To analyze patterns of individual tooth movement

ORIGINAL ARTICLE Three-dimensional analysis of the tooth movement and arch dimension changes in Class I malocclusions treated with first premolar extractions: A guideline for virtual treatment planning Min-Young Cho, a Jeong-Ho Choi, b Seung-Pyo Lee, c and Seung-Hak Baek d Seoul, South Korea Introduction: Our objective was to analyze patterns of tooth movement and changes of arch dimension by superimposing 3-dimensional (3D) virtual models. Methods: The sample consisted of 24 Korean adults with Class I malocclusion and minimal crowding, treated by first premolar extractions, sliding mechanics (0.022-in MBT brackets [3M Unitek, Monrovia, Calif] with 0.019 3 0.025-in stainless steel wire) and moderate anchorage. The 3D virtual maxillary casts at pretreatment and posttreatment were superimposed with the best-fit method. Linear and angular variables were measured with 3Txer program (Orapix, Seoul, Korea). Wilcoxon signed rank and Mann-Whitney tests were used for statistical analysis. Results: There was no significant difference in the individual tooth movement between the right and left sides (P.0.05). For the movement of each tooth, the maxillary central incisors (U1), lateral incisors (U2), and canines (U3) were significantly inclined lingually, extruded, and moved posteriorly and laterally. The maxillary second premolar (U5), first molar (U6), and second molar (U7) had significant mesial inward rotation, anterior movement, and contracted toward the midsagittal plane. The ratio of anteroposterior movement between the maxillary anterior and posterior teeth was 5:1. The amounts of contraction in U5, U6, and U7 were 1.4, 1.3, and 1.2 mm, respectively. When the amount of change between the adjacent teeth were compared, the linguoversion in U1 was significantly greater than that of U2. U3 and U5 showed significant opposite movements in all variables. There were differences only in angulation and vertical displacement between U6 and U7. Conclusions: Superimposition of 3D virtual models could be a guideline for precise virtual treatment planning. (Am J Orthod Dentofacial Orthop 2010;138:747-57) To analyze patterns of individual tooth movement and changes of arch dimensions in the 3-dimensional (3D) spaces is a prerequisite to making a practical treatment plan. Recently, 3D virtual model analysis has been applied to measure tooth size, and width and length of the dental arch, and to analyze tooth movement by mathematical superimposition of pretreatment and posttreatment models. 1-4 From the School of Dentistry, Seoul National University, Seoul, South Korea. a Graduate student. b Clinical lecturer, Department of Orthodontics; Smilefuture Orthodontic Clinic, Kangnam-Ku, Seoul, South Korea. c Assistant professor, Department of Oral Anatomy, Dental Research Institute. d Associate professor, Department of Orthodontics, Dental Research Institute. The authors report no commercial, proprietary, or financial interest in the products or companies described in this article. Reprint requests to: Seung-Hak Baek, Department of Orthodontics, School of Dentistry, Dental Research Institute, Seoul National University, Yeonkun-dong #28, Jongro-ku, Seoul, South Korea 110-768; e-mail, drwhite@unitel.co.kr. Submitted, March 2008; revised and accepted, November 2008. 0889-5406/$36.00 Copyright Ó 2010 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2008.11.033 Three-dimensional scanning is a type of reverse engineering, the original purposes of which were to reduce the period of development and cost, to establish standardization, and to increase the accuracy of products. Now it is applied in the medical engineering area. The basic concepts of the 3D dental scanner (Orapix, Seoul, Korea; accuracy level: 6 0.02 mm/10 mm; resolution: 1024 3 768 pixels) are to shoot the laser light to the target material surface, detect reflection, and calculate its 3D coordinate system by using the trigonometric function. According to DeLong et al, 5 the accuracy of measurement of 10 stone casts of a dental standard with known dimensions using 3D computer models was almost equal to that of a conventional contact digitizer. The median palatal raphe, 6 the palatal rugae, 7-12 and the hard palate around the maxillary right and left first molars 4 have been suggested as reference landmarks and areas for superimposition of the maxillary models. Cha et al 4 reported no significant difference in the horizontal and vertical movements of the maxillary central 747

748 Cho et al American Journal of Orthodontics and Dentofacial Orthopedics December 2010 Fig 1. Superimposition of the 3D virtual models between T0 (gray) and T1 (green). Color-coding system for the degree of surface matching: blue, perfect fit; red, insufficient fit (mismatch level, 1.65 mm). incisor and first molar between superimpositions of the lateral cephalogram and superimpositions of 3D virtual models. However, a few 3D studies have analyzed the angular and linear changes of individual tooth positions in terms of the facial axis (FA) point, 13 which was used as the reference point for bracket bonding. Moreover, some 3D virtual model studies about tooth movement seem to be insufficient to assess 3D tooth movement. Chong et al 2 evaluated the 3D virtual models for only rotational movements of the maxillary posterior teeth in patients whose maxillary first premolars were extracted. Cha et al 4 measured only changes of the maxillary central incisor and first molar in the 3D virtual models, not in the whole dentition. Therefore, the purposes of this study were to analyze patterns of individual tooth movement and changes of the arch dimensions in patients having first premolar extractions by using superimposition of 3D virtual models obtained from pretreatment (T0) and posttreatment (T1) and to present a guideline for precise virtual treatment planning. MATERIAL AND METHODS The sample consisted of 24 young Korean adults (4 men, 20 women; average age, 24 years 8 months 6 4 years 11 months; SNA, 83.29 6 3.98 ; ANB, 3.10 6 1.52 ; U1-SN, 115.22 6 5.47 ; FMA, 26.48 6 2.71 ; lower lip to E-line, 3.80 6 2.02 mm; crowding in the maxillary arch, 2.55 6 1.08 mm; and average treatment period, 21.87 6 4.14 months). Since the patterns of orthodontic tooth movement and the changes in arch dimensions could be various according to the conditions of the malocclusion and the diverse treatment procedures, the sample was Fig 2. The occlusal plane on the 3D virtual model was established by using the midpoint of the maxillary right central incisor edge and the mesiobuccal cusp tip of the maxillary right and left first molars. The angular difference in the occlusal plane between T0 and T1 was measured. limited according to age, skeletal pattern, soft-tissue profile, dentition, and treatment methods: (1) young adults over 18 years old; (2) Class I malocclusion, normodivergent pattern, less than 4 mm of crowding in each arch, and ovoid and symmetric arch form; (3) lip protrusion (lower lip to Ricketts esthetic line.2 mm); (4) treatment including extraction of maxillary and mandibular first premolars with sliding mechanics (0.022-in slot, MBT brackets, 3M Unitek, Monrovia, Calif) and 0.019 3 0.025-in stainless steel wire, maxillary and mandibular second molars banded or bonded in the fixed treatment, and no headgear, transpalatal arches, or orthodontic miniscrews (temporary anchorage devices) used; (5) finished with Class I canine and molar relationships with normal overbite and overjet (.2 and\4 mm, respectively); and (6) after the brackets were removed carefully with debonding pliers, the remnant resin was removed by using an 8-bladed tungsten carbide bur (Fressima, FIT, Turin, Italy), an ideal cutting tool for ductile substrates such as resin materials, with little effect on the enamel structure. 14 The maxillary casts at T0 and T1 were scanned by using the 3D dental scanner and virtually constructed with the 3Txer program (Orapix). In the anterior area of the hard palate, the palatal rugae has been used as a stable landmark. 7-11 Especially, the medial and lateral points of the third palatal rugae seem to be fairly stable for the estimation of changes in spite of vertical growth. 12 In the posterior area of the hard palate, the midpalate area between the maxillary right and left first and second molars seems to

American Journal of Orthodontics and Dentofacial Orthopedics Cho et al 749 Volume 138, Number 6 Fig 3. The angle between the Frankfort horizontal (FH) plane and the occlusal plane on the lateral cephalograms was established by using the maxillary central incisor edge and the mesiobuccal cusp tip of the maxillary first molar (dotted line, parallel displacement of Frankfort horizontal plane at T0). The angular difference between T0 (dotted line) and T1 (solid line) stages was measured. show the least change during treatment, and deformation of the palatal mucosa in this area during impression taking could be minimal because of unmovable soft tissues. Therefore, we chose these areas as the stable landmarks for superimposition of the 3D virtual maxillary models at T0 and T1. Three-dimensional surface-to-surface matching (best-fit method, Fig 1) was used with a mean least squares technique by using polygons created by point data and a function of the Rapidform 2006 (INUS Technology, Seoul, Korea). 2,4 To prevent errors in landmark positioning, superimposition of the 3D virtual maxillary models was confirmed by superimposition of the lateral cephalometric radiographs as follows. 1. After the occlusal planes of the 3D virtual models at T0 and T1 were established, the angular differences between T0 and T1 were measured (Fig 2). 2. After the angles between the Frankfort horizontal plane and the occlusal plane of the lateral cephalograms at T0 and T1 were measured, the differences were evaluated (Fig 3). 3. If the difference between the 3D virtual models and the lateral cephalograms was greater than 5, superimposition of the 3D virtual models was adjusted according to the amount of occlusal plane change in the lateral cephalograms. Fig 4. Definitions of the reference planes and origin: horizontal plane, to which the high-fit region in the midpalatal area was extended; coronal plane, which connects the FA points between the upper right (#17) and left second molars (#27) at T0 and is perpendicular to the horizontal plane; midsagittal plane, which passes through a midpoint between the FA points of #17 and #27 and is perpendicular to the horizontal and coronal planes; the origin was set at the intersection of the 3 reference planes. Fig 5. Definitions of the landmarks and reference planes: 1, gingival point: the lowest and most concave point in the gingival margin; 2, occlusal point: the midpoint of the edge of the incisors, the cusp tip of the canine and the second premolar, and the most concave point between the mesiobuccal and distobuccal cusps of the molars; 3, mesial point: the most mesial point created by the intersection between a parallel line with the Andrews plane and the facial axis of the clinical crown (FACC); 4, distal point: the most distal point created by the intersection between a parallel line with the FACC and the Andrews plane; the FA point (5) and the Andrews plane (6) bisect the clinical crown into gingival and occlusal parts in the FACC (7). 14 Definitions of the reference planes and landmarks are given in Figures 4 and 5. Since the occlusal third including the incisal edge or cusp tip showed greater

750 Cho et al American Journal of Orthodontics and Dentofacial Orthopedics December 2010 Fig 6. A, Example of the coordinate system established at FA, the origin point. X-axis, horizontal axis; y-axis, vertical axis, perpendicular to x-axis; z-axis, sagittal axis, perpendicular to the x-axis and the y-axis. B, Inclination ( ): the labiolingual or buccolingual slope of the clinical crown to the occlusal plane. The difference between T0 and T1 (T0 T1): positive means labioversion or buccoversion; negative means linguoversion. C, angulation ( ): the mesiodistal slope of the clinical crown to the occlusal plane. T0 T1: positive means distal tipping; negative means mesial tipping. D, Rotation ( ): the angle made with the x-axis and the midsagittal plane at the occlusal view. T0 T1: positive means mesial inward rotation; negative means distal inward rotation. anatomic variations than the gingival third and could be changed during treatment because of attrition or fracture, it might not be a proper reference point to measure tooth movement. 15 However, the FA point is easily recognized and used as a relatively stable guide for bracket positioning. In addition, the incisal edge and cusp tip can have greater changes due to the longer distance of the center of rotation than the FA point. Angular and linear variables of the maxillary dentition (central incisor, U1; lateral incisor, U2; canine, U3; second premolar, U5; first molar, U6; and second molar, U7) were measured with the 3Txer program. The coordinate system for angular measurement of each tooth and the definitions of inclination, angulation, and rotation are described in Figure 6. Reference lines and landmarks for the linear measurements and the definitions of vertical, anteroposterior, and lateral displacement are described in Figure 7. The reference points were digitized 3 times with a 2-week interval by 1 examiner (M.Y.C.). Intraclass correlation coefficients (ICC) for reference point identification were computed to assess intraexaminer reliability (repeatability). Since the assessment of the intraexaminer reliability of reference point identification showed excellent ICC values (Table I), the first digitized data were used. Because there was no significant difference in the individual tooth movements between the right and left sides between T0 and T1 (P.0.05, Table II), the data from the 2 sides were merged. Arch dimensions were measured with the 3Txer program. The definitions of arch width and depth are described in Figure 8. To compare the amounts of change in each tooth between T0 and T1, the movement patterns in the adjacent teeth (U1 vs U2, U3 vs U5, and U6 vs U7) and the arch dimensions, the Wilcoxon signed rank and Mann- Whitney tests were used. RESULTS We compared the changes in each tooth between T0 and T1. U1 and U2 showed a similar tendency of change as follows: significantly inclined lingually (12.3, P \0.001; 5.8, P \0.001, Table III), rotated distally (5.1, P \0.001; 6.7, P \0.001, Table III), extruded (2.9 mm, P \0.001; 2.3 mm, P \0.001, Table IV),

American Journal of Orthodontics and Dentofacial Orthopedics Cho et al 751 Volume 138, Number 6 Fig 7. A, Vertical displacement of FA point from the horizontal plane (mm). T0 T1: positive means intrusion; negative means extrusion. B, Anteroposterior displacement of FA point from the coronal plane (mm). T0-T1: positive means posterior movement; negative means anterior movement. C, Lateral displacement of FA point from the midsagittal plane (mm). T0-T1: positive means contraction; negative means distraction. moved backward (5.4 mm, P \0.001; 5.2 mm, P \0.001, Table IV), and moved laterally (0.7 mm, P \0.001; 1.7 mm, P \0.001, Table IV). There was no significant change in angulation of U1 and U2 (Table III). There was no significant change in angulation and rotation of U3 (Table III). It inclined lingually (2.0, P \0.05, Table III), extruded (1.7 mm, P \0.001, Table IV), moved backward (5.5 mm, P \0.001, Table IV), and displaced laterally (2.6 mm, P \0.001, Table IV). U5 did not show significant changes in inclination and angulation (Table III). However, it demonstrated significant mesial inward rotation (5.7, P \0.001, Table III), intrusion (0.9 mm, P \0.001, Table IV), anterior movement (1.4 mm, P \0.001, Table IV), and contracted toward the midsagittal plane (1.4 mm, P \0.001, Table IV). U6 and U7 showed similar tendencies of change as follows: significantly rotated mesially (4, P \0.001, Table III), moved forward (1.3 mm, P \0.001; 1.2 mm, P \0.001, Table IV), and contracted toward the midsagittal plane (1.3 mm, P \0.001; 1.2 mm, P \.001, Table IV). Although U6 did not show significant changes in inclination, angulation, and vertical displacement, U7 inclined buccally (2.5, P\0.001, Table III), tilted mesially (1.5, P \0.01, Table III), and extruded (0.4 mm, P \0.05, Table IV). The maxillary anterior teeth moved backward, and the maxillary posterior teeth moved forward in the ratio of 5:1 approximately (Table IV). In addition, the maxillary canine moved outward from the midsagittal plane, and the maxillary posterior teeth moved inward toward the midsagittal plane to maintain the continuity of the dental arch (Table IV). The amounts of contraction toward the midsagittal plane in U5, U6, and U7 decreased by 1.4, 1.3, and 1.2 mm, respectively (Table IV). When U1 was compared with U2, there was no significant difference in the amounts of change in angulation, rotation (Table V), and anteroposterior displacement (Table VI). That is to say, U1 and U2 showed similar amounts of linguoversion, distal inward rotation, and posterior movement. For inclination, the amount of linguoversion was greater at U1 than at U2 (P \0.001, Table V), but, for lateral displacement, U2 showed more distraction movement than U1 (P \0.001, Table VI). In spite of significance changes in vertical displacement (P \0.05), the difference between U1 and U2 was so small that it was clinically insignificant (0.6 mm, from 2.9 to 2.3 mm, Table VI).

752 Cho et al American Journal of Orthodontics and Dentofacial Orthopedics December 2010 Table I. Intraclass correlation coefficients of intraexaminer reliability Variable Intraexaminer reliability P value #11 x 0.998 0.000 y 0.998 0.000 z 0.950 0.001 #12 x 0.960 0.001 y 0.993 0.000 z 0.993 0.000 #13 x 0.838 0.012* y 0.992 0.000 z 0.988 0.000 #15 x 0.999 0.000 y 0.997 0.000 z 0.891 0.005 #16 x 0.995 0.000 y 0.995 0.000 z 0.948 0.001 #17 x 0.910 0.004 y 0.997 0.000 z 0.985 0.000 #21 x 0.893 0.005 y 0.994 0.000 z 0.910 0.004 #22 x 0.978 0.000 y 0.993 0.000 z 0.997 0.000 #23 x 0.912 0.003 y 0.989 0.000 z 0.993 0.000 #25 x 0.958 0.001 y 0.998 0.000 z 0.968 0.000 #26 x 0.931 0.002 y 0.997 0.000 z 0.991 0.000 #27 x 0.987 0.000 y 0.995 0.000 z 0.998 0.000 Reference points were digitized 3 times with a 2-week interval. Intraexaminer reliability was obtained with the 1-way random effects model. ICC values were significantly different from 0: *P \0.05; P \0.01; P \0.001. #11, the upper right central incisor; #12, the upper right lateral incisor; #13, the upper right canine; #15, the upper right second premolar; #16, the upper right first molar; #17, the upper right second molar; #21, the upper left central incisor; #22, the upper left lateral incisor; #23, the upper left canine; #25, the upper left second premolar; #26, the upper left first molar; #27, the upper left second molar. In the comparison between U3 and U5, there were significant differences in the changes in all variables (Tables V and VI). U3 showed linguoversion, mesial tipping, distal inward rotation, extrusion, posterior movement, and distraction movement. U3 and U5 showed significantly opposite movements in all variables. When U6 and U7 were compared, the amounts of change in inclination, rotation, and anteroposterior and lateral displacements showed no significant differences (Tables V and VI). However, U6 and U7 had opposite movement at significant levels in angulation (P \0.01, Table V) and vertical displacement (P \0.01, Table VI). In the comparison of arch dimension between T0 and T1, most arch variables of width and depth were significantly decreased (P \0.001, Table VII) except for intercanine width. DISCUSSION In this study, U1, U2, and U3 moved backward by 5.4, 5.2, and 5.5 mm, respectively (Table IV), and inclined lingually by 12.3 and 5.8 and buccally by 2.0, respectively (Table III). These values were comparable with those of Koh et al 16 for U1, U2, and U3 of 5.7, 6.1, and 6.8 mm of backward movement and 9.6, 10.6, and 8.4 of lingual inclination, respectively. The differences in the amounts of backward movement and inclination changes of U2 and U3 seemed to be due to the different methodology and treatment mechanics. Koh et al 16 performed a 3D finite element analysis of the ideally aligned dentition using loop mechanics with Mini-Diamond brackets (Roth setup, 0.018-in slot, Ormco, Orange, Calif) and 0.017 3 0.025-in stainless steel wire. On the other hand, we used the real treatment results of Class I malocclusion with sliding mechanics with MBT brackets (0.022-in slot) and 0.019 3 0.025- in stainless steel wire. Creekmore 17 demonstrated that one-third of the first premolar extraction space was used for anterior movement of the molars and two-thirds of it for posterior movement and decrowding of the anterior teeth. In our study, U5, U6, and U7 moved forward by 1.4, 1.3, and 1.2 mm and inclined lingually by 0.4 and buccally by 1.6 and 2.5, respectively (Table III). These results were similar to those of Koh et al 16 (U5, U6, and U7: 1.8, 1.4, and 1.3 mm of anterior movement with 1.8, 1.4, and 1.3 of buccal inclination). In the occlusal view, the individual teeth showed rotation in addition to anteroposterior movement. It seems to be easier to assess rotation when the external reference plane such as the midsagittal plane is used than the internal center of rotation in each tooth. 2,18,19 The

