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. 2025 Jul 4;25:1097. doi: 10.1186/s12903-025-06222-9

The effects of anterior spaces on the intrusion of mandibular incisors with clear aligners in extraction cases: a finite-element analysis

Lei Liang 1,#, Lu Liu 1,#, Yuan Cao 1, Zhiwei Wang 1, Ni Li 2, Yanjiao Li 1,✉, Fang Jin 1,✉
PMCID: PMC12231724  PMID: 40615830

Abstract

Background

The intrusion of mandibular incisors presents significant challenges for orthodontists utilizing clear aligner therapy, primarily due to issues such as reduced accuracy in achieving intrusion and unexpected tipping movements. This study aims to investigate the biomechanical effects of varying anterior tooth spaces on the intrusion of mandibular incisors in extraction cases, offering insights that may enhance treatment outcomes.

Methods

A finite element model was created, encompassing the mandibular dentition (excluding first premolars), mandible, periodontal ligaments, and clear aligners. Vertical rectangular attachments were strategically placed on the canines, second premolars, and first molars. Five model groups were constructed based on the size of the spaces between anterior teeth: G0 (no space), G1 (0.20 mm), G2 (0.40 mm), G3 (0.60 mm), and G4 (0.80 mm). The iterative method was employed to simulate orthodontic tooth movement under a mechanical load applied by clear aligners with a 0.20 mm intrusion step, prior to space closure achieved through sequential distalization of the anterior teeth in extraction cases.

Results

The application of clear aligner therapy resulted in minimal intrusion of incisors accompanied by significant labiolingual tipping when no anterior spaces were present. However, moderate spacing (0.60 mm) significantly enhanced the amount of intrusive displacement while reducing labiolingual displacements. With the introduction of space, the Von Mises stress within the periodontal ligament was distributed more evenly across the incisors. Notably, moderate spacing optimized the distribution of Von Mises stress from the clear aligner in the anterior region, facilitating a more bodily movement pattern during intrusion rather than excessive tipping.

Conclusion

Inefficient tooth intrusion and unintended tipping movements frequently arise in extraction cases treated with clear aligners. Our findings indicate that moderate spacing between anterior teeth is more effective in promoting bodily intrusion of mandibular incisors. It is recommended that appropriate spacing be incorporated into treatment planning to enhance the efficiency of intrusion, thereby minimizing labiolingual tipping movements.

Trial registration

Not applicable.

Keywords: Clear aligner, Extraction, Anterior teeth, Tooth intrusion, Finite element study

Background

With the recent advancements in materials and techniques for clear aligners (CAs), orthodontists have begun utilizing these devices for more complex cases, including those involving extractions and overbites [1]. The approach to treating overbite malocclusions is influenced by their underlying etiology, which encompasses various skeletal and dental factors [2]. Among these, a deep curve of Spee (COS) has been identified as the most significant dental contributor. In clinical practice, intruding on the mandibular anterior teeth is often regarded as the most effective treatment for deep bites in adults who do not exhibit vertical growth tendencies. This intrusion directly influences the automatic rotation of the mandible and alters the aesthetic ratio, which can significantly affect facial aesthetics, as well as physical and mental well-being [3, 4].

Despite its importance, numerous studies [5–8] indicate that mandibular incisor intrusion remains one of the least accurate orthodontic movements. For instance, Khosravi et al. [5]. analyzed lateral cephalograms of treated patients and found that proclination of the mandibular incisors was the primary mechanism for addressing overbite malocclusions, achieving an accuracy rate of only 43.3%. Similarly, Charalampakis et al. [6]. reported that the intrusion of lower incisors is often inaccurate, with clear aligner treatment (CAT) demonstrating an intrusion accuracy of just 44% for central incisors and 45% for lateral incisors [7]. Al-Balaa et al. [8]. also noted that mandibular incisor intrusion with Invisalign yielded the lowest accuracy rate at 44.71%. Thus, despite advancements in CA technology, achieving precise mandibular incisor intrusion continues to pose significant challenges [9]. Additionally, compared to fixed appliances, CAT exhibits a more pronounced roller-coaster effect in extraction cases, often characterized by bite deepening [10]. The process of retracting anterior teeth following extraction has been shown to significantly decrease intrusion accuracy (-15.4%) [11]. Furthermore, the proclination associated with intruding incisors fails to provide adequate space for retraction of the anterior teeth in extraction cases, thereby increasing the risk of fenestration and dehiscence [12]. Consequently, there is an urgent need to explore new and effective methods to enhance the accuracy of anterior teeth intrusion in extraction cases utilizing CAs.

The effectiveness of CAs relies on their proper adaptation around the crowns of teeth and the resilience of their polymer materials, which must provide sufficient strength to facilitate movement toward target positions. Some researchers have focused on optimizing CAT through precise computer-aided design, which has shown promise in creating tiny spaces between anterior teeth during the opening bite and space closure phases in extraction cases. These appropriate inter-tooth spaces can help prevent tipping of the incisors during retraction of maxillary anterior teeth [13] while also aiding in controlling their vertical positioning [14]. Despite the valuable insights gained from previous studies, the specific mechanisms by which these tiny spaces might enhance the accuracy of mandibular incisor intrusion remained unclear.

Three-dimensional finite element analysis (FEA) offers a powerful tool for investigating the biomechanical intricacies of orthodontic tooth movement [15]. FEA has been extensively utilized to simulate stress patterns and tooth movement tendencies under various conditions [10]. Therefore, this study employed FEA to evaluate the biomechanical effects of varying anterior spaces on mandibular incisor intrusion with CAs. Specifically, we aimed to investigate the stress distribution within the initial periodontal ligaments (PDLs) and CAs to identify optimal spacing that facilitates intrusive forces directed close to the center of resistance, thereby promoting pure intrusion.

Materials and methods

A healthy adult orthodontic patient with skeletal and dental Class I occlusion was selected for this study. The patient’s mandibular incisors were positioned within standard cephalometric parameters, with an incisor mandibular plane angle (IMPA) of 97°. The morphology and crown-root ratio of mandibular teeth were found to be normal. Cone beam computed tomography (CBCT) images were imported into Mimics (version 21.0; Materialise NV, Leuven, Belgium) to reconstruct a three-dimensional geometric model of the mandible and dentition. This model was subsequently refined using Geomagic Studio (version 2016; 3D Systems, NC, USA). To simulate the periodontal ligaments (PDLs), a uniform extension of 0.3 mm was applied to the root shapes [16]. The first premolars, along with their PDLs, were then removed to create models of the mandibular dentition and PDLs without the first premolars. A Boolean operation was performed to extract the alveolar fossa of the mandible by subtracting the teeth and PDLs from the mandible. Vertical rectangular attachments measuring 3 mm in height, 2 mm in width, and 1 mm in thickness were placed on the buccal surfaces of the canines, second premolars, and first molars [17]. All components (mandibular dentition, mandible, PDLs, attachments, and aligners) were assembled and converted into a FEA solid model using Hypermesh 2019 (Altair Engineering Inc., Troy, USA). The CAs were modeled on the external surfaces of the tooth crowns and attachments with a nonuniform thickness of 0.4 mm, simulating the thermoforming process based on the constructed dentition and attachments. The mechanical properties of the tissues, attachments, and CAs were set according to previously published literature [12, 18, 19]. No materials were used to fill the extraction space [20]. All materials in this study were assumed to possess linear elastic, homogeneous, and isotropic properties [10]. Surface-to-surface contact was established between the aligner surface and the teeth, with a friction coefficient (μ) set at 0.2 [21]. The friction coefficient between teeth was set at 0.18 [22].

All constructed components were assembled and imported into ANSYS Workbench 2019 (ANSYS, Pennsylvania, USA) to generate a comprehensive mandibular finite element model (Fig. 1).

Fig. 1.

Fig. 1

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Computer-aided designed models

In our research, we identified the beneficial effects of anterior teeth retraction using CA through both FE studies [13] and clinical trials [14]. Considering the previous grouping setting and clinical availability, five experimental groups were designed based on the spacing between the anterior teeth: G0 (0 mm), G1 (0.2 mm), G2 (0.4 mm), G3 (0.6 mm), and G4 (0.8 mm; Fig. 1). In these groups, the lower incisors were set to intrude by 0.2 mm following an initial intrusion of 1.5 mm of the canines. After configuring the loading parameters, FEA was conducted using ANSYS Workbench 2019 software to analyze displacement tendencies and Von Mises stress distributions. Local coordinate systems were established for each tooth, with the X-axis representing the mesiodistal direction (positive towards mesial), the Y-axis indicating the labiolingual direction (positive towards labial), and the Z-axis denoting vertical direction (positive for intrusion). Given that movement patterns of bilateral identical teeth were largely symmetrical, only the right side was analyzed. Measurement points were designated at the midpoint of the incisal edge and the apical point of each anterior tooth’s root. Additionally, tooth displacement tendencies and stress distributions within the PDLs and CAs were thoroughly analyzed to assess treatment outcomes effectively.

Results

Effects of different anterior spaces on the intrusion amount of incisors

As illustrated in Fig. 2A, an increase in the spaces between the anterior teeth correlated with a progressive rise in the intrusion of incisors. However, as the spaces expand further, the rate of this increase begins to taper off. In the absence of spacing, significant intrusion was observed in the crown of the central incisor, while the root exhibited only minor intrusion. Under a spacing condition of 0.6 mm (Fig. 2C), the central incisor's root demonstrated maximum intrusive tendencies, measuring 0.0497 mm. For lateral incisors, the greatest intrusion for both the crown and root occurred at G4, measuring 0.0988 mm and 0.0644 mm, respectively. Interestingly, under these same conditions, lateral incisors demonstrated greater intrusion than central incisors, particularly at the root level.

Fig. 2.

Fig. 2

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Vertical displacement tendencies of central incisor, lateral incisor when different size of space was arranged between anterior teeth. A Vertical displacement tendencies of central incisor, lateral incisor. B Vertical displacement tendencies of crowns. C Vertical displacement tendencies of roots (unit: mm)

Effects of different anterior space on the labiolingual displacement of incisors

Figure 3 revealed that in the labiolingual direction, all incisors displayed labial displacement of their crowns and lingual displacement of their roots across all tested conditions, indicating an unintended labiolingual tipping during intrusion. However, the experimental groups with spaces exhibited improved control over labiolingual displacement. Specifically, for the crowns of central incisors, the minimal labial displacement was recorded at 0.6 mm spacing (0.0260 mm), while for lateral incisors, this minimum occurred at 0.4 mm spacing (0.0247 mm). The roots of the central and lateral incisors showed minimal lingual displacement under G0 (−0.0217 mm) and G2 (−0.0087 mm), respectively.

Fig. 3.

Fig. 3

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Labiolingual displacement tendencies of central incisor, lateral incisor when different size of space was arranged between anterior teeth. A Labiolingual displacement tendencies of central incisor, lateral incisor. B Labiolingual displacement tendencies of crowns. C Labiolingual displacement tendencies of roots (unit: mm)

As demonstrated in Fig. 4A, under a spacing condition of 0.6 mm, both central and lateral incisors exhibited movement patterns that more closely approximated bodily intrusion. As illustrated in Fig. 4B, the minimum labial tipping of both central and lateral incisors was observed under G3(0.6 mm) and G2(0.4 mm) conditions, respectively.

Fig. 4.

Fig. 4

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The size of the anterior space is conducive to bodily intrusion for central incisors and lateral incisors. A Under 0.6 mm space, lower incisors intrusion tended to be bodily movement in vertical direction. B Central incisors and lateral incisors manifested a better labiolingual control respectively under 0.6 mm and 0.4 mm anterior space (unit: mm)

Effects of different anterior space on the vertical and labiolingual displacement of canine

As depicted in Fig. 5A, canines consistently exhibited tendencies for extrusion and lingual tipping displacement. In conditions without spaces, both the crown and root of the canine demonstrated a pronounced extrusion effect alongside a notable lingual tipping tendency. Conversely, in the experimental group with spacing (ranging from 0.2 to 0.6 mm), a diminished extrusion tendency was observed in canines. In terms of labiolingual direction (Fig. 5C), the minimal displacement for canines was noted under 0.4 mm spacing.

Fig. 5.

Fig. 5

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Vertical and labiolingual displacement tendencies of canine when different size of space was arranged between anterior teeth (unit: mm). A Vertical and labiolingual displacement tendencies of canine. B Verticall displacement tendencies of crown and root. C Labiolingual displacement tendencies of crown and root (unit: mm)

Effects of different anterior space on the stress of PDLs

Figure 6 presents the regional stress distribution patterns within the PDL across sagittal and occlusal planes for the entire dentition. The maximum Von Mises stress within the PDL was concentrated around the cervical region of the incisors. For incisors, compressive stress distribution was primarily localized to the cervical third of the labial surface. In contrast to the control group, stress distribution in the PDL was more uniform and extended from the cervical area to the root apex. The stress distribution for lateral incisors mirrored that of central incisors but exhibited higher values and a more uniform periodontal stress distribution (Table 2). For canines, without spaces, compressive stress within the PDL was predominantly concentrated on the cervical third of labial surfaces. However, under G4 conditions, stress distribution became more even compared to scenarios without spaces.

Table 1.

Properties of the materials considered are summarized in Table 1

Model Young’s modulus (Gpa) Poisson’s ratio
Cancellous bone 1.370 0.30
Cortial bone 14.700 0.30
Teeth 20.600 0.30
PDL 6.89 × 10–5 0.49
Aligner 0.2 0.33
Attachment 13.700 0.30
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Fig. 6.

Fig. 6

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Von Mises stress of PDLs of mandibular dention when different size of space was arranged between anterior teeth

Table 2.

The peak values of PDL compressive stress of each tooth under different conditions (MPa)

Anterior space Central incisor Lateral incisor Canine Second premolar First molar Second molar
No space 0.1481 0.1493 0.068 0.027 0.008 0.031
0.2 mm space 0.1444 0.1447 0.050 0.062 0.003 0.037
0.4 mm space 0.1476 0.1490 0.063 0.055 0.005 0.015
0.6 mm space 0.1706 0.1842 0.053 0.068 0.010 0.002
0.8 mm space 0.1343 0.1429 0.067 0.032 0.040 0.033
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Effects of different anterior space on the stress of the CAs

As illustrated in Fig. 7, the presence of spacing significantly influenced both the distribution and magnitude of Von Mises stress within CAs. In the absence of spaces, maximum stress concentrations were observed between lateral incisors and canines, with tensile stress evident in the second molar region. In contrast, with a spacing of 0.6 mm, higher stress levels were noted at the incisal edge between central incisors, with a more uniform distribution of stress across the anterior region compared to conditions without spaces. As spacing between anterior teeth increased, maximum Von Mises stress within CAs was observed at G3(0.6 mm).

Fig. 7.

Fig. 7

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The distribution of Von Mises stress of the clear aligners in the groups with different spaces

Discussion

Clear aligners have emerged as a transformative alternative to traditional fixed appliances in orthodontics, offering notable advantages in aesthetics, comfort, and oral hygiene maintenance [23, 24]. Recent advancements in materials and techniques have further expanded the versatility of clear aligners, enabling effective management of a wide spectrum of malocclusions, from minor tooth movements to more complex cases involving overbite correction and severe crowding [5, 25]. One common scenario in orthodontic practice involves premolar extractions followed by anterior retraction and intrusion. This process necessitates precise biomechanical design to ensure adequate intrusion and torque application on the incisors [10, 24, 26]. However, existing literature [4–8] indicates that incisor proclination often serves as the primary mechanism for opening the overbite, while the intrusion of mandibular incisors remains challenging and frequently leads to unwanted outcomes such as fenestration and dehiscence [12].

The biomechanics associated with clear aligners hinge on their ability to conform to the crown surfaces of teeth, coupled with the inherent resilience of polymer materials. This combination allows for the generation of appropriate orthodontic forces necessary for tooth movement [27]. When properly positioned, clear aligners exert an intrusive force on the incisors while applying an extraction force on the canines and posterior teeth. This results in labial tipping and intrusion of incisors (as illustrated in Figs. 2 and 3), alongside lingual tipping and extrusion of canines. However, the deformation of the aligner creates areas of contact with the teeth as well as gaps where the aligner does not engage, which can diminish the efficacy of tooth movements [28, 29]. Interestingly, the introduction of spaces between anterior teeth significantly enhances the intrusive tendencies observed in incisors. In particular, the central incisor exhibited the highest root apex displacement under a spacing condition of 0.6 mm (G3). The positioning of these spaces alters the fulcrum's location, thereby reducing aligner deformation and optimizing force application. However, it is crucial to note that excessive spacing can negate these benefits. In our experimental models, creating spaces allowed the canines to serve as a fulcrum that shifted distally towards the posterior dentition. This phenomenon resembles a transition from a labor-saving lever to a laborious lever system, where a longer power arm and shorter resistance arm facilitate enhanced intrusion via clear aligners. Moreover, increasing the wrapping area of the clear aligners around the crowns of anterior teeth through space creation has been validated as an effective strategy for mitigating pendulum effects and"roller-coaster"movements, ultimately improving the accuracy of incisor intrusion [13]. Unlike enamel interproximal reduction (IPR), which reduces crown size, our approach utilized distalization of anterior teeth to create space without altering crown dimensions. This strategy not only increased the contact area but also provided greater grip for intrusive forces. Additionally, the presence of spaces minimizes interproximal friction between the targeted intruding teeth [30], thereby preventing unwanted protrusion during intrusion.

As noted in previous studies, true intrusion is defined as the bodily movement of the center of resistance (CR) in relation to either the occlusal plane or a plane aligned with the long axis of the tooth [31]. However, due to geometric asymmetry within the periodontal ligament and inherent variations in tooth morphology, accurately identifying the CR can be problematic [32, 33]. Furthermore, genuine intrusion and tipping movements are often interrelated; thus, the axes of rotation generated by these movements may not intersect in three-dimensional space. Consequently, using CR as a reference point for evaluating three-dimensional movement during tooth intrusion may lead to inaccuracies [33]. To address these complexities, our study employed a more nuanced approach by analyzing the midpoint between the incisal edge and root apex of anterior teeth, along with assessing differences between crown and root displacements. As demonstrated in Fig. 4A, under a spacing condition of 0.6 mm, both central and lateral incisors exhibited movement patterns that more closely approximated bodily intrusion.

Previous research [5] has indicated that the proclination of incisors serves as the primary mechanism for overbite opening. Consequently, the pseudo-intrusion of mandibular incisors, accompanied by labial tipping, fails to create adequate space for maxillary anterior retraction and may actually increase the risk of fenestration and dehiscence [12]. Our findings align with this perspective, revealing a tendency for incisor intrusion characterized by significant labial tipping rather than true bodily movement, particularly evident in the control group. Furthermore, our analysis of labiolingual tipping revealed that incisors across all conditions exhibited a pattern of crown labial tipping coupled with root lingual tipping during the intrusion process. As illustrated in Fig. 4B, the minimum labial tipping of both central and lateral incisors was observed under G3(0.6 mm) and G2(0.4 mm) conditions, respectively. We hypothesize that when the canine acts as a fulcrum and moves distally, the rotational radius of the intruding incisors is extended, resulting in reduced labial tipping. The results indicate that the introduction of space effectively mitigates passive deformation of the aligner, thereby optimizing the transmission and distribution of clear aligner (CA) orthodontic forces. This enhancement contributes to better control over the labial tipping of the incisors. However, it is crucial to note that excessive spacing can diminish these advantages, similar to the complications associated with extraction spaces. The lack of stiffness in the aligner, combined with excessive spacing, can lead to bending effects that theoretically result in unwanted deformation. As depicted in Fig. 7, the maximum Von Mises stress experienced by the clear aligner occurred under G3 (0.6 mm spaces), with a more even distribution observed in the anterior region. In contrast, under conditions without spacing or with 0.8 mm spacing, the maximum Von Mises stress was primarily concentrated in the extraction spaces or between the lateral incisors and canines, respectively. It is important to emphasize that while the recommended spacing of 0.6 mm does not fully counteract labiolingual tipping to achieve absolute bodily intrusion (as shown in Fig. 4), it does represent an improvement over other conditions. Therefore, incorporating additional auxiliary devices may be necessary to mitigate unexpected movements during treatment and enhance overall treatment outcomes.

