Mastering molar mesialization: the role of attachment designs and tipping compensation in clear aligner therapy—a finite element analysis

Abstract

Introduction

To investigate the effects of attachment design and compensation angulation on long-distance molar mesialization in clear aligner therapy (CAT).

Methods

The study used a dental model from an adult volunteer with missing first molar (M1), wherein the second and third molars (M2 and M3) required mesialization. Three attachment designs—horizontal rectangular (HA), single 45°(SA), and double 45°(DA)—were applied to the buccal surface of M2 to assess their influence on movement efficiency. Subsequently, distal tipping overcorrection angles of 0°, 0.5°, 1° and 1.5°were applied to M2 to assess their effect on tipping control. Finite element analysis (FEA) was performed to analyze displacement patterns and stress distribution.

Results

Mesial tipping and transverse crown rotation of the M2 constituted the primary adverse outcomes during molar mesialization. The attachments effectively mitigated these undesirable movements, with the DA design demonstrating the highest efficacy, followed by the SA. For the SA design, a 1.5° distal compensation angle was required to may facilitate near-bodily movement. In contrast, the DA design may facilitate, near-bodily movement with only a 1° compensation angle.

Conclusion

Long-distance molar mesialization primarily results in the adverse effects of mesial tipping and transverse crown rotation in CAT. While attachments can mitigate these adverse effects, applying appropriate angular compensation is more effective in promoting bodily movement of the molars.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12903-026-08471-8.

Introduction

Dental caries remains the most prevalent oral disease worldwide, especially among adolescents, with mandibular first molars(M1) being highly susceptible to extensive decay [1, 2].When M1 becomes non-restorable, their loss can significantly impairs masticatory function, aesthetics, and overall oral health [3]. For adult patients with missing first molars, implant restoration is often the primary treatment option. However, in cases of early loss, particularly when the position of third molars (M3) or its tooth germs is favorable, mesialization of the second and third molars (M2 and M3) presents a viable alternative to implants placement [4]. This approach may offer superior functional and prognostic outcomes, especially for adolescents and patients with well-maitained periodontal health [5]. Additionally, substantial molar mesialization is indicated in other clinical scenarios—such as extraction cases involving the removal of the second premolar (PM2) when the minimal anchorage is desired [6]. In these situations, mesialization is often extensive and plays a critical role in achieving proper molar relationships. Nonetheless, such treatments pose considerable clinical challenges and generally entail longer treatment durations compared to fixed appliance therapy [7].

Conventional fixed appliances have long been the most widely used approach for long-distance molar mesialization, owing to their extensive history and well-established mechanics [8]. However, molar mesialization often results in unavoidable side effects such as mesial tipping, rotation, and the “roller coaster” effect. To approximate bodily movement of molars, adjunct techniques such as Tip-back bend, Toe-in bend, compensation bend [9, 10], temporary skeletal anchorage devices (TSADs) [4], and corticotomy are frequently used to improve molar uprighting and facilitate more controlled mesial movement [11–13]. The current literatures suggest that fixed appliances demonstrate superior efficacy for long-distance molar mesialization compared to clear aligners [14]. Nevertheless, due to advantages such as enhanced aesthetics, improved comfort, and reduced chair time, clear aligners have gained increasing popularity among patients and clinicians alike [15, 16]. Consequently, they remain a frequently selected treatment option even in cases requiring significant molar mesialization [11, 17, 18].

Side effects commonly associated with molar mesialization tend to be more pronounced with clear aligners than with fixed appliances therapy. Researchers are currently exploring various strategies to mitigate or prevent these side effects, with a primary focus on advancements in biomechanics—such as overcorrection of torque and angulation—as well as innovations in aligner design, 3D printing of aligner materials, and other emerging directions [19, 20]. Nevertheless, clear aligner therapy (CAT) frequently presents off-track movement, localized open bite, severe mesial inclination during molar mesialization. These deviations can adversely affect periodontal health, compromise occlusal stability, and prolong treatment duration.

The biomechanics of molar mesialization using clear aligners, particularly when relying solely on aligners and attachments, remain incompletely understood and warrant further investigation. Therefore, to address these challenges, this study utilized three-dimensional finite element analysis (3D-FEA) to systematically evaluate different attachment designs and distal angulation overcorrection strategies. The primary objectives of this research are: (1) to investigate the biomechanical behavior of molar mesialization during CAT, (2) to identify more effective attachment configurations for controlled molar movement, and (3) to establish evidence-based guidelines for effective distal angulation preparation. The findings of this study are expected to improve the predictability and clinical efficacy of long-distance molar mesialization using clear aligner systems.

Methods

Reconstruction of patient‑specific geometric models

A 21-year-old female patient with Angle Class I occlusion and a missing mandibular right M1 was enrolled in this study. The dentition was otherwise complete, with no significant anatomical anomalies [12]. Following informed consent, the treatment plan involved mesialization of M2 and M3 to close the edentulous space.

The cone-beam computed tomography (CBCT) of pre-treatment were imported into Mimics 21.0 software (Materialise, Leuven, Belgium) to reconstruct three-dimensional (3D) models of the teeth and mandible (Fig. 1A). The STL files of teeth and mandible were exported to Geomagic Studio 2017 (3D Systems, Rock Hill, SC, USA) for alignment and preprocessing. To simulate the orthodontic force generated by the clear aligner, a virtual setup approach was employed. The M2 was mesially displaced by 0.2 mm in Geomagic Studio 2017 to create a “target” position. Subsequently, the clear aligner was designed based on this displaced model, with a uniform thickness of 0.75 mm. This modeling strategy was adopted to simulate the elastic deformation of the aligner when it is seated onto the initial dentition. By designing the aligner on the displaced tooth model and then assembling it onto the original dentition, we effectively replicate the clinical scenario where the aligner exerts a corrective force due to the discrepancy between the aligner’s geometry and the initial tooth position [20, 21]. Periodontal ligaments (PDLs) were modeled by offsetting the root surfaces by 0.25 mm outward, followed by Boolean operations [22].

Fig. 1.

Models for FEA. (A) Assembled models including the mandible, periodontal ligament, teeth, attachment and clear aligner; (B) Second molar (M2) without attachment(①), and with horizontal rectangular attachment(②, HA), single 45° attachment(③, SA), and double 45°attachment(④, DA); (C) Local coordinate system of a tooth (crown-centered): a, midpoint of the mesial proximal crown (mesial crown); b, midpoint of the distal proximal crown (distal crown); d, distal root point; d, mesial root point; e, root point of PM2; (D) Design of different degrees of distal inclination angle (0°, 0.5°,1°, 1.5°) for M2; (E) Mathematical model of tooth tipping and rotation angles. The red dashed line represents the long axis of the tooth before movement, while the purple line indicates the long axis after tipping displacement. Angleαdenotes the inclination angle, and angleθrepresents the crown rotation angle. Detailed derivation and computational procedures are provided in Supplementary Information Fig. 1 (SI Fig. 1)

Material properties

The material properties of the components in this study were defined as follows: the jawbone (cortical and cancellous bone), teeth, PDL, clear aligners and attachments were all modeled as homogeneous, isotropic, and linear-elastic materials [22]. The cortical and cancellous bones were modeled as distinct regions, with elastic moduli set to 1.37 × 10⁴ MPa and 1.37 × 10³ MPa, respectively, and a Poisson’s ratio of 0.30 for both [23]. The elastic modulus of the clear aligner (1320 MPa) was determined through nanoindentation testing (detailed in SI excel 1).

Regarding the PDL, although it exhibits non-linear, hyperelastic behavior under physiological conditions, it was modeled as a linear-elastic material in this study. This simplification was adopted to focus on the initial stress distribution and the relative comparison of biomechanical effects between different aligner designs. Previous studies have demonstrated that for small-magnitude tooth displacement, the linear-elastic model provides a reliable approximation of stress patterns and trends while significantly improving computational efficiency and convergence stability [24].

The coordinate system

A global coordinate system was established relative to the occlusal plane to analyze sagittal displacement and overall movement trends of M2 and M3. Local coordinate systems were defined at the centroid of the clinical crown and root apex of each tooth, with axes oriented as follows: “X”-axis (sagittal direction), “Y”-axis (vertical direction), and “Z”-axis (labiolingual direction) (Fig. 1A and C).

Boundary conditions and loading methods

In terms of contact and boundary conditions, the alveolar bone was assigned a fixed support at its base. The interfaces between the teeth and the PDL, the PDL and the alveolar bone, and the teeth and the attachments were all defined as bonded contacts to ensure a continuous stress transfer. The contact interface between the clear aligner and the teeth was defined as frictional contact with a friction coefficient of 0.2 [25]. To simulate the orthodontic force generated by the clear aligner, the elastic recovery of the clear aligner was modeled by applying an interference fit (pre-activation) between the aligner and the teeth, which initiates the contact force required for tooth movement. Detailed material properties are summarized in Table 1.

Table 1.

Material properties

Material	Young modulus, E (Mpa)	Poisson ratio, v
Cortical bone	1.37 × 104	0.30
Cancellous bone	1.37 × 103	0.30
Periodontal ligament	0.69	0.45
Teeth	1.96 × 104	0.30
Clear aligner	1320	0.36
Attachment	1.25 × 103	0.36

To evaluate the efficacy of various attachment designs on the buccal surface of the M2 during mesialization, we first conducted a preliminary study to screen potential geometries, including a 45°angled attachment (Left-angled, L-SA), a 45°angled attachment (Right-angled, SA), a vertical-double attachment (V-DA), and a double-45°angled attachment (DA). Based on the preliminary results (SI Fig. 2), the SA and DA designs demonstrated superior control over M2 movement. Consequently, we selected four configurations for further investigation: ①Control (Con) without an attachment; ②Horizontal Rectangular Attachment (HA, 4 × 3 × 1 mm³); ③Single-Angle Attachment (SA, 3 × 2 × 1 mm³, 45°); and ④Double-Angle Attachment (DA, 3 × 2 × 1 mm³, dual 45°) (Fig. 1B). The Control group served as a baseline for tooth movement without auxiliary control, while the HA was included as a clinical benchmark due to its widespread use in orthodontic practice. Our findings indicate that the SA and DA designs provide significantly better control during molar mesialization compared to the other configurations (SI Fig. 2).