American Journal of Orthodontics and Dentofacial Orthopedics Cho et al 753 Volume 138, Number 6 Table II. Comparison of data between the right and left sides T0 T0 T1 Right side Left side Right side Left side Variable Mean SD Mean SD P value Mean SD Mean SD P value Inclination ( ) U1 67.87 5.05 68.86 6.01 0.5471 11.68 5.17 12.83 4.93 0.4450 U2 76.02 5.97 78.63 5.00 0.1157 6.42 5.66 5.22 5.99 0.4889 U3 83.69 4.85 83.21 4.92 0.7373 2.17 5.97 1.91 6.62 0.8925 U5 79.97 6.26 81.37 6.42 0.4564 0.57 6.17 0.17 5.50 0.8177 U6 80.22 6.65 79.96 5.51 0.8851 2.05 5.04 1.22 4.88 0.5737 U7 83.86 4.49 84.03 3.51 0.8837 2.56 3.76 2.47 4.03 0.9343 Angulation ( ) U1 90.92 0.71 91.55 1.34 0.0533 0.00 1.03 0.33 2.01 0.4845 U2 91.30 1.34 91.56 1.09 0.4703 0.16 1.56 0.43 1.63 0.2126 U3 91.87 1.65 92.03 1.61 0.7382 0.50 1.77 0.55 1.93 0.9199 U5 91.35 1.02 91.78 1.10 0.1769 0.00 1.02 0.21 1.84 0.6447 U6 93.80 2.01 93.96 2.04 0.7859 0.22 2.10 0.11 1.91 0.8603 U7 93.23 1.80 93.66 2.06 0.4505 1.43 2.50 1.52 2.97 0.9154 Rotation ( ) U1 96.31 4.80 96.32 3.29 0.9929 5.45 5.62 4.65 2.86 0.5472 U2 114.47 10.85 115.36 7.54 0.7482 6.96 10.95 6.49 5.57 0.8560 U3 145.57 6.59 146.78 7.63 0.5674 0.53 6.56 0.12 7.46 0.7553 U5 160.05 6.31 162.21 4.25 0.1812 5.21 5.73 6.14 4.36 0.5406 U6 169.62 2.71 168.42 3.84 0.2282 4.36 2.95 3.75 3.01 0.4947 U7 173.08 4.00 171.86 3.69 0.2906 4.41 2.48 3.50 2.53 0.2254 Vertical displacement (mm) U1 31.31 5.30 31.43 5.08 0.9383 2.93 1.68 2.94 1.57 0.9785 U2 30.39 5.16 30.27 4.94 0.9361 2.28 1.64 2.25 1.48 0.9491 U3 29.24 5.00 29.42 4.62 0.9026 1.72 1.50 1.71 1.48 0.9843 U5 27.45 4.90 27.22 4.48 0.8657 0.75 0.91 1.12 1.22 0.2595 U6 26.02 5.05 25.48 5.01 0.7135 0.15 0.81 0.19 1.11 0.8757 U7 25.23 5.77 24.78 5.90 0.7950 0.43 0.83 0.38 1.17 0.8509 Anteroposterior displacement (mm) U1 40.96 4.13 42.57 3.61 0.1673 5.48 1.23 5.35 1.12 0.7174 U2 37.80 3.40 38.47 3.08 0.4865 5.33 1.39 5.04 1.45 0.4828 U3 33.18 2.59 33.16 2.41 0.9762 5.64 1.06 5.40 1.42 0.5323 U5 19.09 1.53 18.90 1.23 0.6439 1.10 0.94 1.59 1.23 0.1367 U6 10.12 0.91 10.29 1.08 0.5656 1.16 0.92 1.52 1.85 0.4066 U7 0.00 0.00 0.00 0.00 NA 1.04 0.97 1.26 0.89 0.4366 Lateral displacement (mm) U1 3.37 1.40 2.97 1.59 0.3663 0.76 0.84 0.55 0.39 0.2913 U2 11.00 2.11 9.99 2.71 0.1634 1.75 1.18 1.57 1.04 0.5780 U3 17.80 2.11 16.69 3.11 0.1611 2.90 1.38 2.25 1.22 0.0967 U5 23.33 2.34 22.65 2.75 0.3725 1.40 2.02 1.34 0.86 0.8874 U6 26.06 2.07 26.01 2.36 0.9390 1.14 0.97 1.49 1.11 0.2727 U7 29.30 1.85 29.19 2.54 0.8740 1.16 1.14 1.28 1.18 0.7241 NA, Not applicable; U1, the upper central incisor; U2, the upper lateral incisor; U3, the upper canine; U5, the upper second premolar; U6, the upper first molar; U7, the upper second molar. findings that U5 significantly rotated about 5.7 mesially and U6 and U7 also tended to rotate 4.0 mesially (Table III) were the same as those of Chon et al, 20 who reported mesial inward rotation of the second premolar with bodily movement, and the findings of Chong et al 2 that suggested that the second premolar rotated more than did the molars to maintain the continuity of the dental arch. These seem to be due to the greater antirotation prescription in the maxillary molar tubes than in the maxillary second premolar bracket (MBT). On the other hand, Koh et al 16 reported almost no rotation of U1 and U2 (distal inward rotations of 0.6

