Introduction
This study aimed to analyze 3-dimensional (3D) tooth movement patterns during mandibular molar intrusion using finite element analysis, with a particular focus on the effects of temporary skeletal anchorage devices positioning and archwire constriction bend (ACB).
Methods
A 3D finite element model of the mandibular dentition was constructed. Intrusive forces of 2.0 N were applied to the archwire either mesial (M6 model) or distal (D6 model) to the first molar, whereas bilateral forces of 1.0 N were applied in the MD6 model. An ACB force of 1.0 N was applied lingually to both ends of the archwire. Tooth displacement, angulation change, and occlusal plane rotation were evaluated in 3 dimensions after 100 cycles of bone remodeling simulation, both with and without ACB during molar intrusion.
Results
Mandibular molars exhibited intrusion accompanied by mesial tipping in the M6 model, distal tipping in the D6 model, and minimal tipping in the MD6 model, regardless of the presence or absence of ACB. The mandibular central incisor (Mn1) demonstrated labioversion in the M6 model and linguoversion in both the D6 and MD6 models without ACB. With ACB applied, Mn1 consistently showed labioversion across all models, with the greatest intrusion and labioversion observed in the M6 model. The occlusal plane angle (OPA) rotated counterclockwise in all models except the M6 model with ACB, which exhibited a slight clockwise rotation. Mandibular posterior teeth showed buccal tipping in all models except the M6 model with ACB, where molars tipped lingually. ACB application reduced buccal tipping of the mandibular posterior teeth and mitigated counterclockwise rotation of the OPA, while promoting intrusion and labioversion of Mn1. Notably, OPA remained nearly stable during molar intrusion in the M6 model with ACB.
Conclusions
The appropriate force direction for mandibular molar intrusion, combined with ACB, facilitates controlled 3D tooth movement patterns.
Highlights
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This study was done to analyze the 3-dimensional tooth movement patterns during mandibular molar intrusion using finite element analysis.
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Archwire constriction bend (ACB) application reduced buccal tipping of the mandibular posterior teeth.
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ACB application mitigated counterclockwise rotation of the occlusal plane angle.
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Occlusal plane angle remained nearly stable during molar intrusion in the M6 model with ACB.
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The appropriate force direction combined with ACB facilitates controlled 3-dimensional tooth movement patterns.
Molar intrusion using temporary skeletal anchorage devices (TSADs) is recognized as a highly effective strategy for reducing anterior facial height and increasing overbite in the treatment of hyperdivergent Class II open bite patients. This approach also facilitates the counterclockwise (CCW) autorotation of the mandible, advancing the pogonion anteriorly and thereby enhancing the facial profile. ,
Hart et al reported that intrusion of the maxillary molars using TSADs effectively reduced the maxillary posterior dentoalveolar height, contributing to the correction of the anterior open bite. However, a compensatory dentoalveolar eruption or extrusion of the mandibular molars was observed, which diminished the overall vertical control achieved through maxillary molar intrusion. To counteract this effect, simultaneous intrusion of the mandibular molars using TSADs has been recommended as a more comprehensive approach to vertical dimension control. ,
Mandibular molar intrusion presents a greater biomechanical challenge than maxillary molar intrusion because of anatomic constraints, such as higher bone density and thicker cortical bone in the mandible. , TSADs are typically placed on the buccal side rather than the lingual side of the mandibular arch. Consequently, intrusive forces are applied buccally relative to the center of resistance (CRes) of the mandibular molars, resulting in buccal crown tipping. This undesired tipping can compromise arch coordination and negatively affect long-term occlusal stability. ,
Finite element analysis (FEA) has become an increasingly valuable tool in orthodontics for simulating and predicting 3-dimensional (3D) tooth movement under the preprogrammed force systems. It enables the evaluation of both initial displacement and long-term remodeling behavior of the periodontal ligament and alveolar bone. ,,,, Moreover, FEA allows for the assessment of how variations in the anteroposterior positioning of TSADs and the incorporation of transverse archwire constriction bends (ACBs) influence tooth movement patterns.
FEA has been employed to investigate the tooth movement patterns of the maxillary dentition during molar intrusion using buccally placed TSADs, as well as the role of ACB in mitigating buccal tipping of the maxillary molars. However, limited research has focused on the mandibular dentition, particularly regarding molar intrusion using buccal TSADs and the biomechanical effects of ACB on mandibular tooth movement patterns.
Therefore, the present study aimed to analyze the 3D tooth movement patterns of the mandibular dentition during molar intrusion using FEA, with a particular focus on comparing conditions with and without ACB.
Material And Methods
Dry cranial imaging was performed using cone-beam computed tomography (3DX, J Morita, Kyoto, Japan), and 3D images of the mandibular dentition were obtained in digital imaging and communication in medicine format. The digital imaging and communication in medicine data were then imported into the 3D image processing software Mimics (version 10.02; Materialize Software, Leuven, Belgium) to generate standard triangle language (STL) models of the mandibular dentition. These STL files were subsequently converted into finite element meshes for analysis.
The STL data were imported into the FEA pre and postprocessing software Patran (version 2017; MSC Software Corp, Los Angeles, Calif) as shell elements to construct a finite element model of the mandibular right dentition. A uniform 0.2 mm-thick periodontal ligament was modeled as a solid layer surrounding the root surface. Based on a previous study, the teeth were assumed to be rigid bodies. The shell elements representing the teeth were assigned a thickness of 3.0 mm, a Young modulus of 204 GPa, and a Poisson ratio of 0.3.
The periodontal ligament was modeled with nonlinear elastic properties, with a modulus of elasticity ranging 0.03-0.3 MPa, and a Poisson ratio of 0.3. Passive self-ligating brackets were incorporated into the model as orthodontic appliances. The bracket, archwire, power arm, and hook were all assumed to be composed of stainless steel, characterized by a Young modulus of 204 GPa and a Poisson ratio of 0.3. FEA was conducted according to the methodology described in previous literature, enabling the evaluation of both the initial small displacement within the periodontal ligament and the long-term tooth movement associated with bone remodeling. The initial displacement of each tooth was calculated under static loading conditions. The alveolar bone remodeling was simulated under the assumption that the long-term tooth movement correlates with the initial displacement, and the geometry of the periodontal ligament was iteratively updated to maintain its constant thickness during the simulation.
Contact interactions were defined between adjacent teeth and between the archwire and the bracket slots.
Contact boundary conditions, which used the node-to-segment function of the Marc software (MSC Software Corp, Newport Beach, Calif), were applied to each interproximal surface of the tooth.
All contact interfaces were modeled without friction (friction coefficient = 0) to focus solely on the effects of the applied force direction and magnitude on tooth displacement.
Because of the symmetry of the mandibular dentition, only the right side was modeled, and the nodes on the midsagittal plane were constrained in the mesiodistal direction.
The bone remodeling simulation was iterated 100 times. A general-purpose finite element solver, Marc (version 2014.1; MSC Software Corp, Newport Beach, Calif), was employed to perform the analysis.
The bracket slot size was 0.022-in × 0.028-in, and the archwire measured 0.019-in × 0.025-in. The vertical position of the TSAD’s head was set at 8.0 mm below the archwire. A vertical intrusive force of 2.0 N was applied to the archwire via TSADs positioned between the mandibular second premolar and first molar (M6 model; Fig 1 , A and D ) and the mandibular first molar and second molar (D6 model; Fig 1 , B and E ). In the MD6 model ( Fig 1 , C and F ), a vertical intrusive force of 1.0 N was applied to the archwire using TSADs, both with and without an ACB .
The 3D finite element models illustrating the application of intrusive forces via the archwire at different mandibular sites: M6 model, D6 model, and on both sites simultaneously (MD6 model), with or without an ACB: A, M6 model without ACB; B, D6 model without ACB; C, MD6 model without ACB; D, M6 model with ACB; E, D6 model with ACB; F, MD6 model with ACB.
At the beginning of loading, the intrusive force was applied in the pure vertical direction. As the teeth moved during the simulation, the direction of the force vector gradually changed because of geometric alterations in the archwire and tooth position.
ACBs were incorporated into the mandibular archwire to prevent buccal tipping of the mandibular molars during intrusion. A constriction force of 1.0 N was applied in the lingual direction at both ends of the passive archwire, which was constricted by 27.4 mm toward the lingual side, as shown in Figure 2 .
Lingual constriction bend applied to the archwire. A force of 1.0 N was exerted at the distal end of the archwire, producing a constriction displacement of 27.4 mm.
3D tooth movement patterns of the mandibular central incisor (Mn1), first premolar (Mn4), first molar (Mn6), and second molar (Mn7) were assessed by analyzing the translational displacements and rotational angles at the center of each bracket slot. The occlusal plane was defined using the incisal edge of Mn1 and the mesiobuccal cusp of the Mn6. The rotation of the occlusal plane in the sagittal plane was subsequently measured to evaluate vertical changes.
Results
Figures 3 and 4 illustrate the 3D displacements and angulation changes of the mandibular teeth during molar intrusion, comparing conditions with and without ACB in the sagittal and coronal views. Detailed measurements are provided in Tables I and II .
Sagittal view of tooth movement patterns at cycle N = 100 under intrusive forces applied to the archwire at 3 locations: M6, D6, and at both sites simultaneously (MD6), with or without ACB: A, M6 model without ACB; B, D6 model without ACB; C, MD6 model without ACB; D, M6 model with ACB; E, D6 model with ACB; F, MD6 model with ACB ( black , initial tooth positions; red , blue , and green , final tooth positions after 100 cycles of bone remodeling).
Coronal tooth movement patterns at cycle N = 100 under intrusive forces applied to the archwire at 3 locations: M6, D6, and both (MD6) with or without an ACB: A, M6 model without ACB; B, D6 model without ACB; C, MD6 model without ACB; D, M6 model with ACB; E, D6 model with ACB; F, MD6 model with ACB ( black , initial tooth positions; red , blue , and green , final positions after 100 cycles of bone remodeling).
Table I
The 3D displacements of the mandibular teeth during molar intrusion using TSADs with or without an ACB
| ACB | Mandibular molar intrusion using buccal TSADs | ||||||
|---|---|---|---|---|---|---|---|
| Without ACB | With ACB | ||||||
| Models measurement points | M6 | D6 | MD6 | M6 | D6 | MD6 | |
| x (mm) | Mn1 | 0.07 | –0.09 | 0.02 | 0.14 | 0.02 | 0.08 |
| Mn4 | 0.58 | 0.31 | 0.46 | 0.14 | 0.25 | 0.29 | |
| Mn6 | 1.23 | 1.16 | 1.19 | –1.05 | –0.26 | –0.60 | |
| Mn7 | 1.74 | 1.64 | 1.70 | –2.43 | –0.98 | –1.63 | |
| y (mm) | Mn1 | –0.26 | 0.79 | 0.48 | –1.18 | –0.17 | –0.85 |
| Mn4 | –0.23 | 0.25 | 0.12 | –0.48 | 0.16 | –0.15 | |
| Mn6 | –0.41 | 0.18 | –0.12 | 0.29 | 0.50 | 0.42 | |
| Mn7 | –0.46 | –0.05 | –0.25 | 0.31 | 0.52 | 0.46 | |
| z (mm) | Mn1 | 0.80 | –0.74 | –0.14 | 1.66 | –0.06 | 0.89 |
| Mn4 | 2.22 | 0.76 | 1.43 | 1.97 | 0.82 | 1.53 | |
| Mn6 | 2.95 | 2.84 | 2.97 | 1.37 | 2.00 | 1.82 | |
| Mn7 | 2.67 | 3.89 | 3.43 | 0.34 | 2.46 | 1.56 | |
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