Subsequently, to determine the ideal compensation angle for minimizing mesial tipping during molar protraction, the SA and DA designs which demonstrated superior biomechanical control in the pilot study were evaluated across four distinct crown distal angle compensations (0°, 0.5°, 1°, and 1.5°) (Fig. 1D). In this test, we excluded the HA because it was less effective at controlling molar tipping than the SA and DA designs, a finding supported by previous studies showing that optimized attachments outperform conventional horizontal ones [26]. Finally, the assembled models were exported to Abaqus/CAE 2016 (Dassault Systèmes Simulia, Providence, RI, USA) for finite element analysis (Fig. 1).

Displacement vectors and stress distributions were calculated for M2, M3 and PM2. During data extraction and processing, four landmarks were defined on the M2 and M3: the mesial (a) and distal (b) points on the crown, and the mesial (c) and distal (d) points along the root. For the PM2, a single apical point was designated as “e” as showed in Fig. 1C. Tooth inclination and rotation angles were computed in three-dimensional space based on Euclidean geometry. Denoting the inclination angle as “α” and the rotation angle as “θ”, the angular relationships were derived as follows “ and (Fig. 1E) [27], the complete derivation is showed in SI Fig. 1.

Statistical analysis

Descriptive analysis was employed to demonstrate the biomechanical effects of molar movement under different attachment types and anchorage preparations [28, 29]. All data analyses were performed using GraphPad Prism 9 (version 9.0; GraphPad Software, La Jolla, CA, USA).

Results

Biomechanical responses of the second premolar and molars during mesialization

Figure 2A illustrates the displacement pattern resulting from a 0.2 mm mesial movement of the M2 in the absence of both an attachment and an angulation compensation. The primary side effect observed during mesial molar movement was sagittal inclination, characterized by mesial tipping of M2 and distal tipping of both the PM2 and M3 (Fig. 2B and D). The severity of tipping decreased in the order of M2 > M3> PM2, with values of 11.042 × 10^− 3°(mesial), 6.021 × 10^− 3°(distal), and 2.230 × 10^− 3°(distal), respectively (Table 2 and SI table 1). While PM2 and M2 inclined toward the edentulous space, M3 tilted distally, maintaining a consistent sagittal displacement pattern. At the individual tooth level, crown and root displacement occurred in opposing directions, with slightly greater mesial movement observed in the sagittal plane compared to distal movement. In conclusion, the most prominent side effect observed during mesial molar movement was pronounced mesial inclination of M2 in the sagittal plane.

Fig. 2.

Effects of molar mesialization. (A–C) Displacement of M3, M2 and PM2 in sagittal and horizontal views; (D, E) Tipping and rotation of teeth during mesialization in mesiodistal and labiolingual directions

Table 2.

Toothmovement of M2 with different attachment types on the buccal surface of tooth M2

Teeth(10− 2mm)	a: mesial-crown	b: distal-crown	c: mesial-root	d: distal-root
No attachment(Control)
Extrusion/Intrusion (×10− 2mm)	6.233I	6.204E	0.254I	3.340E
Buccal/Lingual displacement (×10− 2mm)	1.323B	0.078B	0.951 L	1.135 L
Mesial/Distal displacement (×10–2 mm)	12.56 M	11.260 M	4.806D	4.984D
Mesial/Distal rotation change(×10− 3°)	24.594D(Distobuccal)
Mesial/Distal tipping change(×10− 3°)	11.042 M
Horizontal rectangular attachment (HA)
Extrusion/Intrusion (×10− 2mm)	4.782I	4.947E	0.171I	2.665E
Buccal/Lingual displacement (×10− 2mm)	6.283B	6.989 L	0.050B	3.395 L
Mesial/Distal displacement (×10− 2mm)	9.556 M	8.634 M	3.078D	3.697D
Mesial/Distal rotation change(×10− 3°)	22.417D(Distobuccal)
Mesial/Distal tipping change(×10− 3°)	8.413 M
Single 45° bevel attachment(SA)
Extrusion/Intrusion (×10− 2mm)	3.730I	4.185E	0.0087I	2.313E
Buccal/Lingual displacement (×10− 2mm)	5.541B	6.861 L	2.932 L	2.932 L
Mesial/Distal displacement (×10− 2mm)	8.025 M	7.302 M	2.188D	2.757D
Mesial/Distal rotation change(×10− 3°)	19.444D(Distobuccal)
Mesial/Distal tipping change(×10− 3°)	7.556 M
Double 45° bevel attachment(DA)
Extrusion/Intrusion (×10− 2mm)	3.430I	3.749E	0.0445I	2.056E
Buccal/Lingual displacement (×10− 2mm)	5.463B	6.606 L	2.924 L	2.924 L
Mesial/Distal displacement (×10− 2mm)	7.259 M	6.599 M	1.948D	2.486D
Mesial/Distal rotation change(×10− 3°)	18.051D(Distobuccal)
Mesial/Distal tipping change(×10− 3°)	5.071 M

E, tooth extrusion based on occlusal plane; I, tooth intrusion based on occlusal plane; B, buccal displacement; L, lingual displacement; M, mesial displacement; D, distal displacement; a: mesial-crown; b: distal-crown; c: mesial-root; d: distal-root; The tooth displacement direction is marked after the value based on the local coordinate system

Additionally, transverse rotation of M2 was observed as a concomitant side effect during mesial movement, exhibiting a trend consistent with that of mesial tipping (M2 > M3 > PM2) (Fig. 2C and E). The M2 exhibited rotation aligns with the results of Hakan et al., showing consistent patterns of, mesial tipping, rotation and crown extrusion [30]. Detailed data are presented in Table 2 and Supplementary table 1. The FEA results are consistent with clinical observations and are further supported by existing literature [31].

Influence of attachment designs on tooth displacement and stress distribution

To mitigate the adverse effects of tipping and rotation during molar mesialization, clinicians frequently utilize various attachment designs and angulation adjustments. This study evaluated three attachment configurations on the buccal surface of the tooth M2: HA, SA and DA (Figs. 3A-D) Compared to the control group (Con) without attachments, all three experimental attachment designs—HA, SA, DA—effectively reduced mesial tipping and rotation during molar mesialization, with a clear efficacy hierarchy observed: DA > SA > HA > Con. Both SA and DA attachments exhibited superior clinical performance in facilitating controlled bodily movement (Fig. 3E and Table 2).

Fig. 3.

Tooth movement during molar mesialization with different attachment types on the buccal surface of M2. (A–B) Displacement trends of M2, M3, and PM2 in the Control, HA, SA, and DA groups; (E–G) Three-dimensional displacement of M2; (H) Tipping and rotation trends of M2

However, vertical and transverse analyses (Figs. 3F-G) demonstrated divergent crown-root displacement patterns. Vertical displacement during mesial tipping was characterized by mesial crown intrusion and distal crown extrusion, a pattern mirrored by opposing root movements. Transversely, the control group exhibited maximal rotational movement. In contrast, the buccal attachments induced distobuccal crown rotation—an effect that was least pronounced with the DA design. Notably, all attachment groups induced buccal root displacement. Quantitative analysis is indicated a progressive reduction in both tipping and rotation across groups (Con > HA > SA > DA), with a more pronounced correction observed in tipping compared to rotation (Fig. 3H). These findings suggest that buccal attachments particularly the DA design effectively minimize adverse effects during molar protraction. The SA attachment also represents a clinically viable alternative, especially in cases requiring additional anchorage reinforcement (Fig. 3 and Table 2).

A key subsequent question involves investigating the mechanisms that makes the DA group more resistant to adverse effects from molar mesialization than the SA and HA groups (Fig. 3C). FEA revealed distinct biomechanical behaviors among the three attachment configurations (Fig. 4). Figure 4A-D illustrate the displacement patterns and stress distribution within the tooth, attachments and aligner. Notably, stress concentration was most pronounced at the attachment edges and the adjacent aligner regions. Although all three attachment types produced mesial displacement of the M2, their stress distributions differed significantly (Figs. 4E, F).

Fig. 4.

Movement trends of different attachment designs during molar mesialization.　(A) Stress distribution of HA, SA, and DA; (B) Displacement of molars and premolar with different attachments; (C) Stress distribution on teeth; (D) Stress distribution on the clear aligner; (E) Principal displacement for the three attachment types; (F) Principal stress distribution for the three attachment types

Effects of distal angular compensation on molar control

Based on the principle of torque compensation for controlling the roller-coaster effect in conventional premolar extraction cases [32], this study introduced a distal compensation angle to improve bodily movement of molars using attachments. Based on Long Hu’s finding that 1.7°aligner anchorage preparation and Class II elastics led to the bodily movement of M1 for each aligner stage (0.25 mm) [33]. The experiment evaluated Control, SA and DA attachment configurations with four distal compensation angles (ranging from 0° to 1.5°, Fig. 5) to identify the most effective angle for minimizing mesial tipping and rotation.

Fig. 5.

Tooth movement with Control, SA and DA under different distal compensation angles. (A) Displacement of molars at 0°, 0.5°, 1° and 1.5° at sagittal view; (B) Tipping angle of PM2 at sagittal view; (C) Tipping angle of M2 at sagittal view; (D) Tipping angle of M3 at sagittal view; (E) Molar displacement at 0°, 0.5°, 1°, and 1.5° at transversal view; (F-H) Rotation angle of PM2, M3 and M3 with different compensation angle

Preliminary data suggest that angled SA and DA attachments effectively mitigate M2 mesial tipping. To optimize distal compensation, we compared molar movement patterns across the Control, SA, and DA groups under varying compensation angles (0°–1.5°; Table 2 and Fig. 5).

In the Control group, the absence of compensation resulted in severe mesial tipping and transverse rotation. Although increasing the compensation angle to 1.5° progressively reduced the inclination from 11.0423 × 10⁻³ ° to 1.0313 × 10⁻³ °, distal compensation alone proved insufficient for optimal control.

In contrast, both SA and DA attachments significantly enhanced tipping control. Within the SA group, mesial inclination decreased consistently as the compensation angle increased (7.017 × 10⁻³ ° to 1.069 × 10⁻³ °). While both attachment types performed similarly within the 0° to 1° range, a divergence emerged at 1.5°: the DA group induced a distal tipping tendency, facilitating the simultaneous distal displacement of the crown and root-a mechanism conducive to bodily mesial movement. Consequently, a 1.5°compensation in the SA group and a 1.0°compensation in the DA group demonstrated comparable efficacy in mitigating M2 mesial tipping.

Regarding transverse rotation, the Control group showed persistent distobuccal rotation of the M2; despite a reduction in magnitude with increasing compensation angles, the rotational trend remained evident. The DA group followed a similar rotational pattern but with significantly lower severity. Interestingly, the SA group demonstrated a distinct rotational shift: at a 1° compensation, the rotation transitioned from distobuccal to mesiolingual, suggesting that increasing the compensation angle effectively modulates the rotational tendency. In terms of vertical movement, the SA and DA attachments exhibited divergent effects. At a 1° compensation, the SA attachment not only mitigated mesial tipping but also induced intrusion of both the crown and root. Conversely, at a 0.5° compensation, the DA attachment resulted in simultaneous extrusion. These findings highlight that while both attachments are effective in managing mesial tipping, their influence on vertical and rotational stability varies, necessitating careful selection based on the patient’s specific vertical and transverse requirement (Table 3).

Table 3.

Tooth movement of M2 with different compensation angle on Con, SA and DA group

Compensation angle Attachment /movement		0		0.5		1		1.5
		crown	root	crown	root	crown	root	crown	root
Con	Extrusion/Intrusion (×10 − 2 mm)	0.0145I	1.543E	0.1755I	0.3187E	0.4295I	0.20724I	0.64285I	0.6222I
	Buccal/Lingual displacement (×10 − 2 mm)	0.70044B	1.0432 L	0.045 L	0.0857B	0.0804B	0.0499B	0.1403B	0.0972B
	Mesial/Distal displacement (×10 − 2 mm)	11.91 M	4.895D	4.56 M	1.266D	2.2405 M	0.3537D	0.6272 M	0.3640 M
	Mesial/Distal rotation change(×10− 3 °)	24.5945(Distobuccal)		9.1597(Distobuccal)		4.4651(Distobuccal)		1.663(Distobuccal)
	Mesial/Distal tipping change(×10− 3 °)	11.0423 M		3.7767 M		1.7338 M		1.0313 M
SA	Extrusion/Intrusion (×10 − 2 mm)	0.2275E	0.2276I	0.2590I	0.1571E	1.2985I	1.2225I	0.6690I	0.6369I
	Buccal/Lingual displacement (×10 − 2 mm)	0.6600 L	0.6077 L	0.0569B	0.0526 L	0.5556B	0.4529 L	0.2082B	0.0184B
	Mesial/Distal displacement (×10 − 2 mm)	7.6635 M	2.4730D	3.7365 M	1.0535D	0.7471 M	1.2105 M	0.6375 M	0.3222 M
	Mesial/Distal rotation change(×10− 3 °)	19.444D(Distobuccal)		7.516D(Distobuccal)		2.941 M(Mesiolingual)		1.736 M(Mesiolingual)
	Mesial/Distal tipping change(×10− 3 °)	7.017 M		3.095 M		2.172 M		1.069 M
DA	Extrusion/Intrusion (×10 − 2 mm)	0.1595E	0.1655I	0.0165E	0.1769E	0.0864I	0.1132I	0.2147I	0.4264I
	Buccal/Lingual displacement (×10 − 2 mm)	0.5715 L	0.6716 L	1.386 L	0.2079B	1.4530 L	0.4185B	1.4581 L	0.5616B
	Mesial/Distal displacement (×10 − 2 mm)	6.9290 M	2.217D	2.3725 M	0.37535D	0.9657 M	0.2102 M	0.4792D	0.7987D
	Mesial/Distal rotation change(×10− 3 °)	18.051D(Distobuccal)		7.548D(Distobuccal)		5.380D(Distobuccal)		4.672D(Distobuccal)
	Mesial/Distal tipping change(×10− 3 °)	6.261 M		2.066 M		1.433 M		1.682D

Con, control group without attachment; SA, Single 45° bevel attachment; DA, Double 45° bevel attachment༛E, tooth extrusion based on occlusal plane; I, tooth intrusion based on occlusal plane; B, buccal displacement; L, lingual displacement; M, mesial displacement; D, distal displacement. The tooth displacement direction is marked after the value based on the local coordinate system

Furthermore, the responses of the second premolar (PM2) and the third molar (M3) to counterforce application warrant close attention. In all groups, PM2 exhibited the most pronounced changes: sagittally, it transitioned from distal to mesial tipping, resulting in a shift in inclination. Notably, this mesial tipping trend intensified with increasing attachment angulation, peaking at 1.5°. Regarding rotation, PM2 shifted from a mesio-lingual to a disto-buccal orientation, with the magnitude of rotation increasing proportionally with the attachment angle across all three groups. Similarly, M3 demonstrated significant displacement across all three dimensions. Detailed data and visual representations of these movements are provided in SI Table 2 and Fig. 5.

Mechanistic analysis and identification of the optimal control strategy

In the following section, we describe the biomechanical mechanisms of molar mesialization, incorporating the effects of different attachment types and compensation angle. As shown in Fig. 6D, the initial edentulous span measures 7.2 mm. By applying a 7.0 mm aligner over this span-representing a 0.2 mm reduction per step-a mesial force is exerted on M2, while a distal tipping force is applied to PM2. Figure 6 illustrates the mechanisms by which different attachment types control mesial tipping. The attachments are bonded to the tooth surface and maintain close contact with the clear aligner. Due to variations in tooth morphology and prominence, the concave surface of each attachment conforms to the tooth structure and is referred to as the tooth-facing surface (T-face), while the convex surface contacts the aligner and is termed the aligner-facing surface (A-face) showed in Fig. 6A. In the FEA, which simulates a clinically relevant scenario, a bonded constraint was defined between the attachment and the tooth surface, enabling the attachment to provide mechanical retention to the tooth. In contrast, a frictional interaction exists between the aligner and the attachment surface, resulting in an outward force that may potentially dislodge the attachment.

Fig. 6.

Mechanical analysis of three attachment types. (A-B) Principal displacement of HA, SA, and DA at two different perspectives; (C) Mechanical behavior of HA, SA, and DA; (D) Mechanical analysis without attachments: a, model of molar mesialization with 7.2 mm gap; b, model after 0.2 mm mesial movement; c, mechanism of gap closure via aligner shortening. (T-face, tooth-facing surface; A-face, aligner-facing surface; M, movement; T, tension; C, compressive force; C-aligner, Compressive force from aligner; T-aligner, tension from aligner; MF, the moment of M2 without attachment; MHA, the moment of the M2 with HA; MSA, the moment of the M2 with SA; MDA, the moment of M2 with DA)

When the tooth and attachment are considered as a single integrated unit, the force exerted by the tooth on the attachment is internal, whereas the force from the aligner is external. This external force acts on the tooth-attachment complex and counteracts the tendency for mesial inclination during mesial translation of the molars. By comparing the aligner-induced forces across different attachment designs, their anti-tipping performance can be evaluated. As illustrated in Fig. 6B, under a 0° anti-tipping configuration, stress concentrations were observed in all three attachment types: HA, SA, and DA. In the HA, stress was localized at the upper-right rectangular edge, exhibiting higher compressive stress (C_aligner) and lower tensile stress (T_aligner), which generated larger (M_HA−C) and smaller (M_HA−T) counterclockwise moments, respectively. The SA group exhibited both compressive and tensile stresses in diagonal regions, with compressive stress being dominant, producing corresponding counterclockwise moments M_SA−C and M_SA−T. In the DA, tensile stress was observed on the left side and compressive stress on the right, collectively contributing to counterclockwise moments M_DA−T and M_DA−C, thereby more effectively resisting mesial inclination of the molar. In summary, The DA group generated larger and more numerous counterclockwise force moments compared to the other designs. Thus, in the absence of distal tipping configuration, the DA attachment demonstrated the most effective resistance against mesial inclination.

However, due to the limited force efficiency of the aligner material, the actual tooth movement still resulted in mesial tipping [34]. Based on the mechanism of molar space closure in CAT, as shown in Fig. 6D, gap reduction was achieved through intentional shortening of the aligner. During this process, the M2 was subjected to a mesial force. Since the aligner’s point of force application did not coincide with the center of resistance of M2, a clockwise moment (M_F) was induced. The relative magnitudes of the moments followed the order: M_F > M_HA > M_SA > M_DA, ultimately resulting in mesial crown tipping. Furthermore, the mesial inclination order of M2 decreases sequentially as follows: 11.042 × 10^{− 3} °(M_F) > 8.413 × 10^{− 3} °(M_HA) > 7.556 × 10^{− 3} °(M_SA) > 5.071 × 10^{− 3} °(M_DA).

