ORIGINAL ARTICLE
Effect of occlusal vertical dimension changes on postsurgical skeletal changes in a surgery-first approach for skeletal Class III deformities Jihyun Lee,a Yong-Il Kim,b Dae-Seok Hwang,c Ki Beom Kim,d and Soo-Byung Parke Busan and Yangsan, South Korea, and St Louis, Mo
Introduction: The purposes of this study were to investigate the relationship between occlusal vertical dimension (VD) changes and postsurgical skeletal changes in the surgery-first approach and to derive regression models for the final mandibular setback at B-point. Methods: This retrospective study included 40 patients (16 men, 24 women; ages, 22.6 6 4.0 years) who had undergone a bimaxillary surgery-first approach. Using cephalograms generated from cone-beam computed tomography representing the presurgical, postsurgical, and posttreatment stages, skeletal landmarks in the maxilla and mandible were investigated to derive multivariate linear regression-based prediction models. Additionally, a patient classification based on the VD was established and verified to generate regression models for the classified groups. Results: For the nonincreased VD group, the surgical setback of B-point was its predictor for the final mandibular setback (R2 at 92%). Meanwhile, the final mandibular setback of the increased VD group was predicted according to the surgical upward movement of pogonion, the postsurgical horizontal position of A-point, and the postsurgical vertical position of the coronoid process (R2 at 94%). Conclusions: The results of this study support the clinical observation that the more increased the vertical occlusal dimension after surgery, the less predictable the position of B-point at the posttreatment stage. (Am J Orthod Dentofacial Orthop 2014;146:612-9)
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he surgery-first approach (SFA) is characterized by minimal presurgical orthodontic treatment and orthognathic surgery followed by postsurgical orthodontic treatment. The application of SFA has recently been increasing with the publication of reports1-7 emphasizing its advantages, which include increased patient cooperation, effective compensation, and a
a Postgraduate student, Department of Orthodontics, Pusan National University Hospital, Busan, South Korea. b Assistant professor, Department of Orthodontics, Dental Research Institute, Pusan National University Dental Hospital, Busan, South Korea. c Assistant professor, Department of Oral & Maxillofacial Surgery, Pusan National University Hospital, Busan, South Korea. d Associate professor, Department of Orthodontics, Center for Advanced Dental Education, St Louis University, St Louis, Mo. e Professor, Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Supported by a 2-year research grant from Pusan National University. Address correspondence to: Yong-Il Kim, Department of Orthodontics, School of Dentistry, Pusan National University, Gudeokro 137, Seogu, Busan 602-739, South Korea; e-mail, [email protected]. Submitted, February 2014; revised and accepted, July 2014. 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.07.024
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shortened treatment period.3,4 However, because presurgical orthodontic treatments such as dental decompensation and arch coordination are rarely performed in the SFA, postsurgical occlusal instability clinically leads to more severe forward postoperative mandibular movement than in conventional surgical orthodontic treatment for patients with a skeletal Class III deformity.1,3,4,6,7 Accordingly, the surgical treatment objective for the SFA, often designated as mandibular setback from the horizontal B-point position at the presurgical stage (T0) to the position at the removal of the orthodontic appliance at the posttreatment stage (T2), is not equivalent to the extent of the surgical mandibular setback at T0 to the position immediately after surgery (T1), because of the extent of postoperative mandibular movement from T1 to T2 during active orthodontic treatment. This complicates accurate prediction and simulation of postoperative orthodontic treatment. Therefore, clinical experience is needed for accurate prediction of postoperative orthodontic treatment and assessment of skeletal discrepancy. As for conventional orthognathic surgery, the gonial angle8 and the mandibular occlusal plane angle9 have
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been suggested to correlate with mandibular relapse. Ko et al,5 contrastingly, reported overbite to be a predictor of the extent of vertical mandibular relapse in the SFA. However, in their study, overbite was found to explain only 25.9% of the variation of vertical mandibular relapse, leaving the remaining 74.1% unexplained. Moreover, to support the clinical observation that an increased occlusal vertical dimension (VD) at T1 is related to a strong likelihood of more severe postsurgical mandibular forward movement in the SFA, the factors related to postoperative skeletal changes should be investigated. Among them, the relationship of occlusal VD changes to postoperative skeletal changes is especially relevant. Therefore, the purposes of this study were to investigate the relationship between VD changes and postsurgical skeletal changes in the SFA to orthodontic treatment and to estimate the extent of final mandibular setback (DT2-T0). The specific aims of the study were (1) to derive a prediction model of the final mandibular setback extent at B-point (DT2-T0) as the sum of the observed surgical setback (DT1-T0) and the postoperative mandibular forward movement (DT2-T1), and (2) to assess the correlation between VD changes and mandibular movements during postoperative orthodontic treatment to support the clinical significance of postsurgical VD change. MATERIAL AND METHODS
This study was a retrospective study of 40 patients with skeletal Class III deformities (16 men, 24 women; mean age, 22.6 6 4.0 years) who had undergone bimaxillary surgery with the SFA in the Departments of Oral & Maxillofacial Surgery and Orthodontics at Pusan National University Hospital in South Korea. The exclusion criteria were patients with extractions, severe facial asymmetry, cleft lip and palate, and temporomandibular joint disorders (Table I). LeFort I osteotomy and modified Hunsuck sagittal split ramus osteotomy with rigid internal fixation were performed on all patients by 2 surgeons (D.-S.H. and Y.-I.K.), followed by active orthodontic treatment an average of 1 month later. This study was reviewed and approved by the institutional review board of Pusan National University Hospital (E-2011069). Preliminarily, predictor-variable data were compiled as 2-dimensional coordinates of each skeletal landmark, extracted from cephalograms generated by cone-beam computed tomography (CBCT) with ray-cast and maximum intensity projection using CBCT superimposition10 (Fig 1). CBCT images (DCT Pro; Vatech, Seoul, Korea) were obtained at T0, T1, and T2 with the scanner set at a 20 3 19-cm field of view, 90 kVp, 4.0-mA tube
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current, and scan time of 24 seconds. To create CBCT-generated half-cephalograms, the CBCT data were reformatted to 3-dimensional images with imaging software (Ondemand 3D; Cybermed, Seoul, Korea), superimposed on the anterior cranial base to obtain ray-cast and maximum intensity projection from the right side of the subjects,10,11 and digitized by software (V-ceph version 6.0; Osstem Implant, Seoul, Korea). All measurements were repeated 2 weeks later by the same investigator (J.L.), and the measured data were validated according to the systematic intraexaminer error, with the mean of the 2 measurements used to calculate the corresponding distances of each landmark from the Frankfort horizontal (FH) and sella-perpendicular (S-perp) planes, respectively. The intraclass correlation coefficient for the systematic intraexaminer error was 0.994 (0.990-0.996), and the intraobserver reliability was high for all measurements. Then, using the coordinates obtained at T0, T1, and T2, both the horizontal and the vertical distances of each landmark from the reference planes were calculated, along with the corresponding increment or decrement in such distances over the periods of T0 to T1 (DT1T0) and T1 to T2 (DT2-T1); the corresponding predictor variables were designated as surgical movement (DT1T0) and postsurgical movement (DT2-T1) of each landmark. As for the horizontal position of B-point, the change in its distance from the S-perp plane from T0 to T2 (DT2-T0) was calculated (Fig 1, Table II). The final setback of B-point was predicted by multivariate regression analysis; 78 potential predictors, compiled as described above, were investigated to obtain the best-fit prediction model.12 The model selection criteria for viable predictors were as follows: (1) a high adjusted R2, (2) a statistically significant coefficient estimate, (3) no multicollinearity with respect to statistical model diagnosis, and (4) the fewer predictors the better (Table III). Upon identification of the best-fit prediction model, another regression analysis of patient groups classified based on VD increment was carried out, and the VD of each patient was defined as the distance from the mesial contact of the mandibular first molar to that of the maxillary first molar as projected onto the S-perp plane (Table II). For the 29 patients whose VD had not increased after surgery at T1, classified accordingly as the nonincreased occlusal VD (nonincreased VD) group, a prediction model designated as the nonincreased VD model was constructed by following the same model selection process as with the previously identified general model for the overall 40patient group. A prediction model for the remaining 11 patients whose VD had increased after surgery at T1, designated as the increased VD model, was constructed
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Table I. Demographic data of the subjects Sample size (n) Sex Mean age (y) Maxillary surgical setback (mm)* Mandibular surgical setback (mm)y Final mandibular setback (mm)z
Overall group, mean (SD) 40 24 women, 16 men 22.6 (4.0) 0.5 (2.3) 8.4 (5.7) 7.6 (4.7)
Nonincreased VD group, mean (SD) 29 15 women, 14 men 21.9 (3.5) 0.4 (2.5) 8.7 (6.1) 7.8 (5.1)
Increased VD group, mean (SD) 11 9 women, 2 men 24.4 (5.0) 0.8 (1.9) 7.3 (4.3) 7.1 (3.6)
*Horizontal movement of A-point from T0 to T1 (A10); yhorizontal movement of B-point from T0 to T1 (B10); zfinal mandibular setback measured as horizontal movement of B-point from T0 to T2 (B20).