754 Cho et al American Journal of Orthodontics and Dentofacial Orthopedics December 2010 Fig 8. Arch dimensions: A, arch width; B, arch depth. ICW, intercanine width (distance between the cusp tip of the right and left canines); IP2W, intersecond premolar width (distance between the cusp tip of the right and left second premolars); IM1W, interfirst molar width (distance between the mesiobuccal cusp tip of right and left first molars); IM2W, intersecond molar width (distance between the mesiobuccal cusp tip of the right and left second molars); CD, canine depth (shortest distance from a line connecting the cusp tip of the right and left canines to the contact point between the right and left central incisors); MD, molar depth (shortest distance from a line connecting the mesiobuccal cusp tip of the right and left first molars to the contact point between the right and left central incisors). Table III. Comparison of angular variables between T0 and T1 in each tooth Angular variable ( ) T0 T1 T0 T1 Mean SD Mean SD P value Mean SD Power (1-b) Inclination U1 68.37 5.51 80.63 5.39 0.0000 12.26 5.03 0.999 U2 77.33 5.61 83.15 4.16 0.0000 5.82 5.79 0.999 U3 83.45 4.84 81.41 4.81 0.0160* 2.04 6.23 0.683 U5 80.67 6.31 81.04 6.29 0.8698 0.37 5.78 0.136 U6 80.09 6.04 78.46 6.34 0.0706 1.63 4.93 0.412 U7 83.94 3.98 81.43 4.33 0.0002 2.51 3.85 0.844 Angulation U1 91.24 1.11 91.07 1.13 0.3488 0.17 1.59 0.048 U2 91.43 1.21 91.56 1.27 0.6780 0.13 1.61 0.072 U3 91.95 1.61 92.47 1.34 0.0595 0.52 1.83 0.282 U5 91.57 1.07 91.46 1.22 0.7764 0.10 1.47 0.049 U6 93.88 2.01 93.72 1.89 0.6038 0.17 1.99 0.059 U7 93.45 1.93 94.92 2.92 0.0010 1.47 2.71 0.048 Rotation U1 96.32 4.07 101.37 3.68 0.0000 5.05 4.43 0.998 U2 114.92 9.25 121.65 4.31 0.0000 6.73 8.59 0.801 U3 146.17 7.08 146.38 9.16 0.8058 0.21 6.96 0.07 U5 161.13 5.43 155.46 6.06 0.0000 5.67 5.06 0.993 U6 169.02 3.34 164.97 3.85 0.0000 4.05 2.97 0.12 U7 172.47 3.85 168.51 4.06 0.0000 3.96 2.52 0.292 Wilcoxon signed rank test was done. T0 T1 means change from T0 to T1. *P \0.05; P \0.01; P \0.001. Inclination: labioversion (1) or linguoversion ( ). Angulation: distal tipping (1) or mesial tipping ( ). Rotation: mesial inward rotation (1) distal inward rotation ( ).

American Journal of Orthodontics and Dentofacial Orthopedics Cho et al 755 Volume 138, Number 6 Table IV. Comparison of linear variables between T0 and T1 in each tooth Linear variable (mm) T0 T1 T0 T1 Mean SD Mean SD P value Mean SD Power (1-b) Vertical displacement U1 31.37 5.13 34.30 5.55 0.0000 2.93 1.61 0.999 U2 30.33 4.99 32.60 5.24 0.0000 2.26 1.54 0.999 U3 29.33 4.76 31.05 4.73 0.0000 1.71 1.47 0.788 U5 27.33 4.65 26.40 4.91 0.0000 0.94 1.08 0.973 U6 25.58 5.08 25.75 4.98 0.1479 0.17 0.96 0.124 U7 25.41 5.84 25.00 5.77 0.0150* 0.40 1.00 0.61 Anteroposterior displacement U1 41.77 3.92 36.35 3.78 0.0000 5.42 1.16 0.999 U2 38.14 3.23 32.95 3.04 0.0000 5.18 1.41 0.999 U3 33.17 2.48 27.65 2.33 0.0000 5.52 1.24 0.999 U5 19.00 1.38 20.34 1.91 0.0000 1.35 1.11 0.999 U6 10.20 0.99 11.54 1.95 0.0000 1.34 1.46 0.999 U7 0.00 0.00 1.15 0.93 0.0000 1.15 0.93 0.999 Lateral displacement U1 2.52 1.49 3.17 1.50 0.0000 0.66 0.66 0.999 U2 8.83 2.44 10.49 2.45 0.0000 1.66 1.10 0.999 U3 14.67 2.79 17.25 2.69 0.0000 2.58 1.33 0.999 U5 24.36 2.57 22.99 2.55 0.0000 1.37 1.54 0.999 U6 27.35 2.26 26.04 2.20 0.0000 1.31 1.05 0.999 U7 30.47 2.19 29.25 2.19 0.0000 1.22 1.15 0.999 Wilcoxon signed rank test was done. T0 T1 means change from T0 to T1. *P \0.05; P \0.001. Vertical displacement to the horizontal plane: intrusion (1) or extrusion ( ). Anteroposterior displacement to the coronal plane: posterior movement (1) or anterior movement ( ). Lateral displacement to the midsagittal plane: contraction movement (1) or distraction movement ( ). and 0.2 ) and U3 (mesial inward rotation of 0.3 ) and large mesial inward rotations of U5, U6, and U7 (6.7, 5.0, and 11.7, respectively). The reason that the amount of rotation found by Koh et al 16 was different from this study seemed to be that they used the ideally aligned dentition without crowding and labioversion of the maxillary anterior teeth for 3D finite element analysis and loop mechanics with gable bends and cinch backs with Mini-Diamond brackets and 0.017 3 0.025- in stainless steel wires to close the extraction spaces. In addition, the arch form could have an effect on rotation of the posterior teeth. Because a U-shaped arch has a greater difference of curvature between the anterior and posterior teeth than a V-shaped one, the amount of mesial inward rotation in the posterior teeth could be greater in U-shaped than in V-shaped arches. 