Furthermore, our experimental results demonstrate that without additional distal resistance, the DA attachment exhibited the highest performance, followed by the SA type. This trend was consistently observed across experiments with varying resistance angles. The SA group approached overall bodily movement at 1.5° of distal resistance, whereas the DA group achieved it with only 1°. The results obtained for the SA group align closely with those reported by Professor Long Hu, showing only a minor discrepancy of 0.2° [33]. This slight difference may be attributed to the use of a 0.25 mm aligner activation step and Class II elastics in the referenced study.

Figure 6E-F and SI Fig. 5 depict the force distribution analysis of SA and DA during near-complete translation. Compared to the non-resistance group, stress in both SA and DA remained concentrated along the edges, though the direction and magnitude of forces were altered. In the SA group, compressive forces acted more perpendicularly to the wide side of the attachment, while tensile forces were oriented parallel to it. In the DA group, tensile forces were predominantly localized on the distal attachment. However, distal inclination observed in the DA group at 1.5° resistance indicates possible overloading (Fig. 5). The resulting moments followed this magnitude relationship: M_DA−1.5°> M_F > M_DA−1°> M_SA−1.5°.

Discussion

As the M1 possesses the largest mesiodistal crown width in the dentition, its absence poses considerable clinical challenges and complicates the biomechanical process of tooth movement. This process is influenced by multiple factors, including the tendency of M2 tipping, periodontal conditions (such as root length and alveolar bone height), patient age, among others [4, 35, 36]. Long-distance molar mesialization is also applicable in conventional extraction case, such as those involving the removal of PM2 [6]. Clear aligners often struggle to achieve ideal outcomes in long-distance of molar mesialization due to insufficient anchorage control and suboptimal force transmission mechanisms [34].

This study utilized 3D-FEA to investigate the biomechanical behavior of M2 and M3 during long-distance mesialization in CAT for the loss of M1. Our study demonstrates that molar mesialization is inherently prone to mesial tipping and transverse rotation due to the center of resistance being located apically and the limitations of force transmission in aligners. Mechanistically, the “stress interruption effect” caused by the edentulous space significantly reduces the periodontal support, making the molar highly susceptible to mesial tipping under horizontal force. These findings are aligned with our team’s recent studies on the " stress interruption effect” in clear aligner cases involving extraction sites. The presence of an edentulous gap disrupts continuous stress distribution, leading to adjacent teeth tilting toward the space [37].

Recent literature on molar mesialization in CAT has primarily focused on four domains: aligner design optimization, auxiliary hardware, biomechanical analysis, and digital integration. Regarding aligner design, morphological modifications, such as the semi-pontic structures proposed by Hakan et al., have been shown to mitigate uncontrolled mesial inclination [38]. Similarly, to address the limitations of aligners alone, various auxiliary devices, including buttons, modified lever arms (MLA), and “Albert” cantilevers, have been introduced to control molar rotation and tipping [17, 30, 31]. While these strategies are effective, they often increase clinical complexity. Furthermore, despite these advancements, achieving true bodily movement of molars remains a significant challenge in CAT [39, 40]. Although mesial displacement is inherently susceptible to tipping, the specific biomechanical mechanisms by which varying attachment geometries (e.g., HA, SA, and DA) counteract this tendency remain insufficiently investigated. Our study fills this gap by showing that an optimized attachment geometry, particularly DA, can potentially yield substantial anti - tipping effects without the requirement for additional hardware.

Our key findings indicated that the biomechanical efficacy of molar mesialization in CAT relies on a synergistic interaction between attachment geometry and the incorporation of compensation angles. Among the tested configurations, the DA and SA design generated the most effective counter-clockwise moments, providing superior resistance to mesial inclination compared to HA and without attachments. The DA and SA design utilizes a dual-point contact mechanism to maximize the counter-tipping moment, effectively converting the aligner’s horizontal force into a controlled rotational moment. However, the attachment alone is often insufficient to achieve bodily movement. The incorporation of compensation angles serves as a proactive biomechanical strategy. We observed that the magnitude of the compensation angle is arguably more critical than the attachment type itself; it dictates the “starting point” of the force system, allowing the aligner to exert a corrective moment throughout the entire range of movement. Therefore, the most effective clinical protocol involves a dual-layered approach: utilizing the right attachment to enhance force transmission and simultaneously applying precise compensation angles to neutralize the inherent tipping tendency.

To date, no studies have reported achieving true bodily movement of molars using clear aligners alone. The use of attachments should be considered essential in CAT, especially in challenging cases involving molar mesialization [39, 40]. Unlike previous studies that focus primarily on displacement outcomes, our FEA approach provides a granular analysis of the stress-moment relationship. By elucidating how these configurations counteract mesial inclination, our findings provide a biomechanical foundation for the strategic use of attachments to potentially achieve near-bodily movement, offering a more streamlined clinical alternative to auxiliary devices.

The initial clinical success observed in our asymmetric extraction cases (extraction of #15, #24, #36, and #45 showed in Fig. 7) validates the FEA findings. The application of DA designs effectively maintained molar angulation over a six-month period, suggesting that these geometries can be translated into clinical practice. We recognize that a single case report is only a starting point. We are currently tracking a larger cohort of patients treated with this protocol and intend to conduct a long-term follow-up study to further validate these findings.

Fig. 7.

A case of molar mesialization using a SA and DA. A: Sagittal view, B: Transverse view

Although our primary goal was to counteract sagittal tipping, molar mesialization inherently induces complex side effects, including bucco-lingual tipping and transverse rotation, regardless of attachment design. While the buccal attachments tested effectively mitigated these deviations, the limitations of single-sided force application necessitate further optimization. To better manage these effects during M2 mesialization, future strategies should include:①Lingual Attachment Integration: Implementing a lingual attachment to create a force-couple system that neutralizes transverse rotation and stabilizes the tooth;②Differential Rotation Design: Incorporating compensatory rotation angles into the attachment geometry to offset the tooth’s natural rotation tendency (e.g., applying a distal-buccal rotation to counteract observed mesio-lingual rotation);③Enhanced Bucco-Lingual Control: Refining attachment geometry to precisely regulate bucco-lingual inclination and maintain the long axis during mesialization [27]. However, this approach may increase the difficulty for patients in inserting and removing aligners. It should be noted that clinically, many patients exhibit pre-existing mesial tipping of the second molar following prolonged absence of the first molar, often requiring uprighting before the mesialization can be effectively performed.

However, patient-specific considerations-such as age and periodontal health-significantly influence orthodontic tooth movement and thus affect the prognosis of molar mesialization.Further research is warranted to address several key aspects: the process and physiological limits of alveolar bone remodeling during long-distance mesial movement [35, 36]; the periodontal and gingival health of the M2 and M3 following mesialization; as well as refinements in aligner design and force delivery protocols to optimize bodily tooth movement with less adverse effects. While this study provides foundational biomechanical insights into clear aligner-mediated molar mesialization, clinical validation and multidisciplinary collaboration remain essential to improve treatment efficacy and predictability.

Limitations and future perspectives

Several limitations of this study should be acknowledged. First, the single-patient model limits the generalizability of our findings. While a standardized model is necessary to isolate the effects of attachment designs and overcorrection, it does not account for clinical variability in bone density, root morphology, or periodontal health. Thus, our findings provide a biomechanical framework rather than a definitive clinical protocol. Second, the methodological assumptions inherent in static FEA—such as linear elastic material properties and the exclusion of dynamic biological processes—simplify the complex clinical environment. Factors such as alveolar bone remodeling, periodontal ligament adaptation, masticatory forces, and soft tissue dynamics are not captured, nor is the potential for post-treatment relapse. Finally, as this study provides a static analysis of a dynamic process, it represents an idealized scenario. Future research should integrate multi-patient datasets and dynamic biological modeling to better simulate the long-term biomechanical responses and refine force delivery protocols for diverse clinical conditions.

Conclusion

This FEA study investigated molar biomechanics during long-distance mesial movement in CAT, where mesial tipping and mesiolingual rotation are primary side effects. We identified that distal angular compensation is more critical than attachment design for effective movement control. Specifically, SA with 1.5° and DA with 1° angulation compensations effectively mitigated these side effects. Further clinical validation is required to confirm these biomechanical findings in real-world practice.

Authors’ contributions

Fang Pei contributed to drafting the article, Xinyu Wen contributed to figures, Xinqi Huang and Xiao Cen contributed to linguistic revision, Ying Jin and Zhihe Zhao contributed to designing and composing the study.

Funding

This study was supported by grants from National Natural Science Foundation of China (Nos. 32271416; 32571571; 81900981) and the Science and Technology Project of Sichuan Province (No.2022YFQ0002;2025ZNSFSC0751), and Align Research Grant Program(21H0922); Research and Develop Program, West China Hospital of Stomatology Sichuan University (LCYJ-MS-202501); Research and Development Foundation of West China Hospital of Stomatology (RD-02-202507).

Data availability

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

Declarations

Ethics approval and consent to participate

This study was approved by the Ethics Committee of West China Hospital of Stomatology, Sichuan University (approval number: WCHSIRB-D-2021-331). All participants provided written informed consent prior to participation in the study. All procedures performed were in accordance with the ethical standards of the institutional research committee and with the 1964 Declaration of Helsinki and its later amendments. (Clinical trial number: not applicable.)

Consent for publication

The patient provided written informed consent for the use of their cone-beam computed tomography imaging data and intraoral scans in research and publication. Consent documents are securely archived at our institution and available upon request.

Competing interests

The authors declare no competing interests.