Effects of different patterns of movement for correcting a deep curve of Spee with invisible orthodontic appliances on the anterior teeth: A finite element analysis

doi:10.21203/rs.3.rs-3245587/v1

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Research Article

Effects of different patterns of movement for correcting a deep curve of Spee with invisible orthodontic appliances on the anterior teeth: A finite element analysis

https://doi.org/10.21203/rs.3.rs-3245587/v1

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Journal Publication

published 10 Feb, 2024

Read the published version in BMC Oral Health →

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Objective

To evaluate the effects of five different patterns of mandibular molar movement and to define the most effective configuration to be implemented with clear aligners through finite element analysis.

Methods

A three-dimensional evaluation mandibular model with a deep overbite in the mandible was constructed based on cone beam computerized tomography (CBCT) data. The modelled components included mandibular dentition, mandibular periodontal ligaments, attachments, and aligners.

Results

Configuration A showed the highest distal displacement value, and configuration E showed the lowest value. For the central and lateral incisors, configuration E showed the highest PDL pressure. For canines, the difference between configurations C and D was not significant and the stress distribution differed among the five groups.

Conclusion

First, simultaneously, extruding the premolars during molar distalization could enhance the effectiveness of invisible aligners. Second, when expansion and extrusion are simultaneously performed during the distalization of teeth, attention must be given to the alveolar bone on the labial side of anterior teeth to prevent the occurrence of gingival recession, dehiscence, and fenestration.

clear aligner

deep curve of Spee

different pattern of movement

FEM analysis

The demand for clear aligners has increased significantly over the last decade, presumably due to their aesthetics, comfort, and better ability to facilitate oral hygiene over conventional appliances[1–3]. They offer a desirable alternative to traditional braces, particularly for adults who prioritize the aesthetic aspects of orthodontic treatment [4, 5].

Clear aligners have been found to be highly efficient in various orthodontic treatments, including molar distalization, space closure, and anterior tooth alignment[6, 7, 8]. In 2009, Kravitz et al.[6] conducted a prospective clinical study to address the important issue of the efficacy of clear aligners. They showed that, among the tested movements, molar extrusion and mandibular incisor intrusion are difficult to control. Thus, clear aligners have low efficiency in deep overbite correction.

Deep bite malocclusions are a relatively common type of malocclusion found in adolescents and adults, and their severity can be influenced by a combination of dental and skeletal conditions[9]. Depending on whether deep bite malocclusions have a skeletal or dental aetiology, corrective techniques that involve maxillary and mandibular incisor intrusion, proclination, posterior extrusion, and increasing lower anterior facial height through surgical means have been proven effective[10, 11]. A recent study demonstrated that clear aligners were relatively successful in managing overbite[12]. Khosravi et al.[13] reported that an approximately 1.5 mm overbite improvement could be achieved when Invisalign appliances were used by patients with a deep overbite. Additionally, clear aligners could improve vertical dimensional malocclusions, such as dental deep bites, within a mild to moderate range.

However, for decades, maxillary dentition has been widely used as a classic biomechanical research model; meanwhile, the mandibular model has rarely been evaluated. Therefore, we constructed a deep bite mandibular model on the basis of cone-beam computed tomography (CBCT) and intraoral scan data.

Research has shown that the first molar in the mandible is more difficult to distalize than the second molar. After distalization of the mandibular molars, there is slight labial tipping, intrusion and protrusion of the mandibular incisors. Therefore, here we aim to explore the effects of different movement patterns of the mandibular molars using a three-dimensional finite element model of invisible aligners without brackets on the anterior teeth. The findings of this study will provide a reference for clinical design.

2.1. Modelling reconstruction from CBCT

The 3D geometrical model was constructed based on cone-beam computerized tomography (CBCT) data from a patient with a deep overbite. The study protocol was approved by the Ethics Committee of the Affiliated Stomatological Hospital of DaLian Medical University (DLKQLL202302). The subject provided written informed consent. All methods were performed in accordance with the relevant guidelines and regulations.

The authors confirmed that the patient provided informed consent for data collection. The CBCT images (slice thickness 0.2 mm and pixel size 0.200 mm) were input into Mimics 20.0 software (Materialise NV, Belgium)as digital imaging and communications in medicine (DICOM) files for 3D model reconstruction. For further noise reduction and smoothing, a standard tessellation language (STL) file was input into Geomagic Studio 2014 software (3D System, USA) and NX 1911 software (Siemens, Germany)

2.2. Finite Element Modelling.

Specialized FE software, ANSYS Workbench 2019 (ANSYS, USA), was used to create the models. In the models, isotropic, homogeneous, continuous elastic materials were defined and used; only the right side of the mandibular dentition was modelled because of the models’ bilateral symmetry(Fig. 1a).

To achieve greater simulation accuracy, the interface between the aligner with the tooth crown surface and the attachments was set to be in frictional contact with a friction coefficient of 0.2 [14, 15]. Additionally, friction with a coefficient of 0.18 was established at the contact interfaces between the tooth crown surface[15].

The junctions between other modelled components, such as the connection between the periodontal ligament and bone and the tooth between the periodontal ligament, were set to be rigidly connected. The periodontal ligament (PDL) was modelled as a linear elastic material of 0.25 mm thickness[16]. The Young's modulus and Poisson's ratio were 0.69 MPa and 0.49, respectively. As shown in Table 1, the material properties of the components were set as those reported in previous studies[17–19].

The aligner was developed by making an external offset, with a thickness of 0.5 mm according to the result of repeated measurements[17].

The numbers of nodes and elements for all the components are summarized in Table 2.

Table 1. Material properties

Table 1

Material properties
Component	Young's Modulus (MPa)	Poisson's Ratio
The cortical bone	13,700	0.26
The spongy bone	1,370	0.3
Teeth	19,600	0.3
Periodontium	0.69	0.49
Aligner	528	0.36
Attachment	12,500	0.36

Table 2. Number of nodes and elements of the components of the finite element model

Table 2

Number of nodes and elements of the components of the finite element model
Component	Elements	Nodes
The cortical bone	21,036	41,723
The spongy bone	30,378	50,058
Aligner	17,659	34,514
Bone	51,414	80,515

2.3. Establishment of a coordinate system.

This research involved the utilization of two coordinate systems (Fig. 2). First, the global coordinate system was established from CBCT data.

In the global coordinate system, the X-axis represents the direction of the coronal plane, with the positive direction pointing towards the mesial surface of the tooth; the Y-axis represents the sagittal plane, with the positive direction pointing towards the lingual surface; and the Z-axis represents the vertical plane, with the positive direction being towards the tooth crown surface.

Local coordinates for every tooth were also defined for calculating 3D movements. The local coordinates were separately located at the body centre of the clinical crown. The x-, y-, and z-axes represented the labial lingual, mesiodistal, and tooth long-axis directions, respectively.

2.4. Configuration parameters of the five movement protocols are summarized in Table 3.

Table 3

protocols of five movement
	Configuration A	Configuration B	Configuration C	Configuration D	Configuration E
Distalization (0.25 mm)	7	7	7	7	7
Extrusion (0.15 mm)	-	6	4,5	4,5,6	4,5,6
Expansion (0.15 mm)	-	-	-	-	4,5,6
7 = second molar;6 = first molar;5 = second premolar;4 = first premolar.

Table 4

The maximum (max) and minimum (min) tooth displacements and their ratio (max/min)
	A	B	C	D	E
max	0.092578	0.088289	0.090879	0.085437	0.084502
min	0.032263	0.027868	0.032212	0.027582	0.025845
ratio	2.869479	3.168114	2.821278	3.097564	3.269569

The results of the displacement pattern of the 2nd molar in each direction for the five molar displacement protocols are shown in Fig. 3 and Table 4.

Figure 3 shows that configuration A had the maximum deformation (0.092578 mm), followed by deformations in configuration C (0.090879 mm), configuration B (0.088289 mm), configuration D (0.085437 mm) and configuration E (0.315 mm). All the root apexes moved in the mesial direction, resulting in uncontrolled lingual distal tipping movement.

Four points on the mandibular second molar, i.e., the mesiobuccal (MB), mesiolingual (ML), distobuccal (DB), and distolingual (DL) cusps, were selected to measure the three-dimensional displacement. Table 4 and Fig. 4 and Fig. 1(b) show the results of 47 maximum displacements in the mesial-distal directions.

Figure 5 shows the vector analysis of the overall displacement pattern of the dentition for the five molar distalization protocols

The maximum tooth displacement along the x-axis was obtained with the distalization configuration (configuration A), which showed 0.093723 mm of translation compared to 0.085493 mm obtained with the expansion group (configuration A).

Figures 6 and 7 show the equivalent (von Mises) stress distribution of the PDL of the central incisor, lateral incisor, and canine.

Figure 6 shows that for central incisors, the stress is distributed at the cervical third on the lingual surface. For lateral incisors, the stress was distributed at the cervical area on the labial and distal surfaces, respectively. For canines, the stress distribution differed among the five groups.

