Material and methods

To elucidate tooth movement during the protraction of the whole maxillary dentition, the finite element method (FEM) was used as in previous articles. ^, Figure 1 shows the FEM model. Assuming bilateral symmetry of the maxillary dentition, it modeled only the right side. Three-dimensional (3D) models of teeth were made on the basis of a dental study model (i21D-400C; Nissin Dental Products, Kyoto, Japan). Each tooth was divided into shell elements and defined as a rigid body. Contact elements were overlaid on adjoining surfaces of the crown to prevent penetration of each other.

Finite element model for simulating mesialization of the maxillary dentition.

The periodontal ligament (PDL) was assumed to be a linear elastic film of 0.2 mm thickness. The Young’s modulus and Poisson’s ratio of the PDL were 0.2 MPa and 0.4, respectively. Using these elastic moduli, buccolingual and axial mobilities of a human maxillary first premolar were reproduced by the FEM.

The alveolar bone was assumed to be a rigid body because its value for Young’s modulus is much larger than that of the PDL. On the basis of this assumption, the outer boundary of the PDL was considered to be a rigid surface, too, and was constrained in the current position when we calculated the initial tooth movement. Hence, the alveolar bone was unnecessary for this calculation, so it was excluded from the FEM model.

The archwire was made of 0.019 × 0.022-in stainless-steel (SS) wire. The values for Young’s modulus and Poisson’s ratio were E = 200 GPa and ν = 0.3, respectively. The archwire was divided into 3D solid elements. Symmetrical boundary conditions were applied at the median end of the archwire. Two different sizes of transpalatal arch (TPA) (0.06-in and 0.036-in SS round wire) were used to compare the effects of wire size on tooth movement. They were divided into beam elements and fixed on the first and/or second molars. Brackets with 0.022 × 0.028-in slots were fixed on the crowns. The bracket width was 4 mm for the molars and 3 mm for the other teeth.

Figure 2 shows the geometric relationship of the archwire and bracket slot. There was a uniform clearance gap in the initial positions ( Fig 2 , A ), and the archwire was in contact with the bracket slot after rotating it relatively 7.2° ( Fig 2 , B ).

Initial ( A ) and contact ( B ) positions of the archwire placed into the bracket. The archwire can rotate by 7.2° within the clearance gap.

The brackets were divided into shell elements and were defined as rigid bodies. Contact elements were overlaid on the archwire surfaces and bracket slots which allowed them to slide with a frictional coefficient of 0.15. A force of 3 N was applied to the second molar bracket with interarch and intraarch elastomers, and its direction was varied on the sagittal plane by FAs of −30°, −15°, 0°, 15°, and 30° to the occlusal plane. Negative values of FA mean that the line of action of the force is in an anteroinferior direction along the occlusal plane, whereas positive values mean the forces are in the opposite direction.

The center of resistance (CR) of the whole maxillary dentition was determined to be a specific condition in which the whole dentition moved as 1 rigid body. For this purpose, a rigid archwire having an extremely large Young’s modulus was used.

Three-dimensional displacements were measured at the incisal edge of the central incisor (CIE), the mesiobuccal cusp of the first molar (MBC6), and the distobuccal cusp of the second molar (DBC7). Using vertical displacements of the CIE and DBC7, we calculated the rotational angle of the occlusal plane.

With orthodontic tooth movement, the alveolar socket is moved by the remodeling of the alveolar bone. This process was simulated by FEM. It was assumed that the alveolar socket moved by elastic deformation of the PDL in the same direction and by the same amount as the initial movement of the tooth.

The movement of the teeth and alveolar socket, namely the outer surface of the PDL, were rigid movements. On the basis of this assumption, a tooth-supported by the PDL can be replaced with a single substructure element, which has 2 nodes corresponding to the tooth and alveolar socket. By using these nodes, the rigid movement and positioning of the tooth and alveolar socket can be controlled.

The simulation procedure was similar to that reported in previous articles, ^{, ,} based on the following 2 steps. First, the alveolar sockets were constrained to their current positions, and the initial movements of the teeth were calculated. Then, the new positions of the alveolar sockets were updated by adding the initial movement of the teeth. By repeating these 2 steps, the alveolar sockets were moved by accumulating the initial movements of the teeth. The force system acting on the teeth was updated by each repetition. The number of repetitions, n, corresponded to the time elapsed after force application.

Using FEM software, Ansys (version 19.1; Ansys, Inc, Canonsburg, Pa), the repeated calculations for simulating the tooth movement were executed automatically using a programing language, Ansys APDL.

Results

Figure 3 shows the CR of the whole maxillary dentition, which was determined using a rigid archwire. At an FA of 28°, the line of action of the force passed through the CR.

Location of the CR of the whole dentition as determined using a rigid archwire. At a force angulation of 28°, the line of action of the force passes through the CR.

Figure 4 shows the movement patterns at the outcome of the repeated calculations, N = 400, in which tooth movement patterns were easily understandable. The distribution of the mean stress or the hydrostatic stress in the PDL is depicted on the root with colored contours. Red and blue indicate compressive and tensile stresses, respectively. Initial tooth positions are drawn in a pale color. Tipping angles of the central incisor and second molar are written in Figure 4 .

Tooth movement patterns at N = 400 for 5 FAs to the occlusal plane: A, −30°; B, −15°; C, 0°; D, 15°; E, 30°.

In the x-axis, all measurement points moved anteriorly and showed a decrease from an FA of −30° to 30°, except for the mesial movement of MBC6 and DBC7, which was greater at an FA of −15° than at an FA of −30°. In the y-axis, CIE showed a tiny lateral movement, and MBC6 and DBC7 moved from lingually to buccally over an FA of −30° to 30°. In the z-axis, CIE showed superior movement regardless of the FA, whereas the amount decreased as the FA approached 30°, and MBC6 and DBC7 moved from inferiorly to superiorly with an FA of −30° to 30°. Regardless of the FA, the central incisor showed labial tipping, and the first molar (FM) and second molar (SM) showed mesial tipping, and they showed a decrease as the FA approached 30°. The FM and SM tipped from lingually to buccally from an FA of −30° to 30°. Regardless of the FA, the FM and SM showed mesiolingual rotation, and the rotation tended to increase as the FA approached 30°. The occlusal plane rotated counterclockwise at FAs of −30°, −15°, and 0°, whereas it rotated clockwise at FAs of 15° and 30° ( Fig 4 ; Tables I and II ).

Table I

Three-dimensional displacements of the maxillary teeth

		Force angulation					TPA (stainless-steel wire, inch)
							First molar		Second molar		Both
Displacement		0.019 × 0.025-in stainless-steel archwire					0.036	0.06	0.036	0.06	0.036	0.06
	Measurement Point	−30°	−15°	0°	15°	30°	30°	30°	30°	30°	30°	30°
x (mm)	CIE	−2.55	−2.38	−2.03	−1.49	−0.76	−0.86	−1.08	−0.91	−1.01	−1.01	−0.95
	MBC6	−2.04	−2.11	−1.98	−1.68	−1.25	−1.13	−0.97	−1.26	−1.20	−1.25	−1.14
	DBC7	−2.59	−2.71	−2.69	−2.53	−2.21	−2.06	−1.73	−1.70	−1.39	−1.54	−1.28
y (mm)	CIE	0.07	0.09	0.12	0.14	0.14	0.13	0.11	0.14	0.13	0.13	0.10
	MBC6	−0.95	−0.22	0.56	1.35	2.11	1.48	0.47	1.20	0.41	0.90	0.11
	DBC7	−0.70	0.50	1.70	2.89	3.96	3.15	1.65	1.91	0.34	1.49	0.27
z (mm)	CIE	1.89	1.74	1.40	0.95	0.42	0.50	0.69	0.62	0.76	0.70	0.76
	MBC6	−0.30	0.09	0.56	1.07	1.58	1.44	1.22	1.26	1.06	1.16	1.06
	DBC7	−2.76	−1.95	−0.97	0.23	1.59	1.18	0.69	0.96	0.58	0.85	0.50

Only gold members can continue reading. Log In or Register to continue

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)

Related

Related posts:

1. Evaluations of the facial attractiveness of young women with severe maxillary anterior crowding by orthodontists and laypeople with and without orthodontic treatment experience in Japan
2. Microimplant assisted rapid palatal expansion vs surgically assisted rapid palatal expansion for maxillary transverse discrepancy treatment
3. Finite element analysis of C-expanders with different vertical vectors of anchor screws
4. Nano-Bio Fusion Gingival Gel in the management of fixed orthodontic treatment-induced gingivitis: An empirical study
5. Individual participant data in meta-analysis
6. Treacher Collins syndrome: Orthodontic treatment with mandibular distraction osteogenesis and orthognathic surgery

Stay updated, free dental videos. Join our Telegram channel

Join