Previous studies [34–36] have demonstrated that the use of auxiliaries significantly enhances both the effectiveness of intrusion movements and the retention of aligners during these procedures. Specifically, in cases involving premolar extractions, vertical rectangular attachments on canines and premolars have been found to provide stronger aligner retention and facilitate more predictable incisor movements compared to optimized canine attachments [34, 35]. In more complex orthodontic cases, it is recommended that attachments be placed on all anchorage teeth to achieve better reciprocal anchorage and improve the predictability of tooth movements [35]. To further refine the accuracy of intrusion, some researchers advocate for the application of horizontal attachments on lateral incisors [36]. This strategy aims to prevent lower incisors from failing to track properly during simultaneous canine intrusion. Notably, the G8 SmartForce features now incorporate automated placement of attachments on lateral incisors undergoing intrusion, reflecting advancements in orthodontic technology. In our study, we employed conventional vertical rectangular attachments on the canines, second premolars, and first molars to establish regular reciprocal anchorage, as supported by previous research. This design allowed us to analyze the effect of anterior spacing on intrusion (Fig. 1). Given that clear aligners achieve tooth movement through the application of elastic forces that wrap around designated crown areas, the introduction of spaces increases the contact area between the clear aligner (CA) and the crowns of the teeth, thereby providing additional surface area for force application [27]. When examining the Von Mises stress within the clear aligner, it becomes evident that both the magnitude and distribution of maximum stress correlate with the size of spaces between anterior teeth. In the control group, maximum compressive stress was concentrated in the area between the lateral incisors and canines. In contrast, in the groups with 0.6 mm spacing, maximum stress was more evenly distributed across areas between the extraction sites and canines, as well as around the incisal edges of the incisors, particularly between the central incisors. The 0.6 mm spacing groups exhibited maximum stress on the aligner, which likely contributed to an increased amount of intrusion displacement observed in these experimental groups. However, it is important to note that while the Von Mises stress on canines, extraction sites, and second premolars increased in Group 3 (0.6 mm spaces), this could lead to potential anchorage loss. Consequently, orthodontists must carefully consider these undesired displacements of anchorage teeth when planning aligner treatment to ensure optimal outcomes.

Previous studies have confirmed that the protocols for anterior tooth intrusion can significantly impact the stability of anchorage. Liu et al. [37] utilized 3D printed clear aligners (CAs) with various procedures to intrude the mandibular incisors and canines on a standardized model (P12P-SB1, Nissin Dental Products Inc., Tokyo, Japan), employing a force sensor to measure vertical force values. Their findings revealed that when canines were intruded independently, they experienced the highest levels of intrusive forces. Conversely, for the lower incisors, the forces applied were not significantly different whether the canines and incisors were intruded simultaneously or if the incisors were subjected to the same amount of activation (0.2 mm) in isolation. Moreover, when canines and incisors were intruded concurrently, the adjacent teeth, both the targeted intruding teeth and the anchorage teeth, were subjected to greater extrusive forces. This observation leads to the recommendation that canines and incisors should be intruded separately, particularly in cases involving severe deep overbite, high bone density, or long roots. Furthermore, it is advisable to intrude the incisors only after the canines have been successfully intruded. This approach allows for a more focused application of intrusive forces on either the canines or incisors while stabilizing the anchorage teeth to prevent unwanted extrusion. In line with previous research, the mandibular incisors in this study were activated for an intrusion amount of 0.2 mm following an initial canine intrusion of 1.5 mm. In comparison to the control group, moderate spacing provided a more stable vertical anchorage for the canines, while exerting only a slight passive effect on lingual tipping movements, which remained minimal and comparable to those observed in the control group.

The current three-dimensional finite element studies often simplify the periodontium as a homogeneous, continuous, and isotropic linear-elastic material [38], which does not reflect its realistic nature and thus potentially influences the accuracy of the results. Due to the relatively high stiffness of both the bone and tooth, orthodontic tooth movement is dominated by deformation of the PDL and principally depends on the stress or strain in the PDL [39, 40]. It has been suggested that different material properties of PDL, including linear-elastic, viscoelastic, hyperelastic, and anisotropic behaviors, do not alter the stress distributions and the direction of tooth movement in the FE modeling of dentition [41, 42]. However, the magnitudes of the stress and tooth movement distance were significantly different among the cases with the tested material properties [42]. For instance, increasing Young’s modulus leads to higher stress on both teeth and the PDL, resulting in greater tooth displacement. The observed intrusion of the root apex (e.g., < 0.05 mm) appears minimal for the mandibular incisors, indicating that future studies should incorporate multi-step simulations to better represent long-term tooth movement. Additionally, although the bilinear and the Mooney-Rivlin type hyperelastic assumptions approximate quite closely the nonlinear behavior of the PDL, the bilinear model does not describe the continuous change of the elastic modulus with the strain, whereas the hyperelastic models do not reproduce well the measured displacement fields in the entire periodontium [43]. Furthermore, geometric nonlinearities are generally negligible under low loads, which is typical for orthodontic treatment [39]; however, they become more significant under high loads, such as those encountered during biting. Although these simplifications may not provide sufficient accuracy for quantitative analysis, they still offer a reasonable assessment and valuable insights into the biomechanical effects of orthodontic treatment.

However, individual patient variations, such as the symmetry of the left and right dental arches, initial labiolingual inclinations, morphology and crown-root ratio of the incisors, alveolar bone levels, and the effects of soft tissues, may influence the results. This analysis was limited to the anterior teeth on the right side, assuming perfect bilateral symmetry, which may not be in line with the actual situation. Different patients have different labiolingual inclinations of the lower incisor, which directly affects the distribution of force and reverses the labiolingual rotation direction of incisors during intrusion [44]. Meanwhile, in real-world situations, the effects of soft tissues in constraining labiolingual tipping should be considered. Consequently, recognizing the significance of these variables, our research group intends to investigate them further in subsequent clinical studies.

Based on the results obtained through FEM analysis, it can be concluded that moderate spacing between anterior teeth significantly enhances the accuracy of intrusion while maintaining the stability of anchorage teeth. This is achieved by eliminating interproximal friction, increasing the contact area of the CAs around the crowns, and facilitating a distal movement of the fulcrum. Furthermore, implementing such spacing in extraction cases appears to be practical and time-efficient, particularly when achieved through sequential anterior retraction. Therefore, this FEM analysis supports the notion that moderate spacing between anterior teeth is a reliable and effective configuration for the intrusion of lower incisors.

However, this FE study does have limitations. Notably, it cannot directly simulate the physiological and biomechanical processes involved in periodontal tissue remodeling during orthodontic tooth movement, which hinders our ability to quantitatively reproduce long-term tooth movement outcomes. Additionally, despite selecting an ideal occlusion, periodontal health, and mandible model for this study, each orthodontic case presents unique conditions like tooth inclination, root length and morphology, periodontal status, and oral environment that could influence the final results. Consequently, future research should prioritize follow-up clinical studies aimed at validating our protocol through in vivo patient treatment trials.

Conclusions

Key findings from this study include

  • The introduction of spacing between anterior teeth effectively eliminates interproximal friction, enhances the retention of aligners, and optimizes the distribution of von Mises stress on both the periodontal ligament (PDL) and the aligners, thereby improving the accuracy of intrusion.

  • Appropriate spacing between anterior teeth (e.g., 0.6 mm in this model) is beneficial for increasing the efficiency of mandibular incisor intrusion while minimizing unintended tipping movements.

  • It is crucial to consider anchorage when utilizing spacing to intrude incisors, ensuring that the desired tooth movement is achieved without compromising the stability of adjacent teeth.

Acknowledgements

We are grateful for the assistance of Shanghai Schaugo Technology Co., Ltd in technical guidance. The authors would like to express their gratitude to EditSprings (https://www.editsprings.cn) for the expert linguistic services provided.

Abbreviations

CA

Clear aligner

CAT

Clear aligner therapy

3D

Three-dimensional

FEA

Finite element analysis

PDLs

Periodontal ligaments

IMPA

Incisor mandibular plane angles

CBCT

Cone beam computer tomography

COS

Curve of Spee

CR

Center of resistance

Authors’ contributions

LL contributed to methodology, formal analysis, writing original draft. LL contributed to conceptualization, writing review and editing. YC contributed to conceptualization. ZWW contributed to formal analysis, NL contributed to writing-review. FJ and YJL contributed to conceptualization, writing review and editing and visualization. All the authors read and approved the final manuscript.

Funding

This study was supported by the National Clinical Research Center for Oral Diseases (LCA202403).

Data availability

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

Declarations

Ethics approval and consent to participate

This present study was approved by the Ethical Committee of the Stomatology Hospital of the The Air Force Medical University (No. KQ-YJ-2024–241). All methods were carried out in accordance with relevant guidelines and regulations and the Declaration of Helsinki. Informed consent was obtained from all subjects.

Consent for publication

No applicable.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Lei Liang and Lu Liu contributed equally to this work as co-first authors.

Contributor Information

Yanjiao Li, Email: ls781076360@163.com.

Fang Jin, Email: jinfang@fmmu.edu.cn.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

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

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