In configurations A and B, the stress was distributed at the cervical third and apex. In configurations C and D, the stress was distributed at the cervical area on the labial and distal surfaces, respectively, and at the apex. In configuration E, the stress was distributed at the cervical area on the labial and lingual surfaces.

Figure 7 shows that in the dentition of anterior teeth, the equivalent stress on the PDL of configurations A, B, C, and D was located at the distal and labial cervical area of the canine, and, to a lesser extent, the root apex of the canine. In configuration E, the equivalent stress on the PDL was located at the labial cervical area of the canine.

Figure 8 shows the equivalent stress (MPa) in the PDL of the central incisor, lateral incisor and canine

Figure 9 and Fig. 10 show that the maximum displacement of the central incisor of the crown was observed in configuration E, which showed a labial crown tipping movement; additionally, the maximum displacement of the lateral incisor of the crown was observed in configuration C. For canines, the maximum displacement was observed in configuration D. The difference between the configurations C and D was not significant.

Skeletal deep bite malocclusion is predominantly characterized by a horizontal growth pattern of the mandible, resulting in a lower anterior face height and a deep curve of Spee[20, 21]. On the other hand, dental deep bite malocclusions are caused by excessive development of the alveolar bone in the anterior teeth region or insufficient development of the alveolar bone in the posterior teeth region. Overeruption (particularly overeruption of the mandibular incisors) often accompanies a Class II malocclusion.

Nonsurgical deep bite correction techniques include molar extrusion, incisor intrusion, or a combination of both[23]. Extrusion of posterior teeth might be viewed as a good option in low-angle growing patients. Traditional orthodontic treatments often require aligning and levelling the dental arch to level the curve of Spee before placing reverse-curve arch wires[24]. However, with clear aligners, the mandibular incisors can be intruded earlier in the treatment process, allowing for more efficient and timely correction of the deep bite[25]. Many studies have reported that movement of mandibular anterior intrusion and molar extrusion has low efficiency[6, 26, 27]. Therefore, in our study, we prepared for extrusion of the posterior teeth and then distalized the second molar, with the goal of finding the most efficient method of invisible orthodontic treatment.

According to the initial displacement results in Fig. 3, the highest maximum tooth displacement (0.092578 mm) was obtained in configuration A (distalization of the second molar), while the lowest (0.084502 mm) was obtained in configuration E (distalization, extrusion and expansion), representing a 0.008076 mm difference. The tooth displacement of configuration C (extrusion 45 simultaneously) was 0.090879 mm, differing from that of configuration A by 0.001699 mm. Nonetheless, the maximum tooth displacement does not provide exhaustive information for analysing the efficacy of tooth movement because it does not provide information about the movement direction.

Therefore, as shown in Table 4,, it was observed that the second molar in the mesial-distal (x-axis) direction underwent the maximum distal displacement at every point in the distalization protocol (configuration A). Each configuration exhibited a certain degree of rotation in the second molars during distalization. The above two results (shown in Table 4 and Fig. 5) are essentially consistent. The difference between configuration A (distalization group) and configuration C (extrusion of 4 and 5 simultaneously) was not significant, indicating that simultaneous distalization of the second molar and extrusion of premolars has a relatively minor impact on the efficiency of the distal movement. With the extrusion of the posterior teeth, the expansion of the arch had little effect on the efficiency of distalization (Fig. 3,4,5 and Table 4). Therefore, in clinical practice, it is possible to simultaneously extrude the premolar teeth while distalizing the molars to improve the efficiency of tooth movement.

The loss of anterior tooth anchorage in orthodontic treatment can lead to labial inclination of the incisors, thereby affecting the efficiency of molar distalization [28, 29]. According to the principle of force interaction, the clear aligners are subjected to opposite forces on the anterior teeth during molar distalization [30, 31]. To increase anterior tooth anchorage, clear aligners perform sequential molar distalization, utilizing the remaining teeth as a group anchor to counteract the reactive forces generated during the distalization process [32]. Studies [33, 34] suggest that elastic traction and mini-implants can be beneficial in enhancing anterior tooth anchorage control during molar distalization with clear aligners. Our studies indicated that distalization and expansion may not increase anchorage loss of anterior teeth. In patients who require levelling of the Spee curve, when sequencing the distalization of the second molar, the teeth anterior to the first molar could maintain immobility in the sagittal direction, which can be used as an anchor to enhance the clinical efficacy of tooth movement. The premolars and the first molar can be simultaneously extruded in the vertical direction to improve efficiency.

Alveolar bone resorption, a potential side effect of orthodontic treatment, arises from the excessive concentrated stress [35, 36]. After orthodontic treatment, patients with significant alveolar ridge resorption may have a higher incidence of gingival recession [37, 38]. Some studies have demonstrated a higher incidence of gingival recession with labial-tipping movements[39].

According to our experiments, clear aligners produced high levels of concentrated stress mainly on the cervical area, indicating that the buccal alveoli fossa might bear higher stress and is prone to the risk of buccal alveoli fossa resorption and gingival recession. According to this study, the equivalent stress on the periodontal membrane of the canines in configurations C and D was twice that of configuration A. However, the equivalent stress distribution in the PDL of configurations C and D was more scattered compared to that of the other configurations. In configuration E (distalization, extrusion and expansion), the central incisors were subjected to significantly greater stress than in the other configurations, and the lateral incisors were also found to be stressed to a greater extent. Comparing the results for configurations D and E, there is a greater force on the incisors during distal movement and expansion of the arch. For patients with a thin alveolar bone in their anterior teeth, it is important to prevent buccal bone resorption and gingival recession during the process. In configuration E, there was a concentration of stress on the buccal cervical area of the canines. During expansion, it is necessary to monitor the condition of the buccal alveolar bone. In the anterior dentition, the maximum stress was concentrated on the cervical area of the canines in all configurations. This indicates that during orthodontic treatment, attention should be given to the cervical area of the incisors. Regardless of whether the patient has good periodontal health or is suffering from periodontal disease, it is important to protect the canines when retracting the upper anterior teeth, ultimately avoiding excessive forces on the canines that can lead to gingival recession, alveolar bone resorption, dehiscences, and fenestrations.

As a result, the anchorage of anterior teeth loss in orthodontics can lead to increased labial tipping and protrusion of the maxillary incisors,[40, 41] which can affect the efficiency of distalizing molars.

This study also has some limitations. One limitation is the inability to fully and accurately simulate the biomechanical principles and effects of temporal factors on tooth movement. The development of new materials, attachment designs, staging techniques, and advanced scanning technology has significantly expanded the scope of clear aligner treatment. The overall mean accuracy of clear aligners ranges from 41–50%, which is a notable increase from that reported in a 2009 study[6, 7]. Meanwhile, as computing technologies continue to advance and more research is conducted on the mechanisms of tooth movement, more realistic finite element models are being developed at an increasing rate. These models will account for factors such as anisotropy, inhomogeneity, and nonlinear elasticity. Furthermore, they will be able to simulate the remodelling of alveolar bone in response to stress. This suggests that future studies may provide more comprehensive insights into the complexities of tooth movement.

In conclusion, this study showed the following: 1) Simultaneously, extruding the premolars during molar distalization not only has little impact on the efficiency of molar distalization but also enhances the effectiveness of invisible aligners. 2) When expansion and extrusion occur simultaneously during the distalization of teeth, attention must be given to the alveolar bone on the labial side of anterior teeth, especially the canines, to prevent the occurrence of gingival recession, dehiscence, and fenestration.

finite element

FEA

finite element analysis

PDL

Periodontal Ligament

CBCT

Cone Beam Computed Tomography.

Ethics approval and consent to participate

This study was approved by the Ethics Committee of the Affiliated Stomatological Hospital of DaLian Medical University (DLKQLL202302).Written informed consent was obtained from the subject. All methods were performed in accordance with the relevant guidelines and regulations.

Consent for publication

Not applicable.

Availability of data and materials

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

Competing interests

WW was employed by Urumql DW Innovation InfoTech Co., Ltd.

The remaining authors declare that they have no competing interests.

Funding

This study was funded by the “Dalian Medical Science Research Program”(19Z11021).

Authors’ contributions

LZ analyzed and interpreted the data obtained, and was a major contributor in writing the manuscript;LL interpreted the data obtained and were a supervisor in writing the paper;WW: built and solved the Finite element model;WWD revised the manuscript;All authors have read and approved the final manuscript.

Acknowledgements

Not applicable.

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Competing interest reported. WW was employed by Urumql DW Innovation InfoTech Co., Ltd. The remaining authors declare that they have no competing interests.

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You are reading this latest preprint version

Effects of different patterns of movement for correcting a deep curve of Spee with invisible orthodontic appliances on the anterior teeth: A finite element analysis

Status:

Journal Publication

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Abstract

Objective

Methods

Results

Conclusion

Figures

INTRODUCTION

MATERIALS AND METHODS

RESULTS

DISCUSSION

CONCLUSIONS

Abbreviations

Declarations

References

Additional Declarations

Status:

Journal Publication

Version 1