Fig 1. Landmarks and linear measurements. The distances were measured from the Frankfort horizontal (FH) plane (vertical) and the sella-perpendicular (S-perp) plane (horizontal) to each landmark. Condylion (Cd), Most superior point of condyle head; coronoid process (Cp), tip of the coronoid process; U1t and L1t, mandibular and maxillary first incisor tips; U1r and L1r, mandibular and maxillary first incisor root apices; U6mc and L6mc, mandibular and maxillary first molar mesial contacts; occlusal VD, distance between mesial contact points of the mandibular right first molar and the maxillary right first molar as projected onto the S-perp plane.
increased VD models was characterized by relatively high adjusted R2 values indicating high predictive power. Based on these R2 values of the models, the minimum required sample size for each corresponding model was calculated using the Cohen effect size f2 (Table IV).13 Moreover, the regression models, as required by the variance inflation factor (VIF)based model diagnostic method, were not tethered by multicollinearity. According to this result, wherein multicollinearity-free models were found, the calculation of the final setback of B-point upon a change of at least 1 predictor variable was feasible for the general patient group, even for the nonincreased VD and increased VD patients, at an improved explanatory power (Table V). As for prediction of the final setback (DT2-T0) (Fig 2, A) of B-point from T0 to T2 (Bs20 ), the following predictor set among all possible predictor sets was found to explain it: the surgical setback of B-point (DT1-T0, horizontal measurement notated as Bs10 ) and menton (DT1-T0, horizontal measurement notated as Mes10 ), the postsurgical horizontal position of A-point (T1, notated as As1 ), and the vertical position of the coronoid process (T1, notated as Cpf1 ). According to this predictor set, the following multivariate regression equation was verified as a general prediction model for the overall 40-patient group with its adjusted R2 at 87% (P \0.000) (Table V). Predicted final mandibular setback Bs20 5 14:33 1 0:36 3 Bs10 1 0:34 3 Mes10 10:23 3 As1 0:18 3 Cpf1
in the same way as the nonincreased VD model. For the statistical analysis of the multivariate regression, Language R (Vienna, Austria), an open-source software program for statistical computation, was used. RESULTS
The general model for the overall 40-patient group and the respective nonincreased VD and
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The prediction models of the final mandibular setback (DT2-T0) varied by the occlusal VD changes (Fig 2, B and C). For the nonincreased VD group, the identified regression model was univariate, validating only the surgical setback of B-point (DT1-T0, Bs10 ) as its predictor for the final mandibular setback (Bs20 ), with its adjusted R2 at 92% (P \0.000). Meanwhile, the final
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Table II. Model-relevant landmarks, planes, distances, and indicators Terms Landmarks B-point (B) Menton (Me) Pogonion (Pog) A-point (A) Coronoid process (Cp) Planes Frankfort horizontal (FH) plane Midsagittal reference (MSR) plane S-perpendicular plane (S-perp) Distances B-point to S-perp (Bs) Menton to S-perp (Mes) Pogonion to FH plane (Pogf) A-point to S-perp (As) Coronoid process to FH plane (Cpf) Occlusal vertical dimension (VD) Indicators Final setback of B-point (Bs20 ) Surgical setback of B-point (Bs10 ) Surgical setback of menton (Mes10 ) Surgical upward movement of pogonion (Pogf10 ) Postsurgical horizontal position of A-point (As1 ) Postsurgical vertical position of coronoid process (Cpf1 ) Patient classification criteria Vertical occlusal dimension (VD) Nonincreased VD Increased VD
Definitions Innermost curvature from chin to alveolar bone junction Lowest point on symphysis of mandible Most anterior point on contour of chin Innermost curvature from maxillary anterior nasal spine to crest of maxillary alveolar process Tip of coronoid process Plane formed by right Pog and both sides of orbitale Perpendicular to FH plane and passing through nasion and basion Perpendicular to FH and MSR planes and passing through sella Distance from B-point to S-perpendicular plane Distance from menton to S-perpendicular plane Distance from pogonion to FH plane Distance from A-point to S-perpendicular plane Distance from tip of coronoid process to FH plane Distance from mesial contact of mandibular first molar to that of maxillary first molar as projected onto S-perpendicular plane Bs changes from T0 to T2, final mandibular movement over presurgical (T0) to posttreatment period (T2) Bs changes from T0 to T1, surgical movement over presurgical (T0) to postsurgical period (T1) Mes changes from T0 to T1, surgical movement over presurgical (T0) to postsurgical period (T1) Pogf changes from T0 to T1, surgical movement over presurgical (T0) to postsurgical period (T1) Distance from A-point to S-perpendicular plane measured at T1 Distance from tip of coronoid process to FH plane measured at T1
Distance from mesial contact of mandibular first molar to that of maxillary first molar VD measured at T1 not increased from VD at T0 VD measured at T1 increased from VD at T0
mandibular setback (Bs20 ) of the increased VD group was predicted by surgical upward movement of pogonion (DT1-T0, vertical measurement notated as Pogf10 ), the postsurgical horizontal position of A-point (T1, notated as As1 ), and the vertical position of the coronoid process (T1, notated as Cpf1 ), with the adjusted R2 at 94% (P \0.0001) (Table V). The following equations were derived for the nonincreased VD and increased VD groups. For the nonincreased VD group; Bs20 5 0:98 1 0:7 3 Bs10
horizontal movement of the mandible (Bs10 ) but, rather, its vertical movement (Pogf10 ), which is the only predictor of its distal segment; this implies that if a patient's VD increases after surgery, the surgical vertical movement of the mandible is a concern for the extent of relapse rather than its horizontal movement. As shown below, this equation has a 0.1757 coefficient of determination, indicating that approximately 18% of the variation in vertical movement of the mandible during surgery (Pogf10 ) could be explained by the surgical change of VD (VD10) (r 5 0.5409). Pogf10 5 2:670410:54091VD10 ; R2 50:1757ðP\0:05Þ
For the increased VD group; Bs20 5 53:00 0:76 3 Pogf10 1 0:80 3 As1 0:473Cpf1 There was a relationship between VD changes and postsurgical skeletal changes (DT2-T1). What best characterizes the increased VD outcome was not the surgical
DISCUSSION
After the SFA in this study, the orthodontists encountered increased VD resulting from premature contacts, which led to forward mandibular movement postoperatively. The results showed that the VD change was
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Table III. Variables tested for multivariate regression model Presurgical (T0) variables
Postsurgical (T1) variables
Overall Nonincreased Increased group, VD group, VD group, mean (SD) mean (SD) mean (SD)
Overall Nonincreased Increased group, VD group, VD group, mean (SD) mean (SD) mean (SD)
Horizontal parameters Maxilla As 62.5 (4.4) 62.3 (4.7) 63.3 (3.5) 63.0 (4.5) 62.7 (4.4) 64.0 (4.8) PNSs 20.0 (3.1) 20.0 (3.0) 20.2 (3.3) 20.3 (3.1) 20.1 (3.1) 20.9 (3.4) Distal segment of mandible Bs 66.6 (7.0) 66.9 (7.4) 65.4 (5.6) 58.2 (6.7) 58.2 (7.1) 58.1 (5.4) 68.3 (7.5) 68.6 (8.1) 67.4 (5.7) 61.1 (7.4) 61.3 (8.0) 60.4 (5.5) Pogs Mes 62.1 (7.4) 62.4 (8.0) 61.2 (5.5) 54.4 (7.0) 54.5 (7.6) 54.0 (5.1) Proximal segment of mandible Cds 12.0 (3.3) 12.2 (3.4) 11.2 (3.4) 11.2 (3.4) 11.7 (3.5) 9.8 (3.0) 25.1 (3.7) 25.4 (4.0) 24.4 (2.6) 25.7 (3.8) 25.7 (4.1) 25.4 (2.5) Cps Dental parameters U1s 69.3 (5.0) 69.2 (5.5) 69.9 (3.7) 69.1 (5.2) 69.2 (5.3) 69.0 (5.3) 58.3 (4.5) 58.1 (4.9) 58.9 (3.2) 58.9 (4.8) 58.5 (4.8) 60.2 (4.7) U1rs L1s 70.7 (6.6) 71.3 (7.0) 69.2 (5.2) 62.1 (5.6) 62.0 (6.0) 62.5 (4.8) L1rs 63.7 (7.2) 64.0 (7.6) 62.8 (6.0) 55.4 (6.8) 55.4 (7.2) 55.2 (5.8) U6s 43.3 (4.2) 42.9 (4.3) 44.3 (4.1) 43.5 (4.7) 43.1 (4.6) 44.6 (5.2) 47.1 (17.6) 47.0 (20.3) 47.4 (4.7) 38.8 (14.4) 38.1 (16.4) 40.8 (5.5) L6s Vertical parameters Maxilla Af 31.2 (3.3) 31.5 (3.6) 30.4 (2.3) 28.2 (3.5) 28.2 (3.7) 28.3 (2.8) 24.9 (2.8) 24.9 (3.0) 25.0 (2.1) 20.2 (3.9) 20.3 (4.1) 20.2 (3.5) PNSf Distal segment of mandible Bf 77.9 (6.5) 78.7 (7.0) 75.4 (4.3) 75.0 (5.4) 75.1 (5.7) 75.0 (4.7) Pogf 91.8 (8.0) 92.5 (8.6) 89.6 (5.7) 88.1 (6.6) 88.1 (7.0) 88.3 (5.1) 98.3 (8.1) 99.2 (8.5) 95.8 (6.3) 94.3 (6.6) 94.3 (6.7) 94.3 (6.6) Mef Proximal segment of mandible Cdf 2.6 (2.0) 2.5 (2.2) 2.9 (1.3) 3.4 (2.4) 3.0 (2.3) 4.6 (2.6) 9.8 (4.8) 9.2 (4.9) 11.5 (4.0) 11.3 (4.6) 10.7 (4.8) 13.4 (3.2) Cpf Dental parameters U1f 55.2 (5.1) 55.6 (5.5) 53.9 (3.8) 53.4 (4.7) 53.5 (4.9) 52.9 (4.3) U1rf 34.3 (4.2) 34.9 (4.5) 32.4 (2.5) 31.3 (3.8) 31.6 (4.0) 30.7 (2.8) 55.6 (5.2) 56.3 (5.6) 53.4 (2.7) 52.4 (4.3) 52.4 (4.5) 52.3 (3.8) L1f L1rf 74.8 (6.1) 75.5 (6.4) 72.5 (4.8) 71.5 (5.1) 71.8 (5.2) 70.7 (4.7) U6f 47.6 (4.4) 48.0 (4.5) 46.7 (4.0) 44.1 (4.3) 44.3 (4.4) 43.4 (4.2) L6f 54.0 (18.6) 53.7 (21.4) 55.0 (4.4) 50.7 (17.3) 49.9 (19.8) 53.2 (4.9) Occlusal vertical dimension VD 11.8 (3.3) 12.6 (3.3) 9.2 (2.0) 9.9 (1.9) 9.6 (1.7) 11.0 (2.2) Final mandibular Overall mean (SD) 5 7.6 (4.7) Nonincreased VD mean setback (Bs20 ) (SD) 5 7.8 (0.2)
1 factor influencing the postoperative skeletal changes. If a patient's VD was maintained within the presurgical VD (the nonincreased VD group), the surgical horizontal movement of B-point (Bs10 ) alone explained 92% of its final horizontal movement (Bs20 ). Approximately 79% of the surgical movement of B-point was reflected in the final mandibular setback (Bs20 ), and the remaining 21% as relapse from the SFA. In the nonincreased VD group, the postoperative vertical dimension of occlusion was not increased. This might have resulted from the
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Surgical movement-related variables (DT1-T0) Overall group, mean (SD)
Nonincreased Increased VD group, VD group, mean (SD) mean (SD)
0.5 (2.3) 0.3 (2.4)
0.4 (2.5) 0.2 (2.4)
0.8 (1.9) 0.7 (2.2)
8.4 (5.7) 7.3 (6.2) 7.7 (6.2)
8.7 (6.1) 7.3 (6.8) 7.8 (6.8)
7.3 (4.3) 7.1 (3.9) 7.2 (4.0)
0.7 (1.6) 0.5 (1.7)
0.5 (1.3) 0.4 (1.4)
1.4 (2.1) 1.0 (2.4)
0.2 (2.9) 0.6 (2.3) 8.6 (4.8) 8.3 (5.6) 0.2 (2.2) 8.3 (5.9)
0.0 (2.9) 0.4 (2.2) 9.3 (5.0) 8.6 (6.1) 0.2 (2.3) 8.9 (6.2)
0.8 (3.0) 1.3 (2.7) 6.6 (3.5) 7.6 (4.0) 0.3 (2.1) 6.6 (4.4)
3.0 (2.0) 4.7 (2.8)
3.3 (2.0) 4.7 (2.8)
2.1 (1.7) 4.8 (2.8)
2.9 (3.5) 3.7 (3.8) 4.0 (3.5)
3.7 (3.2) 4.4 (3.7) 4.9 (3.3)
0.4 (3.0) 1.4 (3.6) 1.5 (3.0)
0.8 (2.1) 1.5 (2.1)
0.4 (2.1) 1.4 (2.2)
1.7 (1.5) 1.9 (1.8)
1.8 (2.6) 3.0 (2.2) 3.2 (3.4) 3.2 (2.7) 3.6 (1.8) 3.3 (2.8)
2.1 (2.8) 3.4 (2.0) 3.9 (3.3) 3.7 (2.8) 3.6 (1.6) 3.8 (2.5)
1.0 (2.0) 1.8 (2.5) 1.0 (2.6) 1.8 (1.8) 3.3 (2.4) 1.8 (3.1)
1.8 (3.1) 3.0 (2.4) 1.8 (2.4) Increased VD mean (SD) 5 7.1 (2.3)
postoperatively reasonable occlusal intercuspation and aligned arch coordination, even without presurgical orthodontic treatment. Al-Delayme et al14 reported on skeletal relapse after skeletal Class III deformity correction for patients having double-jaw surgeries. One year after surgery, B-point had relapsed by 1.3 6 5.7 mm, representing 38.6% of the mandibular setback. Proffit et al15 reported a B-point relapse of 2.7 mm (adjusted mean) 1 year after surgery. Relative to the relapse typically incurred in conventional orthognathic surgery,
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Table IV. Sample size validation Observed R2 Cohen's effect size f2 Statistical power level Number of predictors Alpha Minimum required sample size at 99% power level Size of sample used
Overall group 0.87 6.14 0.99 3 0.01 (0.05) 13 (11*) 40
Nonincreased VD group 0.92 11.50 0.99 1 0.01 (0.05) 7 (5*) 29
Increased VD group 0.94 15.67 0.99 4 0.01 (0.05) 9 (7*) 11
*Minimum required sample size when statistical power level is 0.95.
Table V. Summary of derived regression models for final mandibular setback (Bs20 ) Adjusted F P value Coefficient t Summary statistics R2 R2 statistic (F statistic) estimate 6 SE value Overall model indicators (n 5 40) Model statistics 0.87 0.86 59.90 0.0000 Intercept 14.33 6 4.07 3.52 Surgical setback of B-point (Bs10 ) 0.36 6 0.14 2.44 Surgical setback of menton (Mes10 ) 0.34 6 0.13 2.63 Postsurgical horizontal A-point 0.23 6 0.06 3.55 position (As1 ) Postsurgical vertical level of 0.18 6 0.06 2.81 coronoid process (Cpf1 ) Predicted final mandibular setback Bs20 5 14:33 1 0:36 3 Bs10 1 0:34 3 Mes10 1 0:23 3 As1 0:18 3 Cpf1 Nonincreased VD model indicators (n 5 29) Model statistics 0.92 0.91 291.00 0.0000 Intercept 0.98 6 0.50 1.97 Surgical setback of B-point (Bs10 ) 0.79 6 0.05 17.06 Predicted final mandibular setback Bs20 5 0:98 1 0:79 3 Bs10 Increased VD model indicators (n 5 11) Model statistics 0.94 0.91 35.00 0.0001 Intercept 53.00 6 7.75 6.84 Surgical upward movement 0.76 6 0.14 5.35 of pogonion (Pogf10 ) Postsurgical horizontal A-point 0.80 6 0.11 7.06 position (As1 ) Postsurgical vertical level of 0.47 6 0.09 5.48 coronoid process (Cpf1 ) Predicted final mandibular setback Bs20 5 53:00 0:76 3 Pogf10 1 0:80 3 As1 0:47 3 Cpf1
P DW statistic value (P value) VIF* 1/VIF* 2.28 (0.356) 0.0012 0.0200 0.0126 0.0011
8.187 0.122 7.948 0.126 1.025 0.975
0.0080
1.091 0.916
2.39 (0.346) 0.0589 0.0000
1.93 (0.852) 0.0002 0.0011
1.840 0.544
0.0002
1.935 0.517
0.0009
1.071 0.934
DW, Durbin-Watson; VIF, variance inflation factor. *VIF higher than 10 suggests linear relationship between predictors; 1/VIF (tolerance statistic) below 0.1 indicates multicollinearity.
our 21% result for the nonincreased VD model was clinically acceptable.14,15 On the other hand, with regard to the increased VD group, the postoperative mandibular forward movement could have been affected by the downward surgical movement of pogonion (Pogf10 ), the horizontal position of A-point at T1 (As1 ), and the vertical position of Cp point at T1 (Cpf1 ). These latter 2 predictors—the horizontal position of the postsurgical A-point (As1 ) and the vertical position of Cp point (Cpf1 )—were 80% and 47% reflected in the final mandibular setback extent (Bs20 ), respectively. In the increased VD group, the maxillary second molar extrusion often induced increased VD. The
counterclockwise rotation of pogonion was shown during postoperative orthodontic treatment, including intrusion of the extruded molars. With respect to the change of pogonion, there were correlations with proximal and distal segment displacements during the healing process. Proffit et al15 and Hwang et al10 insisted that gonion and the proximal segments are closely related to postoperative relapse. This is consistent with the increased VD model variables in this study (Table III). Whereas the maxilla and the mandible are relocated by osteotomies, which are relatively controllable, the coronoid process is relatively difficult to place at the attempted position, making overcorrection in an
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Fig 2. Multivariate model-relevant landmarks and indicators for estimation of final mandibular setback (Bs20 ): A, predictor variables for prediction model based on all 40 subjects; B, predictor variables for nonincreased VD patients; C, predictor variables for increased VD patients. The Cpf1 notations indicate the predicator variables of the coronoid process to the FH plane at T1: As1 for Apoint to S-perp at T1, Bs10 for surgical setback of B-point from T0 to T1, Mes10 for surgical setback of menton from T0 to T1, and Pogf10 for surgical upward movement of pogonion from T0 to T1, based on the derived multivariate prediction models of the predicted final mandibular setback (overall), Bs20 5 14:33 1 0:36 3 Bs10 1 0:34 3 Mes10 1 0:23 3 As1 0:18 3 Cpf1 ; nonincreased VD, Bs20 5 0:98 1 0:7 3 Bs10 ; and increased VD, Bs20 5 53:00 0:76 3 Pogf10 1 0:80 3 As1 0:47 3 Cpf1 :
increased VD group less predictable. Costa et al16 reviewed the usage of condylar positioning devices, concluding that there was no scientific evidence to support their routine use in orthognathic surgery. This means that postoperative manual condylar positioning is sensitive to the oral surgeon's technique. Therefore, to obtain the predicted SFA treatment outcome in an increased VD group, the postoperative vertical position of the Cp (Cpf1 ) should be controllable. Hwang et al10 argued that intentional manual positioning affects the position of B-point after surgery. In the case of the increased VD in the SFA, postoperative orthodontic treatment can encounter a number of difficulties because of the unpredictability of the vertical position of the Cp at T1 (Cpf1 ). For example, the predictability of SFA treatment outcomes can be compromised. Therefore, orthodontists and oral surgeons should be concerned that the more increased the VD after surgery, the less predictable the position of B-point at the posttreatment stage. From the results, the surgical horizontal movement of B-point (Bs10 ) was not included as a variable in the increased VD model. However, the results could not mean that the surgical horizontal movement of B-point (Bs10 ) did not affect the final mandibular position, because the information of Bs10 might overlap the information of Pogf10 ; As1 ; and Cpf1 , since those variables were all correlated in the SFA. There were some reasons that the surgical horizontal movement of B-point (Bs10 )
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was not included as a variable in the increased VD model. First, this regression model did not have the multicollinearity problem. Many clinical studies for dental research have used multiple regression analysis to find the correlations between the predictor and the outcome variables. However, a possible problem from the use of multiple regression analysis is collinearity. In statistics, when there are more than 2 covariates that are highly correlated, this is called multicollinearity. The interpretation of the statistical results from multiple regression models might be distorted from multicollinearity, causing increased inaccuracy and uncertainty. This should be considered in the regression model. Especially, both segments (proximal and distal) after surgery were closely correlated. The cephalometric landmarks in the same segment also were highly correlated. Our multivariate model showed the VIF, which was less than 2. This indicated that the model did not have a multicollinearity problem. If the increased VD model included Bs10 as a variable, multicollinearity problems would be incurred. However, we built the best regression model without multicollinearity problems. In the increased VD model, these variables (Pogf10 ; As1 ; and Cpf1 ), rather than Bs10 , showed a high correlation. The information of the surgical horizontal movement of B-point (Bs10 ) already overlapped with variables (Pogf10 ; As1 ; and Cpf1 ) in the increased VD model. Therefore, this model meant that these variables
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had more strongly influenced the final mandibular position. To determine the effect of VD on the final mandibular setback, the derived prediction models used the overall 40 patients' predictor variables (Fig 2, A). Regardless of the patient classification, a shorter VD at T1 was in turn more likely to achieve better surgical results in the Class III SFA. As in previous studies, occlusal interference, which can increase the occlusal vertical dimension, presumably played a role in postsurgical relapse: our result identifying postsurgical VD as a patient classifier is consistent with that literature.1,5 Indeed, VD was confirmed to be a significant predictive factor for final mandibular setback and, on that basis, a valid patient-classification criterion. As for the shortcomings of our study, first, it was based on a 2-dimensional analysis incorporating CBCT-generated cephalograms, wherein the predictor variables representing the skeletal landmark positions were 2-dimensional projections of the actual 3-dimensional distances. Therefore, for improved prediction model precision, a 3-dimensional analysis of postsurgical skeletal stability should follow this study. Second, for general application of the derived prediction model to patients operated on by other surgeons in different hospitals, a multicenter study should be undertaken. Last, a cast model analysis should be performed to improve the precision of the measurements.
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CONCLUSIONS
Using derived regression models, predictor-specific skeletal analysis and model-based determination of overcorrection is possible during SFA treatment planning. Studying the mandibular position in relation to the postsurgical VD, our investigation highlighted the importance of vertical control of the mandible for skeletal Class III SFA patients. Orthodontists and oral surgeons should be alert to the fact that the more increased the vertical occlusal dimension after surgery, the less predictable the position of B-point at the posttreatment stage. REFERENCES
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1. Baek SH, Ahn HW, Kwon YH, Choi JY. Surgery-first approach in skeletal class III malocclusion treated with 2-jaw surgery: evaluation of
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surgical movement and postoperative orthodontic treatment. J Craniofac Surg 2010;21:332-8. Nagasaka H, Sugawara J, Kawamura H, Nanda R. “Surgery-first” skeletal class III correction using the skeletal anchorage system. J Clin Orthod 2009;43:97-105. Liou EJ, Chen PH, Wang YC, Yu CC, Huang CS, Chen YR. Surgeryfirst accelerated orthognathic surgery: postoperative rapid orthodontic tooth movement. J Oral Maxillofac Surg 2011;69:781-5. Liou EJ, Chen PH, Wang YC, Yu CC, Huang CS, Chen YR. Surgeryfirst accelerated orthognathic surgery: orthodontic guidelines and setup for model surgery. J Oral Maxillofac Surg 2011;69:771-80. Ko EW, Lin SC, Chen YR, Huang CS. Skeletal and dental variables related to the stability of orthognathic surgery in skeletal Class III malocclusion with a surgery-first approach. J Oral Maxillofac Surg 2013;71:e215-23. Leelasinjaroen P, Godfrey K, Manosudprasit M, Wangsrimongkol T, Surakunprapha P, Pisek P. Surgery first orthognathic approach for skeletal Class III malocclusion corrections—a literature review. J Med Assoc Thai 2012;95:S172-80. Kim JH, Mahdavie NN, Evans CA. Guidelines for “surgery first” orthodontic treatment. In: Bourzgui F, editor. Orthodontics—basic aspects and clinical considerations. Available at: http://www. intechopen.com/books/orthodontics-basic-aspects-and-clinicalconsiderations/orthodontic-guidelines-for-the-surgery-first-treat ment-of-severe-malocclusions. Accessed May 1, 2013. Guglielmi M, Schneider KM, Iannetti G, Feng C, Martinez AY. Orthognathic surgery for correction of patients with mandibular excess: don’t forget to assess the gonial angle. J Oral Maxillofac Surg 2013;71:e1063-72. Kor HS, Yang HJ, Hwang SJ. Relapse of skeletal class III with anterior open bite after bimaxillary orthognathic surgery depending on maxillary posterior impaction and mandibular counterclockwise rotation. J Craniomaxillofac Surg 2014;42:e230-8. Hwang DS, Kim YI, Lee KM. Effect of intended manual condylar positioning on skeletal and dental changes in skeletal Class III deformities: CBCT-generated half-cephalograms. J Craniomaxillofac Surg 2014;42:7-12. Choi JH, Mah J. A new method for superimposition of CBCT volumes. J Clin Orthod 2010;44:303-12. Myers R. Classical and modern regression with application. 2nd ed. Boston: Duxbury; 1990. p. 12-20. Dattalo P. Determining sample size: balancing power, precision, and practicality. New York: Oxford University Press; 2008. p. 11-37. Al-Delayme R, Al-Khen M, Hamdoon Z, Jerjes W. Skeletal and dental relapses after skeletal class III deformity correction surgery: single-jaw versus double-jaw procedures. Oral Surg Oral Med Oral Pathol Oral Radiol 2013;115:466-72. Proffit WR, Phillips C, Turvey TA. Stability after mandibular setback: mandible-only versus 2-jaw surgery. J Oral Maxillofac Surg 2012;70:e408-14. Costa F, Robiony M, Toro C, Sembronio S, Polini F, Politi M. Condylar positioning devices for orthognathic surgery: a literature review. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008; 106:179-90.
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Effect of occlusal vertical dimension changes on postsurgical skeletal changes in a surgery-first approach for skeletal Class III deformities Jihyun Lee,a Yong-Il Kim,b Dae-Seok Hwang,c Ki Beom Kim,d and Soo-Byung Parke Busan and Yangsan, South Korea, and St Louis, Mo
Introduction: The purposes of this study were to investigate the relationship between occlusal vertical dimension (VD) changes and postsurgical skeletal changes in the surgery-first approach and to derive regression models for the final mandibular setback at B-point. Methods: This retrospective study included 40 patients (16 men, 24 women; ages, 22.6 6 4.0 years) who had undergone a bimaxillary surgery-first approach. Using cephalograms generated from cone-beam computed tomography representing the presurgical, postsurgical, and posttreatment stages, skeletal landmarks in the maxilla and mandible were investigated to derive multivariate linear regression-based prediction models. Additionally, a patient classification based on the VD was established and verified to generate regression models for the classified groups. Results: For the nonincreased VD group, the surgical setback of B-point was its predictor for the final mandibular setback (R2 at 92%). Meanwhile, the final mandibular setback of the increased VD group was predicted according to the surgical upward movement of pogonion, the postsurgical horizontal position of A-point, and the postsurgical vertical position of the coronoid process (R2 at 94%). Conclusions: The results of this study support the clinical observation that the more increased the vertical occlusal dimension after surgery, the less predictable the position of B-point at the posttreatment stage. (Am J Orthod Dentofacial Orthop 2014;146:612-9)
T
he surgery-first approach (SFA) is characterized by minimal presurgical orthodontic treatment and orthognathic surgery followed by postsurgical orthodontic treatment. The application of SFA has recently been increasing with the publication of reports1-7 emphasizing its advantages, which include increased patient cooperation, effective compensation, and a
a Postgraduate student, Department of Orthodontics, Pusan National University Hospital, Busan, South Korea. b Assistant professor, Department of Orthodontics, Dental Research Institute, Pusan National University Dental Hospital, Busan, South Korea. c Assistant professor, Department of Oral & Maxillofacial Surgery, Pusan National University Hospital, Busan, South Korea. d Associate professor, Department of Orthodontics, Center for Advanced Dental Education, St Louis University, St Louis, Mo. e Professor, Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Supported by a 2-year research grant from Pusan National University. Address correspondence to: Yong-Il Kim, Department of Orthodontics, School of Dentistry, Pusan National University, Gudeokro 137, Seogu, Busan 602-739, South Korea; e-mail, [email protected]. Submitted, February 2014; revised and accepted, July 2014. 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.07.024
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shortened treatment period.3,4 However, because presurgical orthodontic treatments such as dental decompensation and arch coordination are rarely performed in the SFA, postsurgical occlusal instability clinically leads to more severe forward postoperative mandibular movement than in conventional surgical orthodontic treatment for patients with a skeletal Class III deformity.1,3,4,6,7 Accordingly, the surgical treatment objective for the SFA, often designated as mandibular setback from the horizontal B-point position at the presurgical stage (T0) to the position at the removal of the orthodontic appliance at the posttreatment stage (T2), is not equivalent to the extent of the surgical mandibular setback at T0 to the position immediately after surgery (T1), because of the extent of postoperative mandibular movement from T1 to T2 during active orthodontic treatment. This complicates accurate prediction and simulation of postoperative orthodontic treatment. Therefore, clinical experience is needed for accurate prediction of postoperative orthodontic treatment and assessment of skeletal discrepancy. As for conventional orthognathic surgery, the gonial angle8 and the mandibular occlusal plane angle9 have
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been suggested to correlate with mandibular relapse. Ko et al,5 contrastingly, reported overbite to be a predictor of the extent of vertical mandibular relapse in the SFA. However, in their study, overbite was found to explain only 25.9% of the variation of vertical mandibular relapse, leaving the remaining 74.1% unexplained. Moreover, to support the clinical observation that an increased occlusal vertical dimension (VD) at T1 is related to a strong likelihood of more severe postsurgical mandibular forward movement in the SFA, the factors related to postoperative skeletal changes should be investigated. Among them, the relationship of occlusal VD changes to postoperative skeletal changes is especially relevant. Therefore, the purposes of this study were to investigate the relationship between VD changes and postsurgical skeletal changes in the SFA to orthodontic treatment and to estimate the extent of final mandibular setback (DT2-T0). The specific aims of the study were (1) to derive a prediction model of the final mandibular setback extent at B-point (DT2-T0) as the sum of the observed surgical setback (DT1-T0) and the postoperative mandibular forward movement (DT2-T1), and (2) to assess the correlation between VD changes and mandibular movements during postoperative orthodontic treatment to support the clinical significance of postsurgical VD change. MATERIAL AND METHODS
This study was a retrospective study of 40 patients with skeletal Class III deformities (16 men, 24 women; mean age, 22.6 6 4.0 years) who had undergone bimaxillary surgery with the SFA in the Departments of Oral & Maxillofacial Surgery and Orthodontics at Pusan National University Hospital in South Korea. The exclusion criteria were patients with extractions, severe facial asymmetry, cleft lip and palate, and temporomandibular joint disorders (Table I). LeFort I osteotomy and modified Hunsuck sagittal split ramus osteotomy with rigid internal fixation were performed on all patients by 2 surgeons (D.-S.H. and Y.-I.K.), followed by active orthodontic treatment an average of 1 month later. This study was reviewed and approved by the institutional review board of Pusan National University Hospital (E-2011069). Preliminarily, predictor-variable data were compiled as 2-dimensional coordinates of each skeletal landmark, extracted from cephalograms generated by cone-beam computed tomography (CBCT) with ray-cast and maximum intensity projection using CBCT superimposition10 (Fig 1). CBCT images (DCT Pro; Vatech, Seoul, Korea) were obtained at T0, T1, and T2 with the scanner set at a 20 3 19-cm field of view, 90 kVp, 4.0-mA tube
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current, and scan time of 24 seconds. To create CBCT-generated half-cephalograms, the CBCT data were reformatted to 3-dimensional images with imaging software (Ondemand 3D; Cybermed, Seoul, Korea), superimposed on the anterior cranial base to obtain ray-cast and maximum intensity projection from the right side of the subjects,10,11 and digitized by software (V-ceph version 6.0; Osstem Implant, Seoul, Korea). All measurements were repeated 2 weeks later by the same investigator (J.L.), and the measured data were validated according to the systematic intraexaminer error, with the mean of the 2 measurements used to calculate the corresponding distances of each landmark from the Frankfort horizontal (FH) and sella-perpendicular (S-perp) planes, respectively. The intraclass correlation coefficient for the systematic intraexaminer error was 0.994 (0.990-0.996), and the intraobserver reliability was high for all measurements. Then, using the coordinates obtained at T0, T1, and T2, both the horizontal and the vertical distances of each landmark from the reference planes were calculated, along with the corresponding increment or decrement in such distances over the periods of T0 to T1 (DT1T0) and T1 to T2 (DT2-T1); the corresponding predictor variables were designated as surgical movement (DT1T0) and postsurgical movement (DT2-T1) of each landmark. As for the horizontal position of B-point, the change in its distance from the S-perp plane from T0 to T2 (DT2-T0) was calculated (Fig 1, Table II). The final setback of B-point was predicted by multivariate regression analysis; 78 potential predictors, compiled as described above, were investigated to obtain the best-fit prediction model.12 The model selection criteria for viable predictors were as follows: (1) a high adjusted R2, (2) a statistically significant coefficient estimate, (3) no multicollinearity with respect to statistical model diagnosis, and (4) the fewer predictors the better (Table III). Upon identification of the best-fit prediction model, another regression analysis of patient groups classified based on VD increment was carried out, and the VD of each patient was defined as the distance from the mesial contact of the mandibular first molar to that of the maxillary first molar as projected onto the S-perp plane (Table II). For the 29 patients whose VD had not increased after surgery at T1, classified accordingly as the nonincreased occlusal VD (nonincreased VD) group, a prediction model designated as the nonincreased VD model was constructed by following the same model selection process as with the previously identified general model for the overall 40patient group. A prediction model for the remaining 11 patients whose VD had increased after surgery at T1, designated as the increased VD model, was constructed
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Table I. Demographic data of the subjects Sample size (n) Sex Mean age (y) Maxillary surgical setback (mm)* Mandibular surgical setback (mm)y Final mandibular setback (mm)z
Overall group, mean (SD) 40 24 women, 16 men 22.6 (4.0) 0.5 (2.3) 8.4 (5.7) 7.6 (4.7)
Nonincreased VD group, mean (SD) 29 15 women, 14 men 21.9 (3.5) 0.4 (2.5) 8.7 (6.1) 7.8 (5.1)
Increased VD group, mean (SD) 11 9 women, 2 men 24.4 (5.0) 0.8 (1.9) 7.3 (4.3) 7.1 (3.6)
*Horizontal movement of A-point from T0 to T1 (A10); yhorizontal movement of B-point from T0 to T1 (B10); zfinal mandibular setback measured as horizontal movement of B-point from T0 to T2 (B20).
Fig 1. Landmarks and linear measurements. The distances were measured from the Frankfort horizontal (FH) plane (vertical) and the sella-perpendicular (S-perp) plane (horizontal) to each landmark. Condylion (Cd), Most superior point of condyle head; coronoid process (Cp), tip of the coronoid process; U1t and L1t, mandibular and maxillary first incisor tips; U1r and L1r, mandibular and maxillary first incisor root apices; U6mc and L6mc, mandibular and maxillary first molar mesial contacts; occlusal VD, distance between mesial contact points of the mandibular right first molar and the maxillary right first molar as projected onto the S-perp plane.
increased VD models was characterized by relatively high adjusted R2 values indicating high predictive power. Based on these R2 values of the models, the minimum required sample size for each corresponding model was calculated using the Cohen effect size f2 (Table IV).13 Moreover, the regression models, as required by the variance inflation factor (VIF)based model diagnostic method, were not tethered by multicollinearity. According to this result, wherein multicollinearity-free models were found, the calculation of the final setback of B-point upon a change of at least 1 predictor variable was feasible for the general patient group, even for the nonincreased VD and increased VD patients, at an improved explanatory power (Table V). As for prediction of the final setback (DT2-T0) (Fig 2, A) of B-point from T0 to T2 (Bs20 ), the following predictor set among all possible predictor sets was found to explain it: the surgical setback of B-point (DT1-T0, horizontal measurement notated as Bs10 ) and menton (DT1-T0, horizontal measurement notated as Mes10 ), the postsurgical horizontal position of A-point (T1, notated as As1 ), and the vertical position of the coronoid process (T1, notated as Cpf1 ). According to this predictor set, the following multivariate regression equation was verified as a general prediction model for the overall 40-patient group with its adjusted R2 at 87% (P \0.000) (Table V). Predicted final mandibular setback Bs20 5 14:33 1 0:36 3 Bs10 1 0:34 3 Mes10 10:23 3 As1 0:18 3 Cpf1
in the same way as the nonincreased VD model. For the statistical analysis of the multivariate regression, Language R (Vienna, Austria), an open-source software program for statistical computation, was used. RESULTS
The general model for the overall 40-patient group and the respective nonincreased VD and
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The prediction models of the final mandibular setback (DT2-T0) varied by the occlusal VD changes (Fig 2, B and C). For the nonincreased VD group, the identified regression model was univariate, validating only the surgical setback of B-point (DT1-T0, Bs10 ) as its predictor for the final mandibular setback (Bs20 ), with its adjusted R2 at 92% (P \0.000). Meanwhile, the final
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Table II. Model-relevant landmarks, planes, distances, and indicators Terms Landmarks B-point (B) Menton (Me) Pogonion (Pog) A-point (A) Coronoid process (Cp) Planes Frankfort horizontal (FH) plane Midsagittal reference (MSR) plane S-perpendicular plane (S-perp) Distances B-point to S-perp (Bs) Menton to S-perp (Mes) Pogonion to FH plane (Pogf) A-point to S-perp (As) Coronoid process to FH plane (Cpf) Occlusal vertical dimension (VD) Indicators Final setback of B-point (Bs20 ) Surgical setback of B-point (Bs10 ) Surgical setback of menton (Mes10 ) Surgical upward movement of pogonion (Pogf10 ) Postsurgical horizontal position of A-point (As1 ) Postsurgical vertical position of coronoid process (Cpf1 ) Patient classification criteria Vertical occlusal dimension (VD) Nonincreased VD Increased VD
Definitions Innermost curvature from chin to alveolar bone junction Lowest point on symphysis of mandible Most anterior point on contour of chin Innermost curvature from maxillary anterior nasal spine to crest of maxillary alveolar process Tip of coronoid process Plane formed by right Pog and both sides of orbitale Perpendicular to FH plane and passing through nasion and basion Perpendicular to FH and MSR planes and passing through sella Distance from B-point to S-perpendicular plane Distance from menton to S-perpendicular plane Distance from pogonion to FH plane Distance from A-point to S-perpendicular plane Distance from tip of coronoid process to FH plane Distance from mesial contact of mandibular first molar to that of maxillary first molar as projected onto S-perpendicular plane Bs changes from T0 to T2, final mandibular movement over presurgical (T0) to posttreatment period (T2) Bs changes from T0 to T1, surgical movement over presurgical (T0) to postsurgical period (T1) Mes changes from T0 to T1, surgical movement over presurgical (T0) to postsurgical period (T1) Pogf changes from T0 to T1, surgical movement over presurgical (T0) to postsurgical period (T1) Distance from A-point to S-perpendicular plane measured at T1 Distance from tip of coronoid process to FH plane measured at T1
Distance from mesial contact of mandibular first molar to that of maxillary first molar VD measured at T1 not increased from VD at T0 VD measured at T1 increased from VD at T0
mandibular setback (Bs20 ) of the increased VD group was predicted by surgical upward movement of pogonion (DT1-T0, vertical measurement notated as Pogf10 ), the postsurgical horizontal position of A-point (T1, notated as As1 ), and the vertical position of the coronoid process (T1, notated as Cpf1 ), with the adjusted R2 at 94% (P \0.0001) (Table V). The following equations were derived for the nonincreased VD and increased VD groups. For the nonincreased VD group; Bs20 5 0:98 1 0:7 3 Bs10
horizontal movement of the mandible (Bs10 ) but, rather, its vertical movement (Pogf10 ), which is the only predictor of its distal segment; this implies that if a patient's VD increases after surgery, the surgical vertical movement of the mandible is a concern for the extent of relapse rather than its horizontal movement. As shown below, this equation has a 0.1757 coefficient of determination, indicating that approximately 18% of the variation in vertical movement of the mandible during surgery (Pogf10 ) could be explained by the surgical change of VD (VD10) (r 5 0.5409). Pogf10 5 2:670410:54091VD10 ; R2 50:1757ðP\0:05Þ
For the increased VD group; Bs20 5 53:00 0:76 3 Pogf10 1 0:80 3 As1 0:473Cpf1 There was a relationship between VD changes and postsurgical skeletal changes (DT2-T1). What best characterizes the increased VD outcome was not the surgical
DISCUSSION
After the SFA in this study, the orthodontists encountered increased VD resulting from premature contacts, which led to forward mandibular movement postoperatively. The results showed that the VD change was
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Table III. Variables tested for multivariate regression model Presurgical (T0) variables
Postsurgical (T1) variables
Overall Nonincreased Increased group, VD group, VD group, mean (SD) mean (SD) mean (SD)
Overall Nonincreased Increased group, VD group, VD group, mean (SD) mean (SD) mean (SD)
Horizontal parameters Maxilla As 62.5 (4.4) 62.3 (4.7) 63.3 (3.5) 63.0 (4.5) 62.7 (4.4) 64.0 (4.8) PNSs 20.0 (3.1) 20.0 (3.0) 20.2 (3.3) 20.3 (3.1) 20.1 (3.1) 20.9 (3.4) Distal segment of mandible Bs 66.6 (7.0) 66.9 (7.4) 65.4 (5.6) 58.2 (6.7) 58.2 (7.1) 58.1 (5.4) 68.3 (7.5) 68.6 (8.1) 67.4 (5.7) 61.1 (7.4) 61.3 (8.0) 60.4 (5.5) Pogs Mes 62.1 (7.4) 62.4 (8.0) 61.2 (5.5) 54.4 (7.0) 54.5 (7.6) 54.0 (5.1) Proximal segment of mandible Cds 12.0 (3.3) 12.2 (3.4) 11.2 (3.4) 11.2 (3.4) 11.7 (3.5) 9.8 (3.0) 25.1 (3.7) 25.4 (4.0) 24.4 (2.6) 25.7 (3.8) 25.7 (4.1) 25.4 (2.5) Cps Dental parameters U1s 69.3 (5.0) 69.2 (5.5) 69.9 (3.7) 69.1 (5.2) 69.2 (5.3) 69.0 (5.3) 58.3 (4.5) 58.1 (4.9) 58.9 (3.2) 58.9 (4.8) 58.5 (4.8) 60.2 (4.7) U1rs L1s 70.7 (6.6) 71.3 (7.0) 69.2 (5.2) 62.1 (5.6) 62.0 (6.0) 62.5 (4.8) L1rs 63.7 (7.2) 64.0 (7.6) 62.8 (6.0) 55.4 (6.8) 55.4 (7.2) 55.2 (5.8) U6s 43.3 (4.2) 42.9 (4.3) 44.3 (4.1) 43.5 (4.7) 43.1 (4.6) 44.6 (5.2) 47.1 (17.6) 47.0 (20.3) 47.4 (4.7) 38.8 (14.4) 38.1 (16.4) 40.8 (5.5) L6s Vertical parameters Maxilla Af 31.2 (3.3) 31.5 (3.6) 30.4 (2.3) 28.2 (3.5) 28.2 (3.7) 28.3 (2.8) 24.9 (2.8) 24.9 (3.0) 25.0 (2.1) 20.2 (3.9) 20.3 (4.1) 20.2 (3.5) PNSf Distal segment of mandible Bf 77.9 (6.5) 78.7 (7.0) 75.4 (4.3) 75.0 (5.4) 75.1 (5.7) 75.0 (4.7) Pogf 91.8 (8.0) 92.5 (8.6) 89.6 (5.7) 88.1 (6.6) 88.1 (7.0) 88.3 (5.1) 98.3 (8.1) 99.2 (8.5) 95.8 (6.3) 94.3 (6.6) 94.3 (6.7) 94.3 (6.6) Mef Proximal segment of mandible Cdf 2.6 (2.0) 2.5 (2.2) 2.9 (1.3) 3.4 (2.4) 3.0 (2.3) 4.6 (2.6) 9.8 (4.8) 9.2 (4.9) 11.5 (4.0) 11.3 (4.6) 10.7 (4.8) 13.4 (3.2) Cpf Dental parameters U1f 55.2 (5.1) 55.6 (5.5) 53.9 (3.8) 53.4 (4.7) 53.5 (4.9) 52.9 (4.3) U1rf 34.3 (4.2) 34.9 (4.5) 32.4 (2.5) 31.3 (3.8) 31.6 (4.0) 30.7 (2.8) 55.6 (5.2) 56.3 (5.6) 53.4 (2.7) 52.4 (4.3) 52.4 (4.5) 52.3 (3.8) L1f L1rf 74.8 (6.1) 75.5 (6.4) 72.5 (4.8) 71.5 (5.1) 71.8 (5.2) 70.7 (4.7) U6f 47.6 (4.4) 48.0 (4.5) 46.7 (4.0) 44.1 (4.3) 44.3 (4.4) 43.4 (4.2) L6f 54.0 (18.6) 53.7 (21.4) 55.0 (4.4) 50.7 (17.3) 49.9 (19.8) 53.2 (4.9) Occlusal vertical dimension VD 11.8 (3.3) 12.6 (3.3) 9.2 (2.0) 9.9 (1.9) 9.6 (1.7) 11.0 (2.2) Final mandibular Overall mean (SD) 5 7.6 (4.7) Nonincreased VD mean setback (Bs20 ) (SD) 5 7.8 (0.2)
1 factor influencing the postoperative skeletal changes. If a patient's VD was maintained within the presurgical VD (the nonincreased VD group), the surgical horizontal movement of B-point (Bs10 ) alone explained 92% of its final horizontal movement (Bs20 ). Approximately 79% of the surgical movement of B-point was reflected in the final mandibular setback (Bs20 ), and the remaining 21% as relapse from the SFA. In the nonincreased VD group, the postoperative vertical dimension of occlusion was not increased. This might have resulted from the
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Surgical movement-related variables (DT1-T0) Overall group, mean (SD)
Nonincreased Increased VD group, VD group, mean (SD) mean (SD)
0.5 (2.3) 0.3 (2.4)
0.4 (2.5) 0.2 (2.4)
0.8 (1.9) 0.7 (2.2)
8.4 (5.7) 7.3 (6.2) 7.7 (6.2)
8.7 (6.1) 7.3 (6.8) 7.8 (6.8)
7.3 (4.3) 7.1 (3.9) 7.2 (4.0)
0.7 (1.6) 0.5 (1.7)
0.5 (1.3) 0.4 (1.4)
1.4 (2.1) 1.0 (2.4)
0.2 (2.9) 0.6 (2.3) 8.6 (4.8) 8.3 (5.6) 0.2 (2.2) 8.3 (5.9)
0.0 (2.9) 0.4 (2.2) 9.3 (5.0) 8.6 (6.1) 0.2 (2.3) 8.9 (6.2)
0.8 (3.0) 1.3 (2.7) 6.6 (3.5) 7.6 (4.0) 0.3 (2.1) 6.6 (4.4)
3.0 (2.0) 4.7 (2.8)
3.3 (2.0) 4.7 (2.8)
2.1 (1.7) 4.8 (2.8)
2.9 (3.5) 3.7 (3.8) 4.0 (3.5)
3.7 (3.2) 4.4 (3.7) 4.9 (3.3)
0.4 (3.0) 1.4 (3.6) 1.5 (3.0)
0.8 (2.1) 1.5 (2.1)
0.4 (2.1) 1.4 (2.2)
1.7 (1.5) 1.9 (1.8)
1.8 (2.6) 3.0 (2.2) 3.2 (3.4) 3.2 (2.7) 3.6 (1.8) 3.3 (2.8)
2.1 (2.8) 3.4 (2.0) 3.9 (3.3) 3.7 (2.8) 3.6 (1.6) 3.8 (2.5)
1.0 (2.0) 1.8 (2.5) 1.0 (2.6) 1.8 (1.8) 3.3 (2.4) 1.8 (3.1)
1.8 (3.1) 3.0 (2.4) 1.8 (2.4) Increased VD mean (SD) 5 7.1 (2.3)
postoperatively reasonable occlusal intercuspation and aligned arch coordination, even without presurgical orthodontic treatment. Al-Delayme et al14 reported on skeletal relapse after skeletal Class III deformity correction for patients having double-jaw surgeries. One year after surgery, B-point had relapsed by 1.3 6 5.7 mm, representing 38.6% of the mandibular setback. Proffit et al15 reported a B-point relapse of 2.7 mm (adjusted mean) 1 year after surgery. Relative to the relapse typically incurred in conventional orthognathic surgery,
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Table IV. Sample size validation Observed R2 Cohen's effect size f2 Statistical power level Number of predictors Alpha Minimum required sample size at 99% power level Size of sample used
Overall group 0.87 6.14 0.99 3 0.01 (0.05) 13 (11*) 40
Nonincreased VD group 0.92 11.50 0.99 1 0.01 (0.05) 7 (5*) 29
Increased VD group 0.94 15.67 0.99 4 0.01 (0.05) 9 (7*) 11
*Minimum required sample size when statistical power level is 0.95.
Table V. Summary of derived regression models for final mandibular setback (Bs20 ) Adjusted F P value Coefficient t Summary statistics R2 R2 statistic (F statistic) estimate 6 SE value Overall model indicators (n 5 40) Model statistics 0.87 0.86 59.90 0.0000 Intercept 14.33 6 4.07 3.52 Surgical setback of B-point (Bs10 ) 0.36 6 0.14 2.44 Surgical setback of menton (Mes10 ) 0.34 6 0.13 2.63 Postsurgical horizontal A-point 0.23 6 0.06 3.55 position (As1 ) Postsurgical vertical level of 0.18 6 0.06 2.81 coronoid process (Cpf1 ) Predicted final mandibular setback Bs20 5 14:33 1 0:36 3 Bs10 1 0:34 3 Mes10 1 0:23 3 As1 0:18 3 Cpf1 Nonincreased VD model indicators (n 5 29) Model statistics 0.92 0.91 291.00 0.0000 Intercept 0.98 6 0.50 1.97 Surgical setback of B-point (Bs10 ) 0.79 6 0.05 17.06 Predicted final mandibular setback Bs20 5 0:98 1 0:79 3 Bs10 Increased VD model indicators (n 5 11) Model statistics 0.94 0.91 35.00 0.0001 Intercept 53.00 6 7.75 6.84 Surgical upward movement 0.76 6 0.14 5.35 of pogonion (Pogf10 ) Postsurgical horizontal A-point 0.80 6 0.11 7.06 position (As1 ) Postsurgical vertical level of 0.47 6 0.09 5.48 coronoid process (Cpf1 ) Predicted final mandibular setback Bs20 5 53:00 0:76 3 Pogf10 1 0:80 3 As1 0:47 3 Cpf1
P DW statistic value (P value) VIF* 1/VIF* 2.28 (0.356) 0.0012 0.0200 0.0126 0.0011
8.187 0.122 7.948 0.126 1.025 0.975
0.0080
1.091 0.916
2.39 (0.346) 0.0589 0.0000
1.93 (0.852) 0.0002 0.0011
1.840 0.544
0.0002
1.935 0.517
0.0009
1.071 0.934
DW, Durbin-Watson; VIF, variance inflation factor. *VIF higher than 10 suggests linear relationship between predictors; 1/VIF (tolerance statistic) below 0.1 indicates multicollinearity.
our 21% result for the nonincreased VD model was clinically acceptable.14,15 On the other hand, with regard to the increased VD group, the postoperative mandibular forward movement could have been affected by the downward surgical movement of pogonion (Pogf10 ), the horizontal position of A-point at T1 (As1 ), and the vertical position of Cp point at T1 (Cpf1 ). These latter 2 predictors—the horizontal position of the postsurgical A-point (As1 ) and the vertical position of Cp point (Cpf1 )—were 80% and 47% reflected in the final mandibular setback extent (Bs20 ), respectively. In the increased VD group, the maxillary second molar extrusion often induced increased VD. The
counterclockwise rotation of pogonion was shown during postoperative orthodontic treatment, including intrusion of the extruded molars. With respect to the change of pogonion, there were correlations with proximal and distal segment displacements during the healing process. Proffit et al15 and Hwang et al10 insisted that gonion and the proximal segments are closely related to postoperative relapse. This is consistent with the increased VD model variables in this study (Table III). Whereas the maxilla and the mandible are relocated by osteotomies, which are relatively controllable, the coronoid process is relatively difficult to place at the attempted position, making overcorrection in an
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Fig 2. Multivariate model-relevant landmarks and indicators for estimation of final mandibular setback (Bs20 ): A, predictor variables for prediction model based on all 40 subjects; B, predictor variables for nonincreased VD patients; C, predictor variables for increased VD patients. The Cpf1 notations indicate the predicator variables of the coronoid process to the FH plane at T1: As1 for Apoint to S-perp at T1, Bs10 for surgical setback of B-point from T0 to T1, Mes10 for surgical setback of menton from T0 to T1, and Pogf10 for surgical upward movement of pogonion from T0 to T1, based on the derived multivariate prediction models of the predicted final mandibular setback (overall), Bs20 5 14:33 1 0:36 3 Bs10 1 0:34 3 Mes10 1 0:23 3 As1 0:18 3 Cpf1 ; nonincreased VD, Bs20 5 0:98 1 0:7 3 Bs10 ; and increased VD, Bs20 5 53:00 0:76 3 Pogf10 1 0:80 3 As1 0:47 3 Cpf1 :
increased VD group less predictable. Costa et al16 reviewed the usage of condylar positioning devices, concluding that there was no scientific evidence to support their routine use in orthognathic surgery. This means that postoperative manual condylar positioning is sensitive to the oral surgeon's technique. Therefore, to obtain the predicted SFA treatment outcome in an increased VD group, the postoperative vertical position of the Cp (Cpf1 ) should be controllable. Hwang et al10 argued that intentional manual positioning affects the position of B-point after surgery. In the case of the increased VD in the SFA, postoperative orthodontic treatment can encounter a number of difficulties because of the unpredictability of the vertical position of the Cp at T1 (Cpf1 ). For example, the predictability of SFA treatment outcomes can be compromised. Therefore, orthodontists and oral surgeons should be concerned that the more increased the VD after surgery, the less predictable the position of B-point at the posttreatment stage. From the results, the surgical horizontal movement of B-point (Bs10 ) was not included as a variable in the increased VD model. However, the results could not mean that the surgical horizontal movement of B-point (Bs10 ) did not affect the final mandibular position, because the information of Bs10 might overlap the information of Pogf10 ; As1 ; and Cpf1 , since those variables were all correlated in the SFA. There were some reasons that the surgical horizontal movement of B-point (Bs10 )
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was not included as a variable in the increased VD model. First, this regression model did not have the multicollinearity problem. Many clinical studies for dental research have used multiple regression analysis to find the correlations between the predictor and the outcome variables. However, a possible problem from the use of multiple regression analysis is collinearity. In statistics, when there are more than 2 covariates that are highly correlated, this is called multicollinearity. The interpretation of the statistical results from multiple regression models might be distorted from multicollinearity, causing increased inaccuracy and uncertainty. This should be considered in the regression model. Especially, both segments (proximal and distal) after surgery were closely correlated. The cephalometric landmarks in the same segment also were highly correlated. Our multivariate model showed the VIF, which was less than 2. This indicated that the model did not have a multicollinearity problem. If the increased VD model included Bs10 as a variable, multicollinearity problems would be incurred. However, we built the best regression model without multicollinearity problems. In the increased VD model, these variables (Pogf10 ; As1 ; and Cpf1 ), rather than Bs10 , showed a high correlation. The information of the surgical horizontal movement of B-point (Bs10 ) already overlapped with variables (Pogf10 ; As1 ; and Cpf1 ) in the increased VD model. Therefore, this model meant that these variables
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had more strongly influenced the final mandibular position. To determine the effect of VD on the final mandibular setback, the derived prediction models used the overall 40 patients' predictor variables (Fig 2, A). Regardless of the patient classification, a shorter VD at T1 was in turn more likely to achieve better surgical results in the Class III SFA. As in previous studies, occlusal interference, which can increase the occlusal vertical dimension, presumably played a role in postsurgical relapse: our result identifying postsurgical VD as a patient classifier is consistent with that literature.1,5 Indeed, VD was confirmed to be a significant predictive factor for final mandibular setback and, on that basis, a valid patient-classification criterion. As for the shortcomings of our study, first, it was based on a 2-dimensional analysis incorporating CBCT-generated cephalograms, wherein the predictor variables representing the skeletal landmark positions were 2-dimensional projections of the actual 3-dimensional distances. Therefore, for improved prediction model precision, a 3-dimensional analysis of postsurgical skeletal stability should follow this study. Second, for general application of the derived prediction model to patients operated on by other surgeons in different hospitals, a multicenter study should be undertaken. Last, a cast model analysis should be performed to improve the precision of the measurements.
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CONCLUSIONS
Using derived regression models, predictor-specific skeletal analysis and model-based determination of overcorrection is possible during SFA treatment planning. Studying the mandibular position in relation to the postsurgical VD, our investigation highlighted the importance of vertical control of the mandible for skeletal Class III SFA patients. Orthodontists and oral surgeons should be alert to the fact that the more increased the vertical occlusal dimension after surgery, the less predictable the position of B-point at the posttreatment stage. REFERENCES
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