20 In the analysis of lateral displacement, U2 showed more distraction movement than U1 (P \0.001, Table VI). This means that the circumference of the dental arch form was changed according to the rotation of U1 located in the flat line. U3 was distracted from the midsagittal plane about 2.6 mm (P \0.001, Table IV) and U5, U6, and U7 contracted toward the midsagittal plane about 1.4, 1.3, and 1.2 mm, respectively (P \0.001, Table IV). However, Koh et al 16 reported that U5 and U6 contracted toward the midsagittal plane about 2.8 and 1.7 mm, but U7 distracted from the midsagittal plane about 0.2 mm. These differences seemed to be caused by smaller wire sizes and loop mechanics, 16 which could have more chance to deform the arch form than larger wires and sliding mechanics, as used in this study. In the vertical displacement, U1, U2, and U3 extruded about 2.9, 2.3, and 1.7 mm, respectively, after treatment (P \0.001, Table IV). In the posterior teeth, although U6 did not show significant change, U5 intruded about 0.9 mm (P \0.001, Table IV), and U7 extruded about 0.4 mm (P \0.05, Table IV). These were different from the results of Koh et al 16 that showed 0.2 to 0.4 mm of extrusion in the maxillary anterior and posterior teeth. As mentioned above, this difference seemed to be caused by the ideally aligned dentition for the 3D finite element analysis and the loop mechanics with gable bends used by Koh et al. 16 The results that most arch dimension variables were significantly decreased (P \0.001, Table VII) except intercanine width were in accord with changes in individual tooth positions between T0 and T1 (Tables III and IV). However, the amounts of change in Table VII seemed to be larger than those in Tables III and IV. The reasons were as follows. First, the arch dimension variables

756 Cho et al American Journal of Orthodontics and Dentofacial Orthopedics December 2010 Table V. Comparison of the angular variables between adjacent teeth at T0 and T1 U1 U2 U3 U5 U6 U7 Angular variable ( ) Mean SD Mean SD P value Mean SD Mean SD P value Mean SD Mean SD P value Inclination T0 68.37 5.51 77.33 5.61 0.0000 83.45 4.84 80.67 6.31 0.0217 80.09 6.04 83.94 3.98 0.0019 T1 80.63 5.39 83.15 4.16 0.0219* 81.41 4.81 81.04 6.29 0.9969 78.46 6.34 81.43 4.33 0.0132* Diff 12.26 5.03 5.82 5.79 0.0000 2.04 6.23 0.37 5.78 0.0231* 1.63 4.93 2.51 3.85 0.1755 Power (1-b) 0.969 0.692 0.071 Angulation T0 91.24 1.11 91.43 1.21 0.3527 91.95 1.61 91.57 1.07 0.3309 93.88 2.01 93.45 1.93 0.2462 T1 91.07 1.13 91.56 1.27 0.0583 92.47 1.34 91.46 1.22 0.0003 93.72 1.89 94.92 2.92 0.0250* Diff 0.17 1.59 0.13 1.61 0.3388 0.52 1.83 0.10 1.47 0.0411* 0.17 1.99 1.47 2.71 0.0032 Power (1-b) 0.066 0.357 0.05 Rotation T0 96.32 4.07 114.92 9.25 0.0000 146.17 7.08 161.13 5.43 0.0000 169.02 3.34 172.47 3.85 0.0000 T1 101.37 3.68 121.65 4.31 0.0000 146.38 9.16 155.46 6.06 0.0000 164.97 3.85 168.51 4.06 0.0001 Diff 5.05 4.43 6.73 8.59 0.0620 0.21 6.96 5.67 5.06 0.0000 4.05 2.97 3.96 2.52 0.9875 Power (1-b) 0.1 0.4 0.054 Mann-Whitney Test was done. Diff, Change from T0 to T1 (T0 T1). *P \0.05; P \0.01; P \0.001. Inclination: labioversion (1) or linguoversion ( ). Angulation: distal tipping (1) or mesial tipping ( ). Rotation: mesial inward rotation (1) or distal inward rotation ( ). Table VI. Comparison of the linear variables between adjacent teeth at T0 and T1 U1 U2 U3 U5 U6 U7 Linear variable (mm) Mean SD Mean SD P value Mean SD Mean SD P value Mean SD Mean SD P value Vertical displacement T0 31.37 5.13 30.33 4.99 0.2478 29.33 4.76 27.33 4.65 0.0844 25.75 4.98 25.00 5.77 0.6008 T1 34.30 5.55 32.60 5.24 0.1410 31.05 4.73 26.40 4.91 0.0000 25.58 5.08 25.41 5.84 0.9222 Diff 2.93 1.61 2.26 1.54 0.0435* 1.71 1.47 0.94 1.08 0.0000 0.17 0.96 0.40 1.00 0.0061 Power (1-b) 0.608 0.999 0.171 Anteroposterior displacement T0 41.77 3.92 38.14 3.23 0.0000 33.17 2.48 19.00 1.38 0.0000 10.20 0.99 0.00 0.00 0.0000 T1 36.35 3.78 32.95 3.04 0.0000 27.65 2.33 20.34 1.91 0.0000 11.54 1.95 1.15 0.93 0.0000 Diff 5.42 1.16 5.18 1.41 0.5450 5.52 1.24 1.35 1.11 0.0000 1.34 1.46 1.15 0.93 0.9720 Power (1-b) 0.074 0.999 0.054 Lateral displacement T0 2.52 1.49 8.83 2.44 0.0000 14.67 2.79 24.36 2.57 0.0000 27.35 2.26 30.47 2.19 0.0000 T1 3.17 1.50 10.49 2.45 0.0000 17.25 2.69 22.99 2.55 0.0000 26.04 2.20 29.25 2.19 0.0000 Diff 0.66 0.66 1.66 1.10 0.0000 2.58 1.33 1.37 1.54 0.0000 1.31 1.05 1.22 1.15 0.4725 Power (1-b) 0.498 0.999 0.049 Mann-Whitney test was done. Diff, Change from T0 to T1 (T0 T1). *P \0.05; P \0.01; P \0.001. Vertical displacement to the horizontal plane: intrusion (1) or extrusion ( ). Anteroposterior displacement to the coronal plane: posterior movement (1) or anterior movement ( ). Lateral displacement to the midsagittal plane: contraction movement (1) or distraction movement ( ). were measured by using the cusp tip of each tooth. Second, the amount of change in incisal edge or cusp tip could be exaggerated more than in the FA point. Therefore, the FA point might be a better landmark to analyze pattern of the individual tooth movement and change of the arch dimension than incisal edge or cusp tip. This study might introduce a basic step of how to select and use the reference points and planes in the

American Journal of Orthodontics and Dentofacial Orthopedics Cho et al 757 Volume 138, Number 6 Table VII. Comparison of the arch dimension variables at T0 andt1 Variable (mm) T0 maxillary model for superimposition before and after treatment by using 3D virtual technology. Until now, 3D computed tomography data have not been able to reproduce the occlusal surfaces of the teeth because of limitations of the slice thickness. However, improvements in 3D computed tomography technology will provide a breakthrough for combining data from the 3D virtual models and 3D computed tomography. 21-23 In addition, soft-tissue changes can also be predicted by using these combined methods. Further studies to set the methodology for superimposition of the mandibular dentition and to investigate the changes according to the type of arch form and Class II and Class III malocclusions will be needed. CONCLUSION Superimposition of 3D virtual models in first premolar extraction cases could be a guideline for precise virtual treatment planning for arch dimension and tooth position. REFERENCES 1. Redmond WR. Digital models: a new diagnostic tool. J Clin Orthod 2001;35:386-7. 2. Chong DY, Jang YJ, Chun YS, Jung SH, Lee SK. The evaluation of rotational movements of maxillary posterior teeth using three dimensional images in cases of extraction of maxillary first premolar. Korean J Orthod 2005;35:451-8. 3. Mavropoulos A, Karamouzos A, Kiliaridis S, Papadopoulos MA. Efficiency of noncompliance simultaneous first and second upper molar distalization: a three-dimensional tooth movement analysis. Angle Orthod 2005;75:532-9. T1 Mean SD Mean SD P value ICW 35.72 1.50 36.04 1.59 0.029* IP2W 48.47 3.02 45.08 1.56 0.0000* IM1W 53.31 3.27 50.41 1.70 0.0000* IM2W 60.43 2.73 57.12 1.80 0.0000* CD 9.98 1.23 9.06 0.98 0.0006* MD 31.22 1.75 22.72 1.51 0.0000* Wilcoxon signed rank test was done. 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