- Email: [email protected]
Statistical shape analysis-based determination of optimal midsagittal reference plane for evaluation of facial asymmetry
ORIGINAL ARTICLE
Statistical shape analysis-based determination of optimal midsagittal reference plane for evaluation of facial asymmetry Sang Min Shin,a You-Min Kim,b Na-Ri Kim,c Yong-Seok Choi,d Soo-Byung Park,e and Yong-Il Kimf Busan and Yangsan, South Korea
Introduction: The purpose of this study was to determine, by statistical shape analysis of original and mirrored skeletal landmarks, the optimal landmark-based midsagittal reference plane for evaluation of facial asymmetry. Methods: The study sample comprised 69 patients with facial asymmetry (36 men, 33 women; mean age, 23.0 6 4.1 years). All landmarks were obtained with cone-beam computed tomography using a 3-dimensional coordinate system. For identifying the landmark-based midsagittal reference plane, the 3 landmarks nearest to the symmetric midsagittal reference plane were selected by ordinary and generalized Procrustes analyses. To verify the 3-landmark-based midsagittal reference plane's compatibility with the symmetric midsagittal reference plane, asymmetry measurements were calculated and tested for each. Results: The 3 nearest landmarks (nasion, anterior nasal spine, and posterior nasal spine) were selected for the 3-landmark-based midsagittal reference plane. The averages of the sums of the squared Euclidean distance and the squared Procrustes distance differences between the 2 configurations and shapes fabricated by the symmetric and landmark-based midsagittal reference planes, respectively, were calculated as 0.121 6 0.241 mm and 1.69 3 106 6 3.25 3 106. The testing results for the symmetric and landmarkbased midsagittal reference planes were almost the same. Conclusion: The results indicated that a 3dimensional midsagittal reference plane constructed of nasion, anterior nasal spine, and posterior nasal spine could be a valuable tool for the evaluation of patients with facial asymmetry. (Am J Orthod Dentofacial Orthop 2016;150:252-60)
a Researcher, Department of Orthodontics, School of Dentistry, Pusan National University, Busan, South Korea; researcher, Department of Statistics, College of Nature, Pusan National University, Busan, South Korea. b Resident, Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. c Postgraduate student, Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. d Professor, Department of Statistics, College of Nature, Pusan National University, Busan, South Korea. e Professor, Department of Orthodontics, Dental Research Institute, Pusan National University Dental Hospital, Yangsan, South Korea. f Assistant professor, Department of Orthodontics, Institute of Translational Dental Sciences, School of Dentistry, Pusan National University, Yangsan, South Korea; assistant professor, Biomedical Research Institute, Pusan National University Hospital, Busan, South Korea. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Supported by the National Research Foundation of Korea grant funded by the Korean government (MSIP) (2015R1C1A1A01051832) and by the Research Fund Program of Research Institute for Basic Sciences, Pusan National University, Korea, 2014, Project No. RIBS-PNU-2014-109. Address correspondence to: Yong-Il Kim, Dental Research Institute, Pusan National University Dental Hospital, Geumoro 20, Mulgeumeup, Yangsan, South Korea 626-787; e-mail, [email protected]. Submitted, May 2015; revised and accepted, January 2016. 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved. http://dx.doi.org/10.1016/j.ajodo.2016.01.017
252
I
n the past, most patients with facial asymmetry who underwent orthognathic surgery had severe maxillofacial deformities, but lately, amid improved socioeconomic conditions and with the increased interest in appearance, many people are eager to correct even a slight facial asymmetry.1 The need for accurate analysis of facial asymmetry has increased concomitantly and now includes the factors that directly contribute to asymmetry and determine its treatment.2 Unfortunately, a perfectly symmetric face is rare. Bilateral landmarks tend to show the asymmetric positions from the skull base to the chin area. This means that reference planes constructed with such craniofacial structural landmarks could be used for a uniquely effective assessment of facial asymmetry. The reference plane setup, therefore, is the most important step in treatment planning for facial asymmetry. Most studies on facial asymmetry have been based on 2-dimensional imaging methods such as clinical photography and posteroanterior cephalography.3,4
Shin et al
These methods, however, cannot account for the 3-dimensional (3D) nature of the face. In response to this problem, various 3D imaging techniques have been developed.5 Hwang et al6 proposed a facial asymmetry analysis method that uses computed tomography and offers, as reference planes, the Frankfort horizontal plane and the midsagittal plane composed of 3 landmarks: opisthion, crista galli, and anterior nasal spine (ANS). Hajeer et al7 established an alternative, softtissue reference plane using an individual symmetric configuration that was computed according to the average of the original and mirror images in 3D stereophotogrammetry. They used that reference plane to assess facial asymmetry before and after orthognathic surgery. Wong et al8 proposed, for evaluation of facial asymmetry, a voxel-based matching optimal symmetry plane method that automatically overlaps with an optimized algorithm and can set up a midsagittal plane without a landmark. For effective correction of facial asymmetry, accurate evaluation is essential, for which it is necessary to set up the midsagittal reference plane. Previous studies, for the purposes of accurate analysis, determined the reference plane with superimposition between the original and mirror images.6,7 These reference planes were individualized without specific cephalometric landmarks. However, cephalometric landmark-based reference planes should be easier to use and, thus, preferable to orthodontic practitioners. The aim of this study, therefore, was to find, using ordinary Procrustes analysis from original and mirror skeletal landmarks, the optimal landmark-based midsagittal reference plane for evaluation of facial asymmetry. Our specific aims were (1) to establish the symmetric midsagittal reference plane from the bilateral skeletal landmarks of the original shape and its mirrored shape with the ordinary Procrustes analysis superimposition method, and (2) to propose a clinically useful landmark-based midsagittal reference plane composed of the existing cephalometric landmarks nearest to the symmetric midsagittal reference plane. MATERIAL AND METHODS
This was a retrospective study. The study group comprised 69 patients with facial asymmetry (36 men, 33 women; mean ages: women, 23.0 6 4.2 years; men, 22.9 6 4.1 years; total, 23.0 6 4.1 years) undergoing treatment at the Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. The Angle classifications of patients were as follows: Class I, 10 patients; Class II, 12 patients; Class III, 47 patients (Table I). All had a mildly to moderately
253
Table I. Demographic data for subjects (means and standard deviations) Class I (n 5 10) 6/4
Class II (n 5 12) 7/5
Sex (female/ male) Age (y) 21.23 6 3.35 24.25 6 3.41 SNA ( ) 80.26 6 2.25 81.84 6 2.60 SNB ( ) 79.16 6 2.32a 77.81 6 2.93a ANB ( ) 1.11 6 0.45a 4.02 6 1.34b
Class III (n 5 47) 23/24
P value 0.524
23.18 6 4.14 80.02 6 2.60 82.86 6 3.14b -2.84 6 2.06c
0.217 0.108 0.000 0.000
Chi-square and ANOVA tests were used for group comparisons; the same superscript letter means no statistical significance.
deviated menton (mean deviation, 3.6 6 2.3 mm) on posteroanterior cephalography regardless of the Angle classification. The exclusion criteria were cleft lip or palate, craniofacial syndrome, and facial trauma. This study was reviewed and approved by the institutional review board of Pusan National University Dental Hospital (PNUDH-2015-003). The landmarks were acquired from cone-beam computed tomography (CBCT) images. The skeletal landmarks were obtained on 3D CBCT images. The CBCT scanner (Zenith3D; Vatech, Seoul, Korea) was set to a 90-kVp tube voltage, a 4-mA tube current, 0.3-mm voxel size, and a 24-second scan time, with the Frankfort horizontal plane parallel to the floor. The CBCT data thus acquired were processed in 3D x-, y-, z-coordinate images by Ondemand3D software (Cybermed, Seoul, Korea). The axes were defined as follows. The x-axis, determined first, included nasion (Na) and ran between the right and left orbitales. The y-axis included Na and ran perpendicular to the x-axis on the Frankfort horizontal plane. The z-axis included Na and ran perpendicular to the x-axis and y-axis. The common origin (0, 0, 0) of the 3 axes was Na. The landmarks were as follows (Table II). The bilateral landmarks were the foramen ovale, foramen rotundum, foramen spinosum, hypoglossal canal, internal acoustic meatus, jugular foramen, orbitale, infraorbitale, supraorbitale, porion, and greater palatine canal, as well as the most inferior points of the frontozygomatic and zygomaticomaxillary sutures. The landmarks on the midline were Na, sella, basion, opisthion, A-point, anterior nasal spine (ANS), posterior nasal spine (PNS), and nasopalatine canal. All landmark positions were recorded in their x, y, z coordinates. The individual symmetric midsagittal reference planes were each generated in the following steps (Figs 1-3): (1) establishing the center of the original configuration as the origin, (2) obtaining the mirrored
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
254
Table II. Definitions of landmarks Landmark Bilateral landmarks (right and left) Foramen ovale Foramen rotundum Foramen spinosum Frontozygomatic suture Greater palatine canal Hypoglossal canal Infraorbitale Orbitale Porion Supraorbitale Zygomaticomaxillary suture Landmarks on midline structure A-point ANS Basion Inferior nasopalatine canal Nasion Nasopalatine canal Opisthion PNS Sella B-point Menton Genial tubercle
Definition Center of the foramen ovale Center of the foramen rotundum Center of the foramen spinosum Medial point of the orbital rim of the zygomaticofrontal suture Center of the opening of the greater palatine canal Center of the right hypoglossal canal Center of the opening of the greater palatine canal Lowest point in the inferior margin of the orbit Superior point of the upper contour of the external auditory meatus Center of the supraorbital foramen Superior medial point of the zygomaticomaxillary suture Deepest point on the innermost curvature from the maxillary ANS to the crest of the maxillary alveolar process Tip of the bony ANS Mid-dorsal point of the anterior margin of the foramen magnum Most inferior point of the posterior border of the nasopalatine canal Most anterior point of the frontonasal suture on the median plane Lowest point of the opening of the nasopalatine canal Middle point on the posterior margin of the foramen magnum, opposite the basion Tip of the bony PNS Center of the hypophyseal fossa (sella turcica) Deepest point between the chin and the mandibular incisors Most inferior point on the chin in the lateral view Most posterior point of the genial tubercle
Fig 1. A, Original configuration and B, its mirrored configuration.
configuration from the original configuration around the YZ plane, (3) superimposing the original on its mirrored configuration and the mirrored on the
August 2016 Vol 150 Issue 2
original configuration using partial ordinary Procrustes analysis, and (4) after aligning 2 superimposed configurations called Procrustes fits, creating the
American Journal of Orthodontics and Dentofacial Orthopedics
Shin et al
255
Fig 2. Superimpositions of the original on its mirrored configuration and of the mirrored on the original configuration using partial ordinary Procrustes analysis.
Table III. Mean distances between the symmetric
midsagittal reference plane and the landmarks on midline structures (n 5 67) Na ANS PNS NPC A-point Opisthion Sella Basion Mean 0.697 0.755 0.775 0.819 0.823 1.047 1.064 1.041 SD 0.542 0.527 0.723 0.681 0.570 0.869 0.999 1.071 NPC, Nasopalatine canal.
Fig 3. Symmetric configuration created according to the arithmetic mean of 2 Procrustes fits. The individual symmetric midsagittal reference plane was calculated on that basis.
individual symmetric configuration according to the arithmetic mean of those fits. The individual symmetric midsagittal reference plane was calculated on that basis.
For the purpose of identifying the landmark-based symmetric midsagittal reference planes, the cephalometric landmarks on the midline structure were tested to find those at the smallest distance from the symmetric midsagittal reference plane. To measure the distances between the individual symmetric midsagittal reference plane and the landmarks on the midline structure, all original and corresponding mirrored configurations were superimposed by full generalized Procrustes analysis, and the mean values were calculated (Table III). The 3 landmarks with the smallest distances were then used to draw the landmarks-based symmetric midsagittal reference plane. The 3-landmark-based plane's compatibility with the individual symmetric midsagittal reference plane was verified by measuring the asymmetry for each and testing it based on the study of Mardia et al.9 The asymmetry of the 3-landmark-based plane was measured as follows (Figs 4 and 5): (1) estimating the multiple
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
256
Fig 4. Landmark-based midsagittal reference plane with selected landmarks (Na, ANS, and PNS).
Fig 5. Asymmetry measurements for each configuration using the distance between the symmetric configuration and the ordinary Procrustes analysis fit onto the symmetric configuration.
regression line of the 3-landmark coordinates for each centered original configuration (the response variable of the regression line is the x-axis coordinate), (2) obtaining Xi for i 5 1, ., n, which is the configuration of rotating the original configuration as the estimated regression line is perpendicular to the x-axis, (3) determining the mirrored configuration Yi from the rotated configuration Xi around the YZ plane, (4) calculating the individual symmetric configurations Si of the Procrustes fits by the interactive ordinary Procrustes analysis of the Xiand Yi, and (5) measuring the asymmetry for each configuration as follows (see the Supplemental Material for more details). Let Xi for i 5 1, ., n be the ith configuration, and let Si be the individual symmetric configuration of Xi and
August 2016 Vol 150 Issue 2
the mirrored configuration Yi of Xi. Then the sum of the squared Euclidean distances is defined as the sum of distances between the corresponding landmarks of Xi and Si. However, the sum of the squared Euclidean distances depends on location, scale, and rotational effects of Xi. So, we consider another measure to analyze asymmetry, the squared Procrustes distances of the shapes. Here, “shape” means all the geometric information that remains when location, scale, and rotational effects are filtered out from a configuration. Therefore, first we must obtain a centered configuration from Xi. Then to remove the scale effect from Xi, we divide the centered configuration to the centroid size of Xi, and we call it the centered preshape. Since the location and scale effects are filtered out, all centered preshapes
American Journal of Orthodontics and Dentofacial Orthopedics
Shin et al
have the same scale. Then the squared Procrustes distances can be obtained by matching the centered preshape of Xi for i 5 1,., n and that of Si as closely possible over rotations. It can be obtained by the ordinary Procrustes analysis solution. Hence, the squared Procrustes distance is a measure for the asymmetry that does not depend on location, scale, and rotational effects of the original configuration, Xi. Based on the same manner as the sum of the squared Euclidean distances and the squared Procrustes distances, the amount of asymmetry was calculated as follows: (1) by comparing landmark changes between the original and symmetric configurations and shapes for the 2 methods, respectively; and (2) by comparing the differences of the amount of asymmetry between the 2 configurations and 2 shapes produced by the 2 methods. We compared the total variations for asymmetry measurements according to 2 (symmetric and 3-landmark-based) midsagittal reference planes. Mardia et al9 proposed an object-symmetry testing procedure that uses the close approximation of the Euclidean metric in the tangent space to the true Procrustes distance. In this way, Procrustes tangent projections XiP and YiP can be obtained from Procrustes fits by the generalized Procrustes analysis of Xi and Yi with respect to the full Procrustes mean shape G. The Procrustes tangent projections XiP and YiP have the same meaning as the centered preshapes, and G is symmetric and has P P the same shape as the ordinary average 12 ðX 1Y Þ, P P P where X and Y are the arithmetic means of Xi and YiP , respectively. Accordingly, it is possible to decompose the asymmetry of all data as follows (see the Supplemental Material for more details). The total variations for the asymmetry of all data are defined as the sum of squares of the distances between the corresponding landmarks of XiP and YiP . The total variation of the asymmetry SST can be decomposed as the variations between mean shapes and the variations within subjects. The variation between mean shapes is defined as the sum of squares of the distances between P P the corresponding landmarks of X and Y ; it means the between-squares side, SSB, for asymmetry. The variations within subjects can be measured by the sum of squares of the distances between the corresponding P P landmarks of XiP X and YiP Y ; the variations can be denoted by the within-subjects sum of squares, SSW. Using this method, it is possible to test the asymmetry of the population in the same manner as 1-way analysis of variance (ANOVA). All landmarks were remeasured at 2-week intervals by 2 investigators (S.M.S., Y-M.K.). The systematic intraexaminer and interexaminer errors between the 2
257
measurements were determined with a paired t test. Also, the magnitudes of those errors were assessed by calculating the intraclass correlation coefficient (ICC). For statistical computation purposes, the language R (Vienna, Austria) was used. RESULTS
The intraexaminer and interexaminer reliabilities of the landmarks were very good. There were no statistically significant differences in landmark identifications. The mean intraexaminer ICC values for the x, y, and z coordinate system were 0.924 (SD, 0.078) for the x-axis, 0.941 (SD, 0.056) for the y-axis, and 0.940 (SD, 0.054) for the z-axis. The mean interexaminer ICC values were 0.811 (SD, 0.228) for the x-axis, 0.865 (SD, 0.277) for the y-axis, and 0.916 (SD, 0.070) for the z-axis. Then we selected the nearest landmarks to the symmetric midsagittal reference plane. After all original and their mirrored configurations were superimposed by full generalized Procrustes analysis, the mean distances between the symmetric midsagittal reference plane and all landmarks on the midline structure were calculated (Table III). The 3 nearest landmarks were, in order, Na (0.697 6 0.542 mm), ANS (0.755 6 0.527 mm), and PNS (0.775 6 0.723 mm). These accordingly were selected for the 3-landmark-based midsagittal reference plane. We compared the landmark changes between the original and symmetric configurations and shapes fabricated by 2 (symmetric and 3-landmark-based) midsagittal reference plane methods. As a means of identifying the extents to which the pairwise landmarks changed according to the 2 midsagittal reference planes, the differences between the original and the fabricated symmetric configurations and shapes were measured using the sum of the squared Euclidean distances of the configurations and the squared Procrustes distances of the shapes, respectively, for the asymmetry measurements. The results showed little difference in the asymmetry measurements (sum of the squared Euclidean distances and squared Procrustes distances) between the symmetry and 3-landmark-based midsagittal reference planes (Table IV). However, the asymmetry measurements (sum of the squared Euclidean distances) for each configuration also were measured using the average of the distances between the symmetric configuration and the ordinary Procrustes analysis fit of the original configuration on the symmetric configuration. The measured asymmetries (sum of the squared Euclidean distances) on the 3-landmark-based plane were somewhat greater than those on the symmetric midsagittal reference plane.
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
258
Table IV. Asymmetry measurements on the symmetric
midsagittal reference plane and the 3-landmark-based plane Average of SSED (mm) Average of SPD Symmetric plane 70.614 6 2.759 9.67 3 104 6 7.28 3 104 Landmark-based 70.655 6 52.770 9.68 3 104 6 7.28 3 104 plane SSED, Sum of the squared Euclidean distance; SPD, squared Procrustes distance.
Differences between configurations and shapes were produced by the 2 (symmetric and 3-landmark-based) midsagittal reference plane methods. The average sum of the squared Euclidean distance and the squared Procrustes distance differences between the 2 configurations and the 2 shapes produced by the symmetric and landmark-based midsagittal reference planes were calculated as 0.121 6 0.241 mm and 1.69 3 106 6 3.25 3 106, respectively. Since the test data were almost identical, there were small differences between 2 plane methods. It meant that the 2 configurations and the 2 shapes produced by the symmetric and landmark-based midsagittal reference planes were similar. We compared the total variations of the asymmetry measurements according to 2 (symmetric and 3-landmark-based) midsagittal reference planes based on the method of Mardia et al.9 To verify the 3-landmark-based plane for compatibility with the symmetric midsagittal reference plane, asymmetry measurements were calculated for each plane and tested according to the method of Mardia et al. Using this method tested the total variation of asymmetry measurements in the same manner as 1-way ANOVA. The results showed Fy5:548 ðPy6:10631024 Þ on the 3-landmark-based midsagittal reference plane and Fy5:548 ðPy6:10631024 Þ on the symmetric midsagittal reference plane. As is apparent, the test data were almost identical; there was no significant difference between the planes. DISCUSSION
The posteroanterior cephalogram has been widely used for analysis of facial asymmetry. Traditionally, the midsagittal reference line has been defined using certain landmarks on 2-dimensional posteroanterior cephalograms: eg, vertical lines passing through Na and ANS, or through crista galli and ANS. Vertical planes passing through the midpoints of bilateral landmarks were used as well.10-13 Unfortunately, there are some limitations in clarifying cephalometric landmarks from overlapped
August 2016 Vol 150 Issue 2
structures using posteroanterior cephalograms. For this reason, facial asymmetry analysis should use 3D computed tomography or CBCT images. Hwang et al6 evaluated facial asymmetry using a midsagittal reference plane incorporating opisthion, crista galli, and ANS. Pelo et al14 emphasized the 3D computed tomography utility of a reference plane passing through the lateral semicircular canals. Meanwhile, Baek et al15 used, as their midsagittal reference, the plane including crista galli and the midpoint of the anterior clinoid processes and running perpendicular to the Frankfort horizontal plane. Authors of other studies have applied midsagittal reference planes incorporating sella, Na, menton, the midpoint of the 2 most lateral points of the foramen magnum, and the midpoint of the foramen spinosum.15-18 Notwithstanding all of the research devoted to this issue, the methods of landmark selection in the clinical field still have limitations. The method should use specific landmarks that are identifiable with good reproducibility. To overcome the possible limitations of setting up cephalometric midsagittal planes, the mirror image has been applied for facial asymmetry analysis.7,19-22 Damstra et al23 discovered that superimposition of mirror images could quantify the differences between anatomically correct anatomy and deformity. They insisted that a morphometrically determined midsagittal reference plane could eliminate the problems associated with anatomically determined planes. Wong et al,8 similarly, used a voxel-based median plane to assess facial bone asymmetry and reported that it was effective for subsequent treatment of patients. Symmetric midsagittal reference planes such as these suggested ones have been shown to produce accurate and reliable reference planes for comparative study.21,22 However, in clinical practice, it is difficult to find symmetric midsagittal reference planes without specific programs or a statistical package. Alternatively, the landmarkbased midsagittal reference plane can easily be applied in the clinical setting. In this study, to find the landmark-based midsagittal reference plane, we used full generalized Procrustes analysis-based superimposition of the original and its mirrored configuration and calculated the mean distances between the symmetric midsagittal reference plane and all landmarks on the midline structure (Table III). The 3 nearest landmarks on the midline structure were determined, in order, as follows: Na (0.697 6 0.542 mm), ANS (0.755 6 0.527 mm), and PNS (0.775 6 0.723 mm). These 3 landmarks, accordingly, were selected for the landmark-based midsagittal reference plane. The data indicated that these were close to the symmetric midsagittal reference plane: the mean differences were within 0.8 mm, and the standard
American Journal of Orthodontics and Dentofacial Orthopedics
Shin et al
deviations were within 0.7 mm. In this study, most of the tested landmarks were on the cranial base. Kwon et al17 reported that the degree of cranial base asymmetry did not differ between patients with asymmetry or symmetry and concluded that cranial base asymmetry severity is not a main factor in facial asymmetry. This suggests that landmarks on the cranial base can be used as reference points for construction of the midsagittal reference plane in patients with mild-to-moderate facial asymmetry. In this study, we selected 3 landmarks on the midline structure for the midsagittal reference plane. Several previous studies also have taken this approach. Trpkova et al,12 using 2-dimensional posteroanterior image analysis, found that vertical lines passing through the midpoints between the bilateral pairs of orbital landmarks are more accurate and valid for various asymmetries. Richardson24 observed that the midsagittal plane running perpendicular to the Frankfort horizontal plane and passing through Na and sella was the most similar to the symmetric midsagittal reference plane. On the other hand, Ferrario et al19 insisted that overall, the symmetric midsagittal reference plane did not include any facial midline landmarks. Our results, however, support the hypothesis that for patients with mild-to-moderate facial asymmetry, the symmetric midsagittal reference plane is almost on the midline. As a means of determining the optimal landmarkbased midsagittal reference plane for orthodontists and oral surgeons, the selected landmark-based midsagittal reference plane was tested with 2 comparisons. The first was for landmark changes between the original and symmetric configurations and shapes fabricated by the 2 (symmetric and 3-landmark-based) midsagittal reference plane methods. For the calculation of the landmark changes between the 2 configurations and the 2 shapes, respectively, the means of the sum of the squared Euclidean distances and the squared Procrustes distances were obtained. But before discussing the comparison results, we should distinguish an object's configuration from its shape. The configuration is the set of measured landmarks on a particular object; the shape is all geometric information on that object when location, scale, and rotational effects are filtered out. Two configurations' difference can be determined using the sum of the squared Euclidean distances between pairwise landmarks, but this might be inaccurate because the distance depends on the measured scale. Therefore, in statistical shape analysis, this difference is measured with reference to the squared Procrustes distances between 2 shapes, since the shape does not vary under translation and scaling of the configuration. In our study, to identify the extents to which the pairwise
259
landmarks changed according to the 2 midsagittal reference planes, the differences between the original and the 2 fabricated configurations or shapes were measured using the sum of the squared Euclidean distances or the squared Procrustes distances, respectively. The results of the comparisons of the landmark changes between the original and symmetric configurations and shapes fabricated by the 2 (symmetric and 3-landmark-based) midsagittal reference plane methods showed no significant differences (Table IV). The second comparison tested for its utility in determining the optimal landmark-based midsagittal reference plane was that between the 2 configurations and shapes produced by the 2 (symmetric and 3-landmarkbased) midsagittal reference plane methods. The asymmetries according to the 2 configurations differed slightly. Specifically, the asymmetries (sum of the squared Euclidean distances and the squared Procrustes distances) measured on the 3-landmark-based plane were somewhat greater than those on the symmetric midsagittal reference plane. On the other hand, comparisons of the landmark changes between the 2 configurations and shapes fabricated from the 2 midsagittal reference planes, respectively, were performed. The average sums of the squared Euclidean distances and squared Procrustes distances differences between the 2 configurations and shapes fabricated based on the symmetric and landmark-based midsagittal reference planes were calculated as 0.121 6 0.241 mm and 1.69 3 106 6 3.25 3 106, respectively. These are clinically acceptable differences. Based on the data obtained in this study, we can suggest 3 landmarks (Na, ANS, and PNS) for determination of the midsagittal reference plane in patients with mild-to-moderate facial asymmetry. Previous reports have introduced 3D image landmarks such as sella, the midpoint of the anterior clinoid process, the foramen spinosum midpoint, and the foramen magnum midpoint.6,15-17 However, finding these landmarks on 3D images is difficult without automatic software to define the midpoint between 2 specific pairwise landmarks. Hence, we endeavored to find the midline structural landmarks nearest to the midsagittal reference plane. Furthermore, the previous several midsagittal reference planes have not been compared for their accuracy. Among several midsagittal reference planes, the most accurate one would be a symmetric midsagittal reference plane. However, our suggested landmark-based midsagittal reference plane proved to be compatible with the symmetric one in this statistical study. Damstra et al23 claimed that use of this symmetric midsagittal reference plane for visually intact, asymmetry-unaffected regions of the skull might be
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
260
more valuable for diagnosis and treatment planning of craniofacial asymmetry. If this approach were to be individualized and automated, it could be useful for clinicians. This notwithstanding, the landmark-based midsagittal reference plane, alternatively, could be a helpful and easy method. In this study, we examined patients with mild-tomoderate facial asymmetry and a skewed distribution of Angle classifications. The utility of the suggested landmark-based midsagittal reference plane for other types of asymmetry has yet to be validated. Also, because soft tissues can offset facial skeletal asymmetry, the clinician should consider these midsagittal reference planes for skeletal and soft tissues differently. Therefore, