Effective en-masse retraction design with orthodontic mini-implant anchorage: A finite element analysis

Transcription

1 ORIGINAL ARTICLE Effective en-masse retraction design with orthodontic mini-implant anchorage: A finite element analysis Sang-Jin Sung, a Gang-Won Jang, b Youn-Sic Chun, c and Yoon-Shik Moon d Seoul and Kunsan, Korea Introduction: The strategic design of an appliance for correcting a bialveolar protrusion by using orthodontic mini-implant anchorage and sliding mechanics must take into account the position and height of the miniimplant, the height of the anterior retraction hook and compensating curve, and midline vertical traction. In this study, we used finite element analysis to examine effective en-masse retraction with orthodontic miniimplant anchorage and sought to identify a better combination of the above factors. Methods: Base models were constructed from a dental study model. Models with labially and lingually inclined incisors were also constructed. The center of resistance for the 6 anterior teeth in the base model was 9 mm superiorly and 13.5 mm posteriorly from the midpoint of the labial splinting wire. The working archwires were assumed to be in or in stainless steel. The amount of tooth displacement after finite element analysis was magnified 400 times and compared with central and lateral incisor and canine axis graphs. Results and Conclusions: The tooth displacement tendencies were similar in all 3 models. The height of the anterior retraction hook and the placement of the compensating curve had limited effects on the labial crown torque of the central incisors for en-masse retraction. The in stainless steel archwire showed more tipping of teeth compared with the in archwire. For high mini-implant traction and 8-mm anterior retraction hook condition, the retraction force vector was applied above the center of resistance for the 6 anterior teeth, but no bodily retraction of the 6 anterior teeth occurred. For high mini-implant traction, 2-mm anterior retraction hook, and 100-g midline vertical traction condition, the 6 anterior teeth were intruded and tipped slightly labially. (Am J Orthod Dentofacial Orthop 2010;137:648-57) Orthodontic mini-implants (OMIs) are used for various anchorages. 1-5 For treatment of bialveolar protrusion, anchorage preservation during space closure is important for maximum retraction of the anterior teeth after premolar extractions. 6,7 OMIs have been reported to be effective anchorage for en-masse space closure (Fig 1). 3 In some patients, however, retroclined anterior teeth after maximum retraction can cause a poor esthetic outcome (Fig 1, B). a Associate professor, Division of Orthodontics, University of Ulsan College of Medicine, Asan Medical Center, Seoul, Korea. b Assistant professor, School of Mechanical Engineering, Kunsan National University, Kunsan, Korea. c Professor, Division of Orthodontics, Department of Dentistry, School of Medicine, Ewha Womans University, Seoul, Korea. d Professor, Division of Orthodontics, University of Ulsan College of Medicine, Asan Medical Center, Seoul, Korea. The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Reprint requests to: Sang-Jin Sung, Pungnap-2dong, Songpa-gu, Seoul , Korea; , ssjmail@amc.seoul.kr. Submitted, April 2008; revised and accepted, June /$36.00 Copyright Ó 2010 by the American Association of Orthodontists. doi: /j.ajodo The working rectangular wires for en-masse anterior retraction with an OMI and sliding mechanics can be made of in (0.022-in slot) or in (0.018-in slot) stainless steel (SS) The anterior retraction hook (ARH) is placed bilaterally between the lateral incisor and the canine at a height of 2 to 5 mm. The position of the OMI is about 10 mm above the posterior archwire. 3,10 Although we designed the retraction force vector through the center of resistance (CR) for the 6 maxillary anterior teeth, bodily tooth movement might not occur. Because these teeth were not splinted rigidly to form a multi-rooted tooth, a relatively flexible continuous full archwire was used. 6,11 Furthermore, application of an experimental 11,12 or estimated CR 7,13,14 to a patient might be limiting. 15 The reaction of teeth to sliding mechanics can be analyzed by using finite element analysis (FEA). 16 With 3-dimensional (3D) computer models, various conditions can be simulated by varying the simulation parameters. The initial reactions of the teeth, periodontal ligament (PDL), and alveolar bone can be evaluated qualitatively and quantitatively. 648

2 American Journal of Orthodontics and Dentofacial Orthopedics Sung et al 649 Volume 137, Number 5 Fig 1. Various OMI placements: A, low OMI traction; B, high OMI traction. Arrows indicate moments generated by force components. C, Combination of anterior and vertical traction. Major factors affect the accuracy of FEA including anatomic accuracy of the geometry of the finite element (FE) model and uncertainties about material properties and boundary conditions. In most previous studies, FE models were obtained by constructing coarse mapped meshes for manually modeled computer aided design (CAD) geometries, so that the resulting analyses cannot avoid inaccuracies. 16,17 Recently, with the help of 3D laser scans and corresponding CAD-computer aided manufacturing technologies, anatomically correct 3D surface modeling has become popular. 9,15,18 Innovatively increased performance of the central processor unit also enables fast FE modeling with fine tetrahedron solid elements with even better accuracy than time-consuming mapped meshes. In addition, the accuracy of FE models has been improved by the publication of newly calibrated material properties of the PDLs obtained from animal 19 and cadaver 20 studies. In this study, we used FEA for an effective en-masse retraction design with orthodontic mini-implant anchorage. We examined the effect of anterior torque control as a function of the original anterior tooth axis, position, and height of the OMI, height of the ARH, compensating curve (CC), and midline vertical traction, and sought to identify a better combination of these factors. MATERIAL AND METHODS The central incisor (tooth 11), lateral incisor (12), and canine (13) from a dental study model (i21d-400g, Nissin Dental Products, Kyoto, Japan) were scanned and aligned with a True-arch form ( A Company, San Diego, Calif). The axes of these teeth were reproduced from the dental study model (base model). The thickness of the PDL was considered to be uniform (0.25 mm). 16 The alveolar bone crest was constructed to follow the curve of the cementoenamel junction (Fig 2, A). Lingual and labial models were also constructed with the anterior teeth tipped lingually or labially by 10 compared with the base model (Fig 2, B and C). Using Ansys version 10 (Canonsburg, Pa), the archwire was modeled by beam 4 elements with a cross section of in or in SS wire. The ARH (0.05-in SS wire) was set between the lateral incisor bracket and the canine bracket bilaterally. The center hook was set at the midpoint of the archwire (Fig 2, A). At the connected nodes between the archwire and the brackets, translational degrees of freedom in the 2 flexural directions of the archwire were coupled to deform together, and translational degrees of freedom in the axial direction of the archwire were unconstrained. Therefore, free axial rotation movement of the archwire in the brackets was allowed, while friction between the archwire and brackets along the axial direction was ignored. In the system studied, the y-axis was the midsagittal line of the dental arch on the occlusal view, and the z-axis was perpendicular to the y-axis. The x, y, and z coordinates of the archwire midpoint were 0, 49.6, 5 in the base model (Fig 2, A). The total numbers of nodes (or total numbers of elements) comprising the model were (249796) for the base model, (246646) for the labial model, and (249796) for the lingual model. For the discretization of the teeth, the PDL, and the alveolar bone, 4-node tetrahedron element (ANSYS solid45) were used, and material properties 15,19,20 in the models were assumed to be isotropic and homogeneous 9,16 (Table I). The position of the OMI was assumed to be 10 mm (low OMI traction) or 12 mm (high OMI traction) (Fig 2, A). Retraction force vectors of 200 g from the ARH (0, 2, 5, and 8 mm) to low or high OMI traction were resolved into components along the x, y, and z axes and applied to the ARH (Fig 2, A; Table II). For the 2-mm ARH and high OMI traction condition, the OMI between the central incisors was assumed to apply midline vertical traction. The additional intrusion force (50 or 100 g) from the center hook was

3 650 Sung et al American Journal of Orthodontics and Dentofacial Orthopedics May 2010 Fig 2. Three FEM models: A, base model with 4,2, and 2 V-bends placed in the archwire to simulate 3-mm CC. B, Lingual model, tipped 10 lingually compared with the base model. C, Labial model, tipped 10 labially compared with the base model. ARH, anterior retraction hook; CH, center hook; CC, compensating curve; LOT, low OMI traction; HOT, high OMI traction; CR, center of resistance. combined to simulate the effect on labial crown torque (Fig 2, A). To simulate a 3-mm CC, 4,2, and 2 V-bends were placed in the archwire between the distal side of the canine bracket and the mesial side of the second molar tube. The vertical distance from the second molar tube to the end of the curved archwire was 3 mm (Fig 2, A). The 6 anterior teeth of the base model were splinted with in SS wire. The wire post was set at the midpoint of the labial splinting wire, and the wire frame was set at the lingual sides of the 6 anterior teeth. To find the CR of the 6 anterior teeth, a 200-g retraction or intrusion force was applied in a superior or posterior direction from the midpoint of the labial splinting wire at 0.5-mm intervals (Fig 3, A). After simulation, the initial tooth displacement was magnified 400 times. 16 The CR was estimated from the point of force application that resulted in bodily movement of the 6 anterior teeth in the base model. The CR was 9 mm superiorly and 13.5 mm posteriorly from the midpoint of the labial splinting wire (Fig 3, B). For the analysis, ANSYS software was used on the personal-computer platform with a Pentium 4 central processor unit (3.0 GHz, Intel, Santa Clara, Calif). The deformed shapes of the teeth were studied with the tooth axis graph in the y-z plane. The axes of teeth 11, 12, and 13 were constructed by connecting the y and z coordinates of the nodes at the root apex and crown (middle of the incisor edge or canine tip; Fig 3, C and D). The y and z coordinates of each node after displacement of the teeth were calculated by adding the initial displacement of the node that was magnified 20 times to the y and z coordinates of each node before displacement. Table I. Material properties Young s modulus (g/mm 2 ) Poisson s ratio Teeth 2E6 0.3 Periodontal ligament Alveolar bone 2E5 0.3 Stainless steel 2E7 0.3 E, times ten raised to the power, as (scientific) E notation. When a force is applied to a tooth, initial movement is produced, and then orthodontic movement starts. Therefore, it is important to clarify the forces applied to the teeth and the stresses produced in the PDL at initial movement. If the magnitudes of these forces and stresses are not suitable to produce bone remodeling, orthodontic movement might not start. In this study, hydrostatic stresses were calculated to investigate the tensile or compressive status of the PDL: sh 5 (s1 1 s2 1 s3)/3, where s1, s2, and s3 denote the principal stresses. 21,22 RESULTS Low OMI traction with in SS wire in the labial, base, and lingual models was measured. For the system with 0-mm CC and 0-mm ARH, teeth 11, 12, and 13 were tipped lingually by en-masse retraction in all 3 models. As the height of the ARH increased (2 or 5 mm), lingual tipping of teeth 11 and 12 reduced more than with the 0-mm ARH (Fig 4, Table III). The incisor axes, however, did not reach the original axes in the 3 models. For the 3-mm CC, tooth 13 reached its original axis, but there was no effect on tooth 11 in any model.

4 American Journal of Orthodontics and Dentofacial Orthopedics Sung et al 651 Volume 137, Number 5 Table II. The components of 200-g retraction force from ARH to OMI Traction type Low OMI traction High OMI traction ARH height 0 mm 2 mm 5 mm 0 mm 2 mm 5 mm 8 mm Fx (g) Fy (g) Fz (g) Fz/Fy (%) Fx, Amount of force in the direction of X axis of the FE model; Fy, amount of force in the direction of Yaxis of the FE model; Fz, amount of force in the direction of Z axis of the FE model; Fz/Fy, ratio of Fz and Fy. Fig 3. CR for the 6 anterior teeth (base model) and tooth axes. A, Wire splinting of the 6 anterior teeth. B, Deformed model (grey contour) shown with original model (white mesh). The initial displacement (magnified 400 times) showed bodily movement by a given intrusion (white arrow) or retraction (black arrow) force. C and D, The axes of teeth were constructed from the y and z coordinates of the nodes at the root apex and crown and compared with the graph in the y-z plane (D). With low OMI traction with in SS wire, the lingual tipping tendencies in the labial, base, and lingual models were similar to that observed for the in SS archwire. For the 2-mm ARH and 0-mm CC condition, the tooth axes after displacement in the 3 models were compared (Fig 5, Table IV). Because in SS wire is more flexible than in wire, there was more labial tipping of tooth 12 and more distal tipping of tooth 13. A 3-mm CC in the in SS wire did not reduce distal tipping of tooth 13 more than with the in SS wire (Fig 6, Tables III and IV). The effects of high OMI traction in the base model were reduced distal tipping of tooth 13 and lingual tipping of tooth 12 compared with low OMI traction conditions. The axis of tooth 13 was almost independent of ARH. The axes of teeth 11 and 12 did not reach their original axes (Fig 7, Table IV). The force vector can be applied just above the CR for the 6 anterior teeth for the high OMI traction and 8-mm ARH condition. Instead of bodily retraction, tooth 11 intruded with controlled tipping, and tooth 12 intruded, and the root apex moved more lingually. Tooth 13 had uncontrolled tipped, and the crown extruded (Fig 8, A; Table IV). For the 2-mm ARH and 100-g midline vertical traction condition, the force vectors were above the CR for the 6 anterior teeth; all teeth were intruded and slightly tipped labially (Fig 8, A; Table IV). The PDL hydrostatic stress contour plot can show tensile and compressive stress distributions. 21

5 652 Sung et al American Journal of Orthodontics and Dentofacial Orthopedics May 2010 Fig 4. Comparison of the effects of ARH and CC for in SS archwire in the labial, base, and lingual models. Labial, labial model; Base, base model; Lingual, lingual model; ARH, anterior retraction hook; CC, compensating curve; 019, in SS wire; LOT, low orthodontic mini-implant traction. Table III. Comparison of the initial tooth displacements in the y and z axes with in SS wire in the base model Low OMI traction Original coordinates 0-mm ARH 5-mm ARH 5-mm ARH 1 3-mm CC Tooth Axis Crown Apex Crown Apex Crown Apex Crown Apex 11 y E E E E E E-03 z E E E E E E y E E E E E E-02 z E E E E E E y E E E E E E-03 z E E E E E E-03 ARH, Anterior retraction hook; CC, compensating curve; E, times ten raised to the power, as (scientific) E notation. For the high OMI traction and 8-mm condition, the lingual apices of teeth 11 and 12, and the labioapical and linguocervical thirds of tooth 13 were compressed areas. The highest tensile stress was distributed at the labiocervical third of tooth 13 (Fig 8, B-D). As the ARH increased from 2 to 8 mm, the ARH and main archwire joint deformation increased (Fig 8, E and F).

6 American Journal of Orthodontics and Dentofacial Orthopedics Sung et al 653 Volume 137, Number 5 Fig 5. Comparison of the effect of in SS archwire for 2-mm ARH, 0-mm CC, and low OMI traction conditions. Base, base model; Labial, labial model; Lingual, lingual model; 016, in SS. DISCUSSION Premolar extraction and maximum en-masse retraction are preferred for patients with lip protrusion to achieve a harmonious lower profile. 3,6 Without torque control, however, the inclination of the incisor will be reduced, and the amount of retraction will be increased (Fig 1, B). To maintain or control the inclination of the incisor, we can build additional torque in the archwire or use high-torque brackets. Reinforcement of incisor torque, however, might cause incisor extrusion or posterior anchorage loss. 23 The OMI can be an efficient tool, not only in solving the anchorage problem but also in controlling anterior torque. Because OMIs are positioned apically to the crown at the proximal root space, they can generate intrusive force vectors. For en-masse retraction with the low OMI traction and the 2-mm ARH condition, the ARH between the lateral incisor and the canine is the point of force application. The intrusive force component (30-60 g, Table II), therefore, was applied anteriorly to the CR for the 6 anterior teeth and was expected to induce a counterclockwise moment that would counterbalance the distal tipping of the incisors (Fig 1, B). The optimum combination of the position of OMI that can generate more intrusive force and the length of ARH that makes the application of the force through CR is necessary to control incisor inclination. Initially, we needed to investigate the CR for the 6 anterior teeth in the base model to apply the force close to the CR. The CR varies among patients, depending on root length, alveolar bone support, and number of teeth ,15,24 The teeth of our FE model were reproduced from a dental study model and arranged according to the Roth arch form. The initial tooth displacement in this study was between 9.815E-4 mm and 1.309E-1 mm (Tables III and IV). We magnified the amount of tooth displacement 400 times to judge the bodily displacement of the central incisor axis superiorly and posteriorly (Fig 3, B). The location of the CR in the base model varied depending on the material properties of the PDL and alveolar bone. This was approximately 1 to 2 mm in the y-z plane. We used the newly calibrated Young s modulus of the PDL (5 g/mm 2 ). 15,20 Pedersen et al 12 reported that the CR for 6 anterior teeth was located on a line 3 mm behind the distal surface of the canines in a study of human autopsy material. Melsen et al 13 deduced the CR for 6 anterior teeth from other studies. Their estimated CR was halfway between the midpoint of the 4 incisors CR and the canines CR. The CR for our base model was located 13.5 mm posteriorly and 9 mm superiorly from the center of the archwire, similar to the estimate of Melsen et al 13 (Figs 3, B, and 8, A). When the ARH increased, the line of action of the force should be closer to the CR for the 6 anterior teeth. 14,25 The vertical force component generated by the vertical difference between the ARH and the OMI, however, will be decreased. Clinically, deflection of the ARH by a retraction force might cause gingival impingement; hence, the ARH (cantilever beam) of a 0.05-in SS was modeled to minimize the deflection. In sliding mechanics, the dimensions of the main archwire can vary according to the bracket slot size to reduce friction of the posterior wire. Generally, in SS wire is recommended for a in slot and in SS wire for a in slot. In a combination of a main wire and a 0.05-in SS ARH, the bending moments are highest at the joint (supported end) of the relatively flexible main archwire, and the deformation of the main archwire will induce labial tipping of the lateral incisor and distal tipping of the canine (Fig 8, E and F). 26 The high bending moments developed depend more on the length of the ARH and the flexibility of the main archwire (Figs 4, A-C, 6, and8, A). Even though the line of action of the force was applied close to the CR for the 6 anterior teeth with an 8-mm ARH, the central and lateral incisors were not bodily retracted. Figure 8, B-D, shows that the maximum PDL compressive stress

7 654 Sung et al American Journal of Orthodontics and Dentofacial Orthopedics May 2010 Table IV. Comparison of the initial tooth displacements in the y and z axes with in SS wire, high OMI traction, and MVT in the base model Low OMI traction High OMI traction Tooth Axis 5 mm ARH (016*022) 5 mm 8-mm ARH 2-mm ARH g MVT Crown Apex Crown Apex Crown Apex Crown Apex 11 y 8.452E E E E E E E E-02 z 8.112E E E E E E E E y 8.239E E E E E E E E-02 z 2.378E E E E E E E E y 6.814E E E E E E E E-02 z 5.576E E E E E E E E-02 The y and z coordinates of each node after the displacement of the teeth. ARH, anterior retraction hook; CC, compensating curve; MVT, midline vertical traction; 016, in SS wire; E, times ten raised to the power, as (scientific) E notation. Fig 6. Differences between in SS and in SS wires for the 5-mm ARH condition in the base model. 016, in SS; 019, in SS; CC, compensating curve. Fig 7. Comparison of the effects of high OMI traction and ARH for the in SS wire in the base model. ( 0.62 g/mm 2 ) was distributed on the lingual root apices of teeth 11 and 12 from intrusion and retraction. The high PDL tensile stress (0.67 g/mm 2 ) was on the labiocervical third of tooth 13 because of extrusion and lingual tipping. The forces generated by the reverse curve of Spee placed in the mandibular achwire transmitted both intrusive and torquing forces to the roots of the incisors and molars, encouraging lingual movement of the incisor roots and mesial movement of the molar roots. 16,27 To overcome the limitations of the ARH, CCs can be placed in the maxillary archwire to encourage labial tipping and intrusion of the incisors. However, the binding between the bracket slot and curved archwire might restrict sliding in the posterior slot. Hence, we assumed a clinically applicable and minimum CC (depth of the curve from the distal aspect of the canine to the distal aspect of the second molar was about 0.5 mm) to reduce friction in the in and in SS archwires. In a previous FEA study, the deactivation force from the curved archwire was analyzed first. 16 The reaction forces that corresponded to the mesial and distal nodes of each bracket were then substituted for CC simulation. However, this approach might cause a large error if the

