Effects of lower central incisors’s biomechanics at different mixed dentition stages using clear aligners for deep overbite treatment: a three-dimensional finite element analysis

Abstract

Background

This study aimed to investigate the effects of various intrusion modes on the movement trends and stress distribution of lower teeth at different stages in lower central incisors during deep overbite in mixed dentition treated with clear aligners.

Methods

Three-dimensional finite element models were constructed to represent lower central incisors at different stages of Demirjian classification (stages F, G and H). Three protocols were designed to intrude lower central incisors (intrusion modes I, II and III). The analysis was conducted on the movement trends and stress distribution of the lower teeth.

Results

Regardless of root developmental stages of lower central incisors, the trend of mesial and labial movements were observed during the intrusion process. The stress in the periodontal membranes was primarily concentrated at the labial neck and lingual root apex of the lower anterior incisors. At stages F and G, intrusion mode III exhibited the most obvious movement trend along the intrusion direction. Conversely, intrusion mode I demonstrated the most significant movement trend in the stage H.

Conclusion

The displacement observed along the Z-axis (intrusion direction) was greatest for Mode III at stages F/G, and greatest for Mode I at stage H. Therefore, the factors such as the development of teeth roots, intrusion amount and modes should be fully considered for a reasonable design in clinic, which could improve the treatment efficiency.

Introduction

Deep overbite is a common malocclusion. Previous research indicated that the prevalence of malocclusion during mixed dentition was 83.5%, with deep overbite constituting a significant proportion at approximately 69.5% [1, 2]. This condition not only impacts aesthetic appearance and psychological well-being but also leads to functional abnormalities within the oral and maxillofacial systems [3]. Consequently, prompt intervention for deep overbite during mixed dentition is essential for restoring normal function in the oral and maxillofacial systems.

Treatment of deep overbite is typically accomplished through techniques such as intruding the anterior teeth and/or raising the posterior teeth. Traditional orthodontic appliances often result in the elevation of posterior teeth while intruding anterior teeth, which poses significant challenges for high-angle cases [4]. Clear aligners are primarily employed to intrude lower anterior teeth in the management of deep bite, effectively preventing posterior tooth extrusion and providing benefits for patients with high-angle [5]. Their widespread clinical application was attributed to their comfort and aesthetic appeal. Common intrusion methods include bodily intrusion and step by step intrusion [6]. However, it remains unclear whether different methods or intrusion amount will influence root development and associated biomechanical changes during mixed dentition.

In recent years, three-dimensional finite element analysis has emerged as a prevalent method for simulating tooth movements in orthodontics, enabling precise analysis of movements and stress across various components with clear aligners [7, 8]. In clinical practice, when root development is classified within Demirjian stages of A, B, C, D and E [9], patients typically fall within the age range of 1–6 years old. Due to the fact that the root development of teeth during these periods is extremely immature, if clear aligner is carried out, there is a possibility of tooth loosening or even loss. This violates the principles of medical ethics, which is fall outside the scope of clear aligner treatment. Furthermore, different teeth correspond to distinct developmental periods due to variations in the eruption sequence of teeth. To minimize experimental errors and ensure methodological rigors, this research specifically targeted lower central incisor at stages F, G and H instead of all anterior teeth. Compared with the permanent dentition, root development in the mixed dentition remains incomplete—particularly in the lower anterior teeth—introducing uncertainty regarding whether the biological response and biomechanical behavior of roots under clear aligner–mediated intrusion are comparable to those observed in mature dentitions. To date, evidence on aligner-based intrusion in the mixed dentition is sparse, limiting treatment plans and potentially compromising clinical predictability. Prior studies in permanent dentition deep overbite cases have consistently demonstrated that step by step intrusion yields greater control over bodily intrusion. However, no such comparative biomechanical data exist for the mixed dentition, we hypothesize that step by step intrusion similarly confers superior precision and safety in deep overbite correction during the mixed dentition. Based on this, this study uses three-dimensional finite element analysis to deeply investigate the effects of using clear aligners on the mixed dentition at different mixed dentition stages with deep overbite. The findings could provide valuable insights for orthodontists employing clear aligners to address deep overbite in mixed dentition, thereby enhancing treatment safety while optimizing treatment plan design.

Materials and methods

Subjects of research

A total of 3 patients with deep overbite were selected from the Orthodontics Department, Affiliated Stomatology Hospital of Kunming Medical University from January 2022 to August 2023. Additionally, they with deep overbite whose lower central incisors root development corresponded to stages F, G and H of the Demirjian classification (As shown in Fig. 1, stage F: root length was equal to or greater than crown height and the root apex foramen was funnel-shaped. Stage G: root canal walls were parallel and root apex foramen has not closed. Stage H: the root apex foramen was completely closed), all of whom signed informed consent. All patients met the following inclusion criteria: (1) Healthy body, no systemic diseases, no history of maxillofacial trauma and no history of orthodontics. (2) No missing teeth, no obvious abnormality in crown shape, no ambushed multiple teeth, no obvious root resorption. (3) Lower central incisors have no obvious labial inclination, specific cephalometric parameters shown as below: 89.5 °≤ IMPA (°) ≤ 99.9 °, 27.7 ° ≤ L1 - NB (°) ≤ 37.7 °, 4.5 ≤ L1 - NB (mm) ≤ 7.5 (Reference: Downs analysis). (4) The periodontal condition was satisfactory, with no significant gingival recession observed. The height and thickness of the alveolar bone appeared normal and lower central incisor were located in the center of the alveolar bone. Exclusion criteria: (1) Inadequate compliance, including failure to attend follow-up appointments in a timely manner or non-adherence to the prescribed use of clear aligners. (2) Lower teeth with dental pulp or restorative interventions. (3) Lower incisors exhibiting abnormal crown morphology, insufficient eruption or inadequate crown height. This study has been reviewed and approved by the Ethics Committee of Affiliated Stomatology Hospital of Kunming Medical University (Approval Number: KYKQ2024MEC0035).

Fig. 1.

Schematic diagrams of lower central incisors in Demirjian stages F, G and H. A: Stage F, the root length is equal to or longer than the crown height and the apical foramen is funnel-shaped. B: Stage G, the root canal wall is parallel and the apical foramen is not closed. C: Stage H, apical foramen is completely closed

Methods

3D finite element models construction

Imported the volunteer’s CBCT data in DICOM format into Mimics 21.0.(Materialise NV, Belgium) for 3D reconstruction. Then a preliminary 3D model of the jaws and dentition was generated by selecting thresholds for appropriate grayscale values of the bone and teeth. The model was imported into the Geomagic Wrap 2017 (Geomagic, USA) and the surface of the model was smoothed. The model was optimized by using the commands of nail removal, feature removal, etc. Through surface fitting, a continuous, spatially closed solid model of mandible and lower dentitions were formed. The roots of mandibular dentition were uniformly shifted outward by 0.25 mm and then the periodontal membranes were established by Boolean operation. The model was then imported into 3-Matic 13.0 (Materialise, Belgium) to design horizontal rectangular attachments (3*2*1 mm) on the buccal side of the mandibular posterior teeth and vertical rectangular attachments (2*3*1 mm) on the labial side of the bilateral deciduous or cusp teeth. A 0.75-mm-thick clear aligner was designed to generate controlled orthodontic forces via elastic deformation. All intrusion vectors were aligned precisely with the anatomic long axis of each tooth to ensure physiologically appropriate force application. Three distinct intrusion modes were implemented: (I) intrusion of all six lower anterior teeth (central and lateral incisors, canines) by 0.25 mm; (II) staged intrusion—canines first (0.25 mm), followed by incisors (0.25 mm); and (III) reversed staging—incisors first (0.25 mm), followed by canines (0.25 mm). Each protocol was realized through dedicated, sequentially staged aligner geometries optimized for targeted tooth movement. The above models were imported into Hypermesh 2019 (Altair, United States) for grid division and finally carried out operational analysis in Abaqus 2021 (Dassault Systemes, France) (as shown in Fig. 2). The number of nodes and units of each model were shown in Table 1.

Fig. 2.

Grid division to establish three-dimensional finite element models. A: Mesh division, boundary setting, the mandibular angle, condyle and coracoid process constraints; B: The 3D finite element model of stage F; C: The 3D finite element model of stage G; D: The 3D finite element model of stage H.

Table 1.

Elements and nodes

Stages	Elements		Nodes
Demirjian stage F		311,140	70,493
Demirjian stage G		226,574	52,357
Demirjian stage H		21,539	51,936

Material properties and conditions setting

Material properties

In this study, each model was set as a continuous, homogeneous and isotropic linear elastic material and the parameters were assigned with reference to those in the three-dimensional finite element study of the mixed dentition period by Tanaka et al. [10], as shown in Table 2.

Table 2.

Material properties

Material	Young’s modulus(MPa)	Poisson’s ratio
Tooth	19,600	0.3
Periodontal ligament	0.68	0.49
Bone	13,700	0.30
Clear aligner	528	0.36
Attachment	12,500	0.36

Condition setting

The teeth and periodontal membranes shared finite element nodes, the periodontal membranes shared finite element nodes with alveolar bone and the contacts between the tooth and clear aligners were defined as face-to-surface contact. Contacts among clear aligners, crowns and attachment surfaces were set to frictional contact with a coefficient of friction of 0.2.

Coordinate axis and constraint settings

Based on the symmetry of the dental arch, in this study, the contact point of the bilateral central incisors was taken as the origin to better present the research results. The X-axis, Y-axis and Z-axis were respectively horizontal (positive value was left, negative value was right), sagittal direction (positive value was distal direction, negative value was mesial direction) and vertical direction (positive value was occlusal direction, negative value was gingival direction). To prevent mandibular displacement induced by tooth movement, isolating dental motion from skeletal adaptation and ensuring that simulated displacements reflect pure orthodontic tooth movement rather than coupled mandibular repositioning. The mandibular angle, condylar process and coracoid process of mandible were constrained in each group, so that they did not move or rotate in the X, Y and Z directions.

Measuring mark points

The midpoint of the incisor margin of the mandibular incisor, the cusp of permanent and deciduous canines and the mesio-buccal cusp of deciduous and permanent molars taken as the measurement markers for the three-dimensional movements of the teeth.

Group classifications

Based on the developmental stages of the lower central incisors, they were categorized into stages F, G and H. The intrusion methods were classified as intrusion mode I (bodily intrusion of all 6 lower anterior teeth), intrusion mode II (initially intruding canines followed by incisors) and intrusion mode III (initially intruding incisors followed by canines). The specific groups were presented in Table 3.

Table 3.

Groups of three-dimensional finite element analysis

Groups	Stages	Intrusion methods
TD-F1	Demirjian stage F		intrusion mode Ⅰ
TD-F2			intrusion mode Ⅱ
TD-F3			intrusion mode Ⅲ
TD-G1	Demirjian stage G		intrusion mode Ⅰ
TD-G2			intrusion mode Ⅱ
TD-G3			intrusion mode Ⅲ
TD-H1	Demirjian stage H		intrusion mode Ⅰ
TD-H2			intrusion mode Ⅱ
TD-H3			intrusion mode Ⅲ

Results

The three-dimensional movement trends and the stress distribution of lower teeth when roots of lower central incisors were at stages F and G, utilizing different modes to intrude lower anterior teeth with clear aligners

When root development of the lower central incisors is at stages F and G, regardless of the mode of intrusion adopted, the parameters of the left teeth on the X-axis are negative values, while those of the right teeth are positive values. On the Y-axis and Z-axis, the parameters of all teeth are negative values. The lower central incisors, lateral incisors and deciduous canines exhibited a trend of mesial labial inclination during the intrusion process, while lower deciduous molars and first molars demonstrated a trend ofTana mesial lingual inclination. The movement trend of deciduous canines on the X-axis was most obvious, whereas that of first molars was minimal. The movement trends of the lower teeth on both the Y-axis and Z-axis decreased from central incisors to first molars. Specifically, central incisors displayed the most apparent movements, while first molars showed minimal movements. Regarding intrusion modes at stages F and G for lower central incisors, mode III exhibited a more distinct intrusion trend compared to the other two modes. (Figures 3A-F and 4A-F).

Fig. 3.

The three-dimensional movement trends and stress distribution of the lower central incisors in different intrusion modes when root development reached stage F. A, B: The movement trend of lower teeth along the X-axis, a, a’ and a’’ denoted intrusion modes I, II and III. C, D: The movement trend of lower teeth along the Y-axis, c, c’ and c’’ represented intrusion modes I, II and III. E, F: The movement trend of lower teeth along the Z-axis, e, e’ and e’’ indicated intrusion modes I, II and III. G-I: Stress distribution of the lower periodontal membranes, teeth and alveolar bone in different intrusion modes.

Fig. 4.

The three-dimensional movement trends and stress distribution of the lower central incisors in different intrusion modes when root development reached stage G. A, B: The movement trend of lower teeth along the X-axis, a, a’ and a’’ denoted intrusion modes I, II and III. C, D: The movement trend of lower teeth along the Y-axis, c, c’ and c’’ represented intrusion modes I, II and III. E, F: The movement trend of lower teeth along the Z-axis, e, e’ and e’’ indicated intrusion modes I, II and III. G-I: Stress distribution of lower periodontal membranes, teeth and alveolar bone in different intrusion modes.

The von Mises stress distribution of the lower teeth indicated that regardless of intrusion modes employed during stages F and G for lower central incisors, stress was concentrated in the anterior teeth region, primarily borne by the incisors, while the stress on deciduous canines was relatively small. Regarding the stress distribution on lower teeth, intrusion mode III generated the highest level of stress, followed by intrusion mode I, while intrusion mode II produced the least. These findings were consistent with the distribution of stress observed in both the periodontal membranes and alveolar bone. Furthermore, in addition to the obvious stress distribution around lower incisors, the significant stress was also noted around lower first molars (Figs. 3G-I and 4G-I).

The three-dimensional movement trend and the stress distribution of lower teeth when roots of lower central incisors were at stage H, utilizing different modes to intrude lower anterior teeth with clear aligners

When root development of the lower central incisors at stage H, irrespective of the intruding modes employed, the values on the X-axis for the left lower teeth were negative, while those for the right were positive. All values on the Y and Z-axis remained negative for lower teeth. The lower central incisors, lateral incisors and canines exhibited a trend of mesial labial inclination during the intrusion process, while lower deciduous molars and first molars demonstrated a trend of mesial lingual inclination. The movement trend of canines on the X-axis was most obvious, whereas that of first molars was minimal. The movement trends of the lower teeth on both the Y-axis and Z-axis decreased from central incisors to first molars. Specifically, central incisors displayed the most apparent movements, while first molars showed minimal movements. In terms of intrusion modes at stage H of lower central incisor development, intrusion mode Ⅰ demonstrated a more obvious intrusion trend than other two modes. (Fig. 5A-F).

Fig. 5.

The three-dimensional movement trends and stress distribution of the lower central incisors in different intrusion modes when root development reached stage H. A, B: The movement trend of lower teeth along the X-axis, a, a’ and a’’ denoted intrusion modes I, II and III. C, D: The movement trend of lower teeth along the Y-axis, c, c’ and c’’ represented intrusion modes I, II and III. E, F: The movement trend of lower teeth along the Z-axis, e, e’ and e’’ indicated intrusion modes I, II and III. G-I: Stress distribution of lower periodontal membranes, teeth and alveolar bone in different intrusion modes

The von Mises stress distribution of the lower teeth indicated that regardless of intrusion modes employed during stage H for lower central incisors, stress was concentrated in the anterior region, primarily borne by incisors and canines, while the stress on deciduous canines was relatively small. Regarding the stress distribution on lower teeth, intrusion mode III generated the highest level of stress, followed by intrusion mode I, while intrusion mode II produced the least. These findings were consistent with the distribution of stress observed in both the periodontal membranes and alveolar bone. Furthermore, in addition to obvious stress distribution around lower incisors, the significant stress was also noted around lower first molars, which was consistent with the results when lower central incisor at stage F and stage G. (Fig. 5G-I).

Discussion

Numerous scholars conducted extensive researches on the orthodontic principles underlying the correction of deep overbite using clear aligners, revealing that the primary treatment approach involved intruding lower anterior teeth, predominantly focusing on permanent dentition [11, 12]. The effects on mixed dentition remained unclear.

This study demonstrated that lower central incisors at stages F, H and G exhibited a trend of mesial and labial movements along the X and Y-axis, irrespective of the intrusion mode employed. The stress in the periodontal membranes was primarily concentrated on the labial neck and lingual root apex of lower anterior teeth, consistent with findings by Li et al. [13]. These suggested a potential risk of labial dehiscence and lingual fenestration during the intrusion process, which may affect root development and potentially lead to root resorption [14]. Furthermore, lower central incisors utilizing intrusion mode III displayed the most obvious movement trend in the Z-axis during stages F and G. In contrast, lower central incisors employing intrusion mode I exhibited the most significant Z-axis movement trend during stage H. This variation may be attributed to differences in root developmental stages: roots at stage H was fully developed with closed apical foramen whereas those at stages F and G remain actively growing. Additionally, roots from stages F and G tended to be relatively round and blunt compared to stage H, making it less prone to stress concentration. The stress can be dispersed and absorbed by the surrounding tissues. Consequently, direct forces acting on these root are comparatively smaller than those observed at stage H—resulting in correspondingly reduced movement trend. These observations suggest that when designing clear aligner treatment protocols for patients with incomplete root development could primarily consider using intrusion mode III while opting for intrusion mode I was advisable for those whose roots have fully matured.

Prior studies had found that treating deep overbite using clear aligners, probably leading to labial inclination of lower anterior teeth [15, 16]. The aligner applies a force directed apically along the tooth’s long axis in this study; however, this resultant force resolves into distinct vertical and horizontal components. Given the relatively thin labial alveolar bone plate, the vertical component dominates, thereby generating a net labial inclination moment—leading to a clinically observable buccal inclination of the tooth. It suggested that clear aligner treatment can leverage this labial inclination trend during intrusion to enhance torque effectiveness and achieve synergistic results for deep overbite patients with upright lower anterior teeth. However, it is crucial to incorporate negative torque into the design of clear aligner treatments to counteract this tendency during intrusions and prevent potential dehiscence [17]. In this study, the lower anterior teeth not only showed a labial inclination movement trend but also a mesial movement trend. It is speculated that during the intrusion process, the length of the aligner decreased and the coverage range reduced, thus resulting in the mesial movement trend. This suggests that in the clinical design of clear aligners, attention should be paid to the design of the mesiodistal inclination of the teeth to avoid excessive movement. The three-dimensional finite element analysis is a classical biomechanical research method and the material parameters of the finite element model are directly related to the reliability of simulation results. In this study, clear aligners serve as the primary force tool for tooth movement, necessitating that their Young’s modulus should closely approximate real conditions. Barone et al. reported that the thickness of the clear aligner diaphragm measured 0.75 mm prior to thermoforming [18]. Additionally, the friction coefficient (µ) between teeth and clear aligners is a critical parameter. Ramalho et al. found that setting µ to 0.2 provides a better fit for friction between enamel and composite materials. Consequently, we designed the thickness of clear aligners to be 0.75 mm while establishing a friction coefficient of 0.2 [19]. Although the three-dimensional finite element analysis is a classic mechanical simulation technique, it could only assess the initial movements and stress distribution of teeth. In contrast, factors such as deformation and rebound of clear aligners, remodeling of alveolar bone and attenuation of orthodontic force during the dynamic process of intruding teeth in clinical practice, which would significantly influence the movement trends and stress distribution [20]. Moreover, cortical and cancellous bone thicknesses in the alveolar process vary significantly across anatomical regions. Given that cortical bone dominates both structural integrity and load-bearing capacity in this region—and exhibits substantially higher stiffness than cancellous bone—the elastic modulus of the alveolar bone was conservatively assigned using cortical bone material properties [21]. In future work, we plan to implement a spatially graded material assignment scheme, informed by region-specific microarchitectural data (e.g., bone volume fraction or Hounsfield unit distributions from clinical CT), to better capture biomechanical heterogeneity and reduce model-induced uncertainty. Although this study reflected the initial movement trends and stress distribution, it does not fully capture the complexities encountered in reality [22]. The model assumes linear elasticity, does not simulate alveolar bone remodeling, does not account for patient compliance and aligner force decay, models are based on data from individual volunteers. Therefore, the findings will be further validated by incorporating clinical cases into in-depth research, aiming to provide a more comprehensive reference basis for future studies.

Conclusion

Different intrusion methods are more appropriate for varying stages of root development. For immature roots, step by step intrusion (initially targeting incisors followed by canines) is recommended, whereas for fully developed roots, bodily intrusion proves to be a more suitable approach.

Abbreviations

3D

Three dimensional

Authors’ contributions

Congchong Shi designed the research. Meiying Wu, Yue Li and Xinyu Xing conducted the experiment. Meiying Wu wrote the paper. Junhan Hu, Yumiao Chen, and Chengle Zhang analyzed the data. All authors read and approved the final manuscript.

Funding

This study was funded by the following grants:

(1) Key project of Yunnan Provincial Basic Research Program (No. 202501AS070168).

(2) Leading Figure in Medical Disciplines of Yunnan Province (D-2024026).

(3) The National Natural Science Foundation of China (No. 82260184),

(4) Scientific and technological innovation team of multi-stage and multidisciplinary integration prevention and treatment of malocclusion deformities of Kunming Medical University (No. CXTD202213).

(5) Research Project of China Dental Disease Prevention Foundation (No. A2023-028).

(6) Scientific Research Fund Graduate Program of Education Department of Yunnan Province (No.2024Y240).

(7) Graduate Education Innovation Fund Project of Kunming Medical University (No.2024S041).

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

This study was carried out in compliance with the ethical guidelines of the Declaration of Helsinki and approved by the Ethics Committee of Affiliated Stomatology Hospital of Kunming Medical University (Approval Number: KYKQ2024MEC0035) and informed consent to participate was obtained from all of the subjects in the study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.