed in the flow diagram established by the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) method generated using the Shiny App online tool by Evidence Synthesis Hackaton (eshackathon.org) (Figure 1) [36].
The results are detailed in Table 1. The studies were published between 2023 and 2024 [24,30,31,32,33]. The studies have been published from Chinese authors [24,30,31,33], except one published from Turkish/Australian authors [32]. The study objectives are related to CAs productive processes and effects on expansion [24] and tooth movement efficiency and strategies [30,31,32,33]. The study protocols all involve comparing different tooth movement simulations (mainly torque variation) with CAs differing in type and configuration [24,30,31,32,33]. In the results, the emerging subtopics are related to the molar tipping [30,31,32] and the influence of the periodontal ligament stress [24,33]. All the studies report in their conclusions side effects during the maxillary expansion with CAs and the need for customized movements that can be better planned by FEA studies [24,30,31,32,33]. The risk of bias is moderate for one study [32] and low for the other studies [24,30,31,33] (Table 2 and Table 3).
A variety of software, such as Ansys Workbench (Ansys R1 2021 and R2 2023 ANSYS Inc., Canonsburg, PA, USA) [24,31,33], Ansys SpaceClaim, a parametric CAD (computer-aided design) software to develop geometric model, and then combined to Ansys for finite element analysis (Ansys R 2023, ANSYS Inc., Canonsburg, PA, USA) [32], and Abaqus (Abaqus 2020, SIMULIA, Providence, RI, USA) [30], were used. All studies employed three-dimensional (3D) models to simulate orthodontic movements [24,30,31,32,33], focusing on different anatomical regions such as the maxillary arch [24,33,34], maxillary molars [32], or the mandibular anterior segment [33]. The geometric models were constructed using data derived from CBCT (cone beam computer tomography) [24,30,31,32,33]. The analyses performed were primarily static structural simulations, designed to evaluate tooth displacements, stress distribution, and biomechanical responses under aligner-induced forces (Table 4).
All five included studies applied orthodontic loads through aligners, simulating clinical tooth movements under different mechanical protocols [24,30,31,32,33]. Most studies did not explicitly report the magnitude of the applied forces [24,30,32,33], relying instead on displacements or aligner thickness to generate stress and simulate tooth movement [34]. The models typically included major dental tissues such as teeth [24,30,31,32,33], periodontal ligament (PDL) [24,30,31,32,33], and alveolar bone [24,32,33], with some also incorporating aligners [24,30,33] and attachments [30]. Material properties were assigned based on established values from the literature or previous validated FEA research [24,30,31,32,33]. These choices reflect the common practice in orthodontic FEA modeling, where precise force quantification is challenging but relative movement and stress behavior are prioritized (Table 5).

4. Discussion

Recent studies utilizing FEA have provided critical insights into the biomechanics of CAs [19,20,21], particularly in maxillary arch expansion. The biomechanical efficiency of CAs in managing maxillary arch discrepancies is a growing area of interest, particularly about their capacity for expansion control and torque management. The studies included in this scoping review—based on finite element analysis (FEA)—provide critical insights into how variations in aligner design, material properties, attachment configurations, and movement protocols influence the predictability and stability of orthodontic tooth movements. While aligners offer aesthetic and comfort-related advantages over fixed appliances, achieving precise biomechanical control remains challenging, especially in complex transverse movements [24,30,31,32,33]. These findings are in line with systematic reviews on clear aligner therapy, which emphasize that while CAs are effective in mild to moderate malocclusions, their efficiency in transverse and torque-controlled movements is still limited compared to fixed appliances [37,38].

4.1. Geometric Model Construction

All included studies employed three-dimensional (3D) finite element models, which are essential for simulating the complex anatomical structures involved in orthodontic biomechanics. The maxillary arch was the most modeled region [24,30,31], with some studies focusing specifically on molars or anterior teeth [32,33]. Model geometries were obtained from cone beam computed tomography (CBCT) [24,30,31,32,33] and derived digital dental templates [30,31], and CAD-based anatomical references [32]. The choice of data sources significantly affects the accuracy of the anatomical representation and the fidelity of force simulations. The CBCT-based models provide higher anatomical realism, but they require more advanced segmentation and processing [39,40]. This methodological aspect is consistent with previous orthodontic FEA research, highlighting that CBCT-derived datasets improve anatomical accuracy, although they increase computational demand [39,41].

4.2. Dimensional Fidelity and Anatomical Assumptions

The fidelity of each geometric model depends on the dimensional input and assumptions made during reconstruction [42]. For example, Zhang et al. and Karslı et al. utilized average anatomical values or standard templates [31,32], which may not fully capture inter-individual variability in dental morphology and bone structure. In contrast, studies like Li et al. incorporated patient-like anatomical features directly from CBCT datasets [24], offering a more clinically realistic simulation. However, the trade-off includes increased modeling complexity and computational demands as hypothesized in less recent observations [43]. Clinical studies have confirmed that inter-individual variability in root morphology and bone density strongly affects expansion outcomes, which suggests that the use of patient-specific CBCT data in FEA is likely more clinically relevant [44].

4.3. Software Platforms Used

The studies reviewed employed industry-standard FEA software such as ANSYS Workbench [24,31,33] and Abaqus [30], sometimes in combination with CAD tools like SpaceClaim for model design [32]. ANSYS was the most used platform, known for its robust structural analysis capabilities and user-friendly interface, which facilitates integration with dental biomechanics studies [45]. Abaqus, used by Yao et al. [30], offers superior performance for nonlinear material modeling and large deformation simulations, making it suitable for evaluating aligner-driven movement protocols involving complex force systems [46]. These choices reflect not only availability but also methodological preferences. ANSYS is particularly favored in orthodontic FEA due to its ease of meshing, predefined material libraries, and convergence stability in static simulations. Conversely, Abaqus may be preferred for studies that require advanced contact modeling or more sophisticated boundary conditions, albeit with a steeper learning curve [45,46,47]. These software preferences mirror the trends in other dental biomechanics fields, where ANSYS dominates preclinical orthodontic research, while Abaqus is more frequent in implant and prosthetic simulations [45].

4.4. Influence of Aligner Thickness on Expansion Forces

Aligner thickness was found to be a major determinant of the magnitude and distribution of orthodontic forces [22,23]. Li et al. conducted a comparative 3D FEA to evaluate different aligner thicknesses during maxillary expansion and reported that thicker aligners (0.75 mm vs. 0.5 mm) generated higher force levels, resulting in greater lateral displacement of posterior teeth with improved torque control [24]. This suggests that mechanical stiffness conferred by increased thickness can enhance the efficiency of bodily movement, mitigating undesired crown tipping—a common side effect in arch expansion with aligners. However, the trade-off may lie in patient comfort and wearability, which are reduced as rigidity increases [48]. These findings complement Yao et al., who also observed that thicker aligners combined with properly positioned attachments and expansion vectors improved torque expression during maxillary arch widening [30]. Clinical studies also confirm that increasing aligner thickness can improve torque control and improved expansion efficiency in posterior segments, although at the expense of comfort and patient compliance [49,50]. Both studies indicate that tailoring aligner thickness on a per case basis—considering individual periodontal and dental characteristics—could optimize clinical outcomes.

4.5. Role of Attachment Configuration in Movement Control

Attachment design and positioning have been extensively discussed to direct and anchor force vectors in clear aligner therapy [51,52,53]. Karslı et al. performed a FEA assessing the impact of different attachment configurations on molar behavior during transverse expansion. Their results demonstrated that vertical rectangular attachments placed on the buccal surface of molars enhanced root control and reduced uncontrolled buccal tipping [32]. In contrast, configurations lacking molar attachments showed less predictable tooth responses, indicating a critical dependency on proper auxiliary features [5]. These results align with Yao et al., who reported that an integrated design combining torque-generating attachments and increased aligner stiffness produced more uniform stress distribution along the dental arch, improving both expansion and root control [30]. Thus, attachment selection should be highly customized, factoring in tooth morphology, anchorage requirements, and the intended movement direction. Notably, randomized controlled trials have also confirmed that optimized attachment configurations significantly reduce treatment refinements in deep bite and overbite correction, further supporting the translational relevance of these FEA findings [54].

4.6. Movement Patterns and Sequencing Strategies

Movement sequencing also plays a key role in determining the effectiveness of clear aligners in addressing transverse and vertical discrepancies. For example, Li et al. and Yao et al. modeled expansion by applying aligner deformation or sequential movement with varying design parameters [24,30]. Zhang et al. investigated different stride lengths and torque angles applied during upper arch expansion and found that gradual expansion, using defined displacement increments (0.1–0.3 mm) combined with controlled torque application resulted in more symmetrical movement and reduced stress concentrations [31]. Improper sequencing or excessive stride per aligner step increased the risk of non-linear movements, highlighting the need for careful calibration of movement stages [55]. Similarly, Zhu et al. analyzed deep curve of Spee correction strategies and found that simultaneous intrusion and retraction of anterior teeth produced more favorable force systems compared to sequential approaches [33]. This underscores the importance of movement pattern design, not only in terms of mechanical effectiveness but also in terms of patient safety and comfort [2,12]. Clinical investigations on sequencing protocols also suggest that smaller step increments (<0.25 mm) are associated with higher predictability of transverse expansion, whereas excessive increments often lead to refinement phases [56].

4.7. Integration and Implications

Taken together, the reviewed studies underscore the interdependence of aligner physical properties, auxiliary features, and programmed movement patterns in achieving efficient and controlled tooth movement [57,58]. In the dental field, FEA provides a powerful platform for preclinical simulation, allowing clinicians and designers to visualize stress distributions and movement trajectories under various scenarios [59]. These insights support the move toward more individualized aligner protocols, where aligner thickness, attachment type, and movement sequencing are tailored to each patient’s biomechanical profile [57,60]. This approach reflects a broader trend in precision orthodontics, where computational simulations are integrated with patient-specific treatment planning to enhance clinical predictability. Interdisciplinary evidence from prosthodontics and oral implantology demonstrates that preclinical FEA integration accelerates the translation of biomechanical hypotheses into clinical protocols, suggesting that orthodontics may benefit from adopting similar translational frameworks [61]. Clinically, the integration of these findings could translate to shorter treatment durations, fewer refinements, and reduced risk of unwanted displacements. The application of FEA also has educational implications, enhancing clinician understanding of the often-invisible force systems involved in aligner-based treatment [62].

4.8. Limitations of Finite Element Models

Despite their utility, finite element models are still inherently limited by their assumptions and simplifications as stated in less recent studies [63]. None of the included studies fully modeled dynamic biological processes such as periodontal ligament remodeling, alveolar bone adaptation, or patient compliance—factors that significantly influence real-world outcomes. Moreover, most models use static loading conditions and idealized material properties that may not accurately reflect intraoral environments, where variables like saliva, mastication, and temperature fluctuations can alter material behavior and force dissipation [64]. Therefore, while FEA is invaluable for hypothesis generation and protocol refinement, its conclusions must be validated through clinical studies before clinical generalization [48]. A further limitation is the underrepresentation of mandibular models; most studies focus on the maxillary arch, although mandibular biomechanics are equally relevant for full-arch expansion and vertical corrections [65].

4.9. Future Directions

Future research should aim to bridge the gap between computational predictions and clinical evidence [66]. Integrating patient-specific anatomical data (e.g., CBCT-derived models), simulating time-dependent tissue responses, and including variability in biological parameters could enhance the accuracy of FEA studies. Furthermore, clinical trials comparing different aligner thicknesses, attachment designs, and sequencing strategies would provide much-needed validation of the computational models and help translate theoretical insights into real-world practice [67]. The development of AI-driven aligner planning tools, incorporating FEA outputs into treatment simulations, could further support clinicians in designing evidence-based and personalized aligner protocols [68,69].

5. Conclusions

This scoping review synthesized current evidence from finite element analysis (FEA) studies regarding the biomechanical behavior of CAs in maxillary arch expansion and torque control. The findings demonstrate that key design and procedural variables—such as aligner thickness, attachment configuration, and movement sequencing—have a significant impact on the predictability and efficiency of tooth movement. Thicker aligners were associated with greater force generation and improved torque control, while optimized attachment designs enhanced root control and reduced undesirable tipping. Additionally, well-planned movement patterns and sequencing contributed to more balanced expansion and minimized stress concentrations on dental structures. Although FEA provides meaningful preclinical data on clear aligner biomechanics, its inherent limitations—such as the lack of biological variability and individual anatomical considerations—underscore the importance of complementary clinical validation. Future studies integrating advanced modeling techniques and real-world patient data will be crucial to refining aligner protocols and improving treatment outcomes. Ultimately, a deeper understanding of the mechanical principles underlying clear aligner therapy will support more predictable, personalized, and effective orthodontic treatment strategies. Future research should aim at developing standardized FEA protocols in orthodontics—particularly regarding boundary conditions, material properties, and validation methods—to enhance reproducibility and strengthen the translation of computational evidence into clinical practice.

Author Contributions

Conceptualization, A.P.; methodology, A.P. and A.G.; validation, A.P. and R.U.; formal analysis, A.P., A.G. and R.U.; investigation, A.P.; resources, A.P., F.A., G.B. and R.U.; data curation, A.P., R.U. and A.G.; writing—original draft preparation, A.P.; writing—review and editing, R.U., V.F. and L.M.; visualization, A.P.; supervision, A.G. All authors have read and agreed to the published version of the manuscript.

Funding

This work was also supported by the Italian Ministry of Health through “current research funds”.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All the data available for this research have been published in this article.

Acknowledgments

Not applicable.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
FEAFinite Element Analysis
CAClear Aligners

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Applsci 15 09514 g001
Figure 1. PRISMA 2020 flow diagram for the selection of studies included in the review. (Automation refers to automatic database functions (duplicate removal, document type, and language filters) applied prior to manual screening.)
Figure 1. PRISMA 2020 flow diagram for the selection of studies included in the review. (Automation refers to automatic database functions (duplicate removal, document type, and language filters) applied prior to manual screening.)
Applsci 15 09514 g001
Table 1. Data collection of the selected studies.
Table 1. Data collection of the selected studies.
Authors, Year,
Country		Study ObjectiveStudy ProtocolResultsConclusions
Li N. et al. (2024), China [24]Assess biomechanical effects of movement strategies and aligner thicknessFEA with 7 patterns and 2 thicknesses (0.5–0.75 mm)Alternating movement most efficient; thicker aligners increase PDL stressThicker aligners improve efficiency but stress tissues; alternating pattern recommended
Yao S. et al. (2023), China [30]Improve tooth movement efficiency and torque control in maxillary expansionFEA with alternating movement, embossment shapes, torque 0–5°Alternating movement more efficient; embossment improves crown movement onlyTorque improves control but reduces efficiency; embossment helps crown displacement
Zhang Y. et al. (2023), China [31]Analyze upper arch expansion with aligners and optimize stride/torqueFEA models with 0.1–0.3 mm stride and 0–1.5° torqueIncreasing torque reduces posterior tipping but also efficiency; 0.2 mm stride and ~2° torque result in bodily movementPosterior buccal tipping is inevitable; torque must be personalized
Karslı N. et al. (2024), Turkey/Australia [32]Evaluate effect of different attachment types (with/without torque) on molar expansion8 models with 0.25 mm expansion and torqueTOHA (occlusal bevel + torque) = least tipping; GHA and NA = highest tippingOcclusal beveled attachments with torque best reduce uncontrolled tipping
Zhu L. et al. (2024), China [33]Evaluate 5 movement strategies to correct Spee curve with alignersFEA with distalization/extrusion of molars and premolarsHighest stress on incisors and labial tipping; less distalization efficiencyExpansion + extrusion requires caution to avoid negative anterior effects
Table 2. ROBFEAD summarized results covering all the 22 questions across 6 domains.
Table 2. ROBFEAD summarized results covering all the 22 questions across 6 domains.
ArticleR (Research of Question)O (Outcome Measures)B (Baseline)F (Findings)E (Effect Size/Significance)A (Applicability/Limitations)D (Domain)
Li et al., 2024 [24]Clear aim: impact of aligner thickness and movement pattern on expansionDisplacement, PDL stress3D FE model, realistic anatomyAlternating movement more effective; thicker aligner produced more force63% more expansion with alternating; no p-valuesIn silico study; clinical correlation unknownBiomechanics; methods
Yao et al., 2023 [30]Focus on torque control and movement efficiencyCrown displacement, torque per mmValidated FEA setupTorque compensation reduced efficiency; embossments improved movement0.26°/mm torque change per 1°; 4.32% efficiency dropSimulated data; no clinical validationBiomechanics; methods
Zhang et al., 2023 [31]Stride and torque compensation in expansionDisplacement, inclination, stress12 FE setups, realistic modelBest movement with 0.1–0.2 mm stride and 1.2–2° torqueStress values within physiological limitsFE simulation only, no in vivo dataBiomechanics; methods
Karslı et al., 2024 [32]Attachment effect on molar tippingMolar tipping, torqueAttachments modeled on molarsOcclusal attachments + root torque improved tipping controlQualitative onlyLimited clinical translationBiomechanics; applicability
Zhu et al., 2024 [33]Distalization pattern for deep curve of SpeeTipping, displacement of incisorsMandibular arch FEA modelConfiguration E caused highest tipping; less effective distalizationReported comparatively, no numerical valuesMandibular only; uncertain generalizabilityBiomechanics; applicability
Table 3. ROBFEAD 22 question detail for each article.
Table 3. ROBFEAD 22 question detail for each article.
AGroup 1: Development of ModelLi et al., 2024 [24]Yao et al., 2023 [30]Zhang et al., 2023 [31]Karsli et., 2024 [32]Zhu et al., 2024 [33]
1Was 3D model developed using DICOM images? YesYesYesYesYes
2Were all the sub-structures as relevant to the study defined? (enamel, dentin, pulp, PDL, cancellous bone, cortical)YesYesYesYesYes
3Were the realistic dimensions of relevant sub structures described? YesYesYesYesYes
4Were appropriate boundary conditions/restraints/segmentation adequately explained? YesYesYesYesYes
5Was convergence testing done during generation of model? (At least 3 different mesh sizes with variable number)YesYesYesYesYes
6Were appropriate contact conditions between interfaces defined? (friction/frictionless/bonded)YesYesYesYesYes
Group 2: Properties of material
7Were appropriate properties given to all substructures of the model? (enamel–anisotropic; dentin, pulp, PDL-isotropic)YesYesYesYesYes
8Was appropriate elastic behavior of each sub structure of the study defined? (linearly elastic/non-linearly elastic)YesYesYesYesYes
9Were the values of Poisson ratio, Young’s modulus, and density of material mentioned with reference?YesYesYesYesYes
10Were age-appropriate properties described for the biological structures as per the clinical context?YesYesYesYesYes
Group 3: Impact load
11Were dynamic loading conditions applied? (if applicable)YesYesYesYesYes
12Was the range of force appropriate for the study purpose?YesYesYesYesYes
13Was/Were the point/s of application of force appropriate for the study purpose?YesYesYesYesYes
Group 4: Endpoints tested
14Is the endpoint tested appropriate for the study purpose? (von Mises stress/max principle stress/ max shear)YesYesYesYesYes
Group 5: Mechanical validation
15Was the validation of test results carried out and using appropriate mechanical model?YesYesYesPartiallyYes
Group 6: Reporting error
16Are points such as shape of elements, number of elements, and nodes described?YesYesYesQualitativeYes
17Is appropriate detailing of different types of models used in the study mentioned?YesYesYesYesYes
18Are the software used for the model synthesis and mesh development mentioned with details of the version?YesYesYesYesYes
19Are the software used for the finite element analysis mentioned with details of license and version?YesYesYesYesYes
20Are study results described as per the objectives?YesYesYesYesYes
21Is clinical replication of the results described?YesYesYesYesYes
22Is limitation of the FEA model described?YesYesYesYesYes
Risk of biasLowLowLowModerateLow
Table 4. Details of model development (CBCT: cone beam computer tomography; CAD: computer-aided design; CT: computer tomography).
Table 4. Details of model development (CBCT: cone beam computer tomography; CAD: computer-aided design; CT: computer tomography).
Author,
Year		SoftwareRegion of ModelSource of Dimensions for Geometric Model2D/3DType of Analysis
Li et al., 2024
[24]		Ansys WorkbenchMaxillary archCBCT-based geometry (standard arch with full dentition)3DStatic structural
Yao et al., 2023 [30]AbaqusMaxillary arch (1st premolar focus)Digital model based on standard dental arch, CBCT-based model3DStatic FEA
Zhang et al., 2023 [31]Ansys WorkbenchMaxillary archStandardized CBCT-based digital dental model 3DNonlinear structural (deformations and contacts)
Karslı et al., 2024 [32]Ansys Workbench combined to Ansys SpaceClaimMaxillary molarsCAD-based model from average anatomical data obtained from CBCT3DStatic linear analysis
Zhu et al., 2024 [33]Ansys WorkbenchMandibular anterior regionCT-derived mandibular model3DStructural FEA with movement simulations
Table 5. Material properties and loading conditions in the included FEA studies.
Table 5. Material properties and loading conditions in the included FEA studies.
Author,
Year		Loading ConditionsStress Criteria Mesh ConvergenceForce MagnitudeMaterial Properties IncludedSource of Material Data
Li et al., 2024 [24]Expansion force via aligners with two thickness levelsVon Mises stress; maximum principal stressNot reportedNot numerically specified; force implied by aligner strainTeeth, PDL, cortical bone, cancellous bone, alignersManufacturer data and literature references
Yao et al., 2023 [30]Sequential movement with embossments and torque compensationVon Mises stress; maximum principal stressNot reportedDisplacements applied; force not quantifiedTeeth, PDL, aligner material, attachmentsPrior FEA studies and published literature
Zhang et al., 2023 [31]Buccal expansion under different stride/torque anglesVon Mises; maximum principal stressNot reportedIndirect force from displacement steps (0.1–0.3 mm)Teeth, PDL, alveolar boneBiomechanical literature and standard references
Karslı et al., 2024 [32]Aligners with different attachment designs and buccal root torqueVon Mises stressNot reportedDirectional forces from aligners; no numerical valuesTeeth, PDL, cortical and cancellous boneCAD data and previously validated FEA sources
Zhu et al., 2024 [33]Aligner-based anterior distalization (five protocols tested)Von Mises; maximum principal stressNot reportedNo explicit force reported; defined by movement strategyTeeth, PDL, alignersPublished literature on dental material properties
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Putrino, A.; Bompiani, G.; Aristei, F.; Fornari, V.; Massafra, L.; Uomo, R.; Galeotti, A. Biomechanical Insights into the Variation of Maxillary Arch Dimension with Clear Aligners: A Finite Element Analysis-Based Scoping Review. Appl. Sci. 2025, 15, 9514. https://doi.org/10.3390/app15179514

AMA Style

Putrino A, Bompiani G, Aristei F, Fornari V, Massafra L, Uomo R, Galeotti A. Biomechanical Insights into the Variation of Maxillary Arch Dimension with Clear Aligners: A Finite Element Analysis-Based Scoping Review. Applied Sciences. 2025; 15(17):9514. https://doi.org/10.3390/app15179514

Chicago/Turabian Style

Putrino, Alessandra, Gaia Bompiani, Francesco Aristei, Valerio Fornari, Ludovico Massafra, Roberto Uomo, and Angela Galeotti. 2025. "Biomechanical Insights into the Variation of Maxillary Arch Dimension with Clear Aligners: A Finite Element Analysis-Based Scoping Review" Applied Sciences 15, no. 17: 9514. https://doi.org/10.3390/app15179514

APA Style

Putrino, A., Bompiani, G., Aristei, F., Fornari, V., Massafra, L., Uomo, R., & Galeotti, A. (2025). Biomechanical Insights into the Variation of Maxillary Arch Dimension with Clear Aligners: A Finite Element Analysis-Based Scoping Review. Applied Sciences, 15(17), 9514. https://doi.org/10.3390/app15179514

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