8 American Journal of Orthodontics and Dentofacial Orthopedics Sung et al 655 Volume 137, Number 5 Fig 8. Comparison of the effects of various force applications above the CR with the in SS wire: A, comparison of tooth displacements of 8 mm for the ARH or midline vertical traction condition; B-D, contour plots of hydrostatic stress (g/mm 2 ) in condition of 8-mm ARH and high OMI traction; comparison of archwire deformation (magnified 20 times) and von Mises stress (g/mm 2 ) distribution between E, 2-mm ARH, and F, 8-mm ARH and high OMI traction. ARH, anterior retraction hook; CC, compensating curve; MVT, midline vertical traction; 019, in SS archwire;, CR for the 6 anterior teeth in the base model; red arrow, 200-g force vector from 8-mm ARH to high OMI traction; blue arrow, resultant force vector from 100-g force of MVT and 200-g force of 2-mm ARH to high OMI traction. archwire is curved much to the out-of-plane direction because the accurate nodal positions of the archwire after connecting brackets cannot be known in advance. In this study, to reduce such errors, we placed small V-bends in the archwire between the brackets to simulate the CC effect. Compared with the previous study, the CC effect on the dentition was similar. 9 The 3-mm CC encouraged distal tipping of the molar and mesial tipping of the canine, and counteracted the distal tipping of the canine caused by side effects of the ARH. No additional labial tipping of the incisors occurred. To produce a more vertical intrusion force component than low OMI traction, the OMI can be placed at the mesial and apical sides of the second premolar (high OMI traction, Figs 1 and 7). In high OMI traction, as ARH increased, the force and the z-y ratios were decreased which was also observed in low OMI traction. For the same ARH height, however, the average Fz/Fy ratio was increased by 218%, and a 5- mm ARH produced the highest ratio (239.5%) (Table II). Although the line of action of the force from 5-mm ARH to high OMI traction passed under the CR for the 6 anterior teeth, lingual tipping of the incisors and distal tipping of the canine (caused by increased ARH) were reduced (Fig 7). Labial tipping of the central incisors beyond their original axes, however, did not occur in the high OMI traction condition. In the 8-mm ARH and high OMI traction condition, the line of action of the force passed above the CR for the 6 anterior teeth without decreasing the Fz and the Fz/Fy ratios compared with the 5-mm ARH and low OMI traction condition (Table II). The central incisor, however, remained in a lingual position with respect to the original axis, and there was less tipping of the lateral incisor and the canine (Figs 8). The design of en-masse retraction appliances for the bodily retraction of 6 anterior teeth so that the line of action of the force passes through the CR is, therefore, desirable. The design should include rigid splinting of the 6 anterior teeth to prevent deformation between the ARH and the main archwire 11,15 and a bilaterally connected rigid palatal lever arm that enables force application around the CR without deflection of the ARH and gingival impingement. 14,25 Placing an OMI between the incisors helps to apply additional vertical intrusion forces, and we can expect a more direct effect on the central incisor (Fig 1, C). 1,5 In the 2-mm ARH, high OMI traction, and midline vertical traction conditions (100 g force

9 656 Sung et al American Journal of Orthodontics and Dentofacial Orthopedics May 2010 applied at the center hook) in the base model, the resultant retraction force vectors passed above the CR for the 6 anterior teeth and were more vertically directed than under the 8-mm ARH and high OMI traction condition (Fig 8, A). With 100 g of midline vertical traction, the 6 anterior teeth tended to tip labially and intrude. Labial tipping of the central incisor occurred; this was not observed under the ARH and CC conditions. An additional OMI to apply midline vertical traction might place a burden on the patient with regard to more surgical procedures, but it is effective in inducing labial tipping of the incisors and intrusion of the 6 anterior teeth. It could, therefore, be the treatment of choice for patients with deep bite and those who need maximum en-masse retraction. These results suggest that en-masse bodily movement of anterior teeth seems to be difficult with conventional sliding mechanics by using OMI. However, these results are right only for the initial movement, which is produced by elastic deformation of the PDL. This is a limitation of this study. Long-term orthodontic movement might not be the same as the initial movement. Especially when many teeth are connected with an archwire, the force system varies with tooth movement. CONCLUSIONS 1. For the 0-mm CC and ARH condition, the central and lateral incisors and the canine were tipped lingually in all 3 models. As the height of the ARH increased, lingual tipping of the central and lateral incisors was reduced. With the 3-mm CC, the canine axis reached its original axis, but there was no effect on the central incisor axis in any model. 2. In the system with in SS wire and 5-mm ARH, labial tipping of the lateral incisor and distal tipping of the canine were worse compared with the system with the in SS wire. 3. For the high OMI traction and 8-mm ARH condition, the force vector was applied just above the CR for the 6 anterior teeth, but no bodily retraction occurred. 4. For the 2-mm ARH and 100-g midline vertical traction condition, the central and lateral incisors and the canine were intruded and slightly tipped labially. REFERENCES 1. Creekmore TD, Eklund MK. The possibility of skeletal anchorage. J Clin Orthod 1983;17: Umemori M, Sugawara J, Mitani H, Nagasaka H, Kawamura H. Skeletal anchorage system for open-bite correction. Am J Orthod Dentofacial Orthop 1999;115: Park HS, Bae SM, Kyung HM, Sung JH. Micro-implant anchorage for treatment of skeletal Class I bialveolar protrusion. J Clin Orthod 2001;35: Park YC, Lee SY, Kim DH, Jee SH. Intrusion of posterior teeth using mini-screw implants. Am J Orthod Dentofacial Orthop 2003;123: Kim TW, Kim H, Lee SJ. Correction of deep overbite and gummy smile by using a mini-implant with a segmented wire in a growing Class II Division 2 patient. Am J Orthod Dentofacial Orthop 2006; 130: Burstone CJ. The segmented arch approach to space closure. Am J Orthod 1982;82: Guray E, Orhan M. En masse retraction of maxillary anterior teeth with anterior headgear. Am J Orthod Dentofacial Orthop 1997; 112: Bennett JP, McLaughlin RP. Orthodontic treatment mechanics and the preadjusted appliance. Alyesbury, United Kingdom: Wolfe Publishing; p Jeong HS, Sung SJ, Moon YS, Cho YS, Lim SM. Factors influencing the axes of anterior teeth during SWA en masse sliding retraction with orthodontic mini-implant anchorage: a finite element study. Korean J Orthod 2006;36: Chung KR, Nelson G, Kim SH, Kook YA. Severe bidentoalveolar protrusion treated with orthodontic microimplant-dependent enmasse retraction. Am J Orthod Dentofacial Orthop 2007;132: Dermaut LR, Vanden Bulcke MM. Evaluation of intrusive mechanics of the type "segmented arch" on a macerated human skull using the laser reflection technique and holographic interferometry. Am J Orthod 1986;89: Pedersen E, Isidor F, Gjessing P, Andersen K. Location of centres of resistance for maxillary anterior teeth measured on human autopsy material. Eur J Orthod 1991;13: Melsen B, Fotis V, Burstone CJ. Vertical force considerations in differential space closure. J Clin Orthod 1990; 24: Hong RK, Heo JM, Ha YK. Lever-arm and mini-implant system for anterior torque control during retraction in lingual orthodontic treatment. Angle Orthod 2005;75: Reimann S, Keilig L, Jager A, Bourauel C. Biomechanical finiteelement investigation of the position of the centre of resistance of the upper incisors. Eur J Orthod 2007;29: Sung SJ, Baik HS, Moon YS, Yu HS, Cho YS. A comparative evaluation of different compensating curves in the lingual and labial techniques using 3D FEM. Am J Orthod Dentofacial Orthop 2003;123: Yu HS, Baik HS, Sung SJ, Kim KD, Cho YS. Three-dimensional finite-element analysis of maxillary protraction with and without rapid palatal expansion. Eur J Orthod 2007;29: Jeong SJ, Kim WS, Sung SJ. Numerical investigation on the flow characteristics and aerodynamic force of the upper airway of patient with obstructive sleep apnea using computational fluid dynamics. Med Eng Phys 2007;29: Ziegler A, Keilig L, Kawarizadeh A, Jager A, Bourauel C. Numerical simulation of the biomechanical behaviour of multi-rooted teeth. Eur J Orthod 2005;27: Poppe M, Bourauel C, Jager A. Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth a study of autopsy

10 American Journal of Orthodontics and Dentofacial Orthopedics Sung et al 657 Volume 137, Number 5 specimens and their conversion into finite element models. J Orofac Orthop 2002;63: Dorow C, Sander FG. Development of a model for the simulation of orthodontic load on lower first premolars using the finite element method. J Orofac Orthop 2005;66: Hohmann A, Wolfram U, Geiger M, Boryor A, Sander C, Faltin R, et al. Periodontal ligament hydrostatic stress with areas of root resorption after application of a continuous torque moment. Angle Orthod 2007;77: Mulligan TF. Common sense mechanics. J Clin Orthod 1980;14: contd. 24. Shroff B, Lindauer SJ, Burstone CJ, Leiss JB. Segmented approach to simultaneous intrusion and space closure: biomechanics of the three-piece base arch appliance. Am J Orthod Dentofacial Orthop 1995;107: Park YC, Choy K, Lee JS, Kim TK. Lever-arm mechanics in lingual orthodontics. J Clin Orthod 2000;34: Thurow RC. Edgewise orthodontics. St Louis: C.V. Mosby; p Clifford PM, Orr JF, Burden DJ. The effects of increasing the reverse curve of Spee in a lower archwire examined using a dynamic photo-elastic gelatine model. Eur J Orthod 1999;21: