Fig 1.
Three-dimensional geometric model.
(A) Lateral view of the mandible; (B) Frontal view of the mandible; (C) Diagonal view of the mandible; (D) Occlusal view of the mandible; (E, F) Frontal view of the mandible, illustrating the curve of Spee and the anatomical structure of the teeth, roots, and periodontal ligament (highlighted in blue); (G, H) Lateral and occlusal views of the final mandibular model with attachments and the aligner (light blue cover over the teeth), respectively; (I) Lateral and occlusal views of the finite element mesh model of the teeth with attachments; (J) Lateral and occlusal views of the finite element mesh model of the complete system, including teeth, attachments, periodontal ligament, bone, and aligner.
Fig 2.
Boundary conditions and symmetry constraints applied to the finite element model.
The light blue cover over the teeth represents the aligner. (A) The purple area represents the symmetry plane used in the simulation. (B) The orange arrows indicate the applied constraints: the model was restricted in the vertical direction at the superior region of the condyle and the inferior region of the mandible, and in the horizontal direction at the posterior part of the mandible. (C) Tooth displacement under three different intrusion designs. The yellow arrows represent the prescribed displacement applied to the aligner surface. S1: Simultaneous intrusion of canines and incisors. S2: Intrusion of only the central and lateral incisors. S3: Intrusion exclusively of the canines.
Table 1.
Properties of linear materials.
Table 2.
Hyper-elastic–viscoelastic properties of the periodontal ligament [17].
Table 3.
Summary of intrusion configurations simulated in the study.
Fig 3.
Different vertical displacement patterns (mm) observed in S1, S2, and S3 during intrusion with clear aligner therapy.
(A) Displacement of the lower anterior and anchorage teeth when canines and incisors are intruded simultaneously. (B) Displacement of the lower anterior and anchorage teeth when only the incisors are intruded. (C) Displacement of the lower anterior and anchorage teeth when only the canines are intruded. In all cases, the first row represents PDL displacement, the second row represents alveolar bone displacement, and the third row represents tooth displacement in occlusal, lingual, and frontal views, respectively. The right column illustrates the vertical displacement of the attachments and aligner.
Fig 4.
Von Mises equivalent strain distribution (mm/mm) under S1, S2, and S3 conditions.
(A, B) Graphical comparison of von Mises equivalent strain values: (A) in the PDL of the lower teeth across S1, S2, and S3; (B) in the lower teeth across S1, S2, and S3 conditions. (C-H) Color-mapped visual representations of equivalent strain distribution: (C, D) under S1 in the PDL and teeth, respectively; (E, F) under S2 in the PDL and teeth, respectively; (G, H) under S3 in the PDL and teeth, respectively. All images (C-H) include buccal, frontal, and lingual views.
Fig 5.
Minimum principal stress (MPa) under S1, S2, and S3 conditions.
(A, B) Graphical comparison of minimum principal stress values: (A) in the PDL of the lower teeth across S1, S2, and S3; (B) in the lower teeth across S1, S2, and S3 conditions. (C-H) Color-mapped visual representations of minimum principal stress distribution: (C, D) under S1 in the PDL and teeth, respectively; (E, F) under S2 in the PDL and teeth, respectively; (G, H) under S3 in the PDL and teeth, respectively. All images (C-H) include buccal, frontal, and lingual views.
Fig 6.
Maximum principal stress (MPa) under S1, S2, and S3 conditions.
(A, B) Graphical comparison of maximum principal stress values: (A) in the PDL of the lower teeth across S1, S2, and S3; (B) in the lower teeth across S1, S2, and S3 conditions. (C-H) Color-mapped visual representations of maximum principal stress distribution: (C, D) under S1 in the PDL and teeth, respectively; (E, F) under S2 in the PDL and teeth, respectively; (G, H) under S3 in the PDL and teeth, respectively. All images (C-H) include buccal, frontal, and lingual views.
Fig 7.
Total movement trend (mm) of the lower teeth under S1, S2, and S3 conditions.
(A) Lateral and frontal views of the entire lower arch, with displacement vectors indicating the movement trend of the teeth when both incisors and canines are intruded together (S1 condition). Additionally, a lateral view of the posterior teeth segment illustrating the anchorage, alongside individual views of the canine, lateral incisor, and central incisor showing their specific displacement vectors. (B) Lateral and frontal views of the entire lower arch, with displacement vectors indicating the movement trend of the teeth when only the incisors are intruded (S2 condition). A lateral view of the posterior teeth segment illustrating the anchorage, alongside individual views of the canine, lateral incisor, and central incisor with their respective displacement vectors. (C) Lateral and frontal views of the entire lower arch, with displacement vectors indicating the movement trend of the teeth when only the canines are intruded (S3 condition). A lateral view of the posterior teeth segment illustrating the anchorage, alongside individual views of the canine, lateral incisor, and central incisor showing their specific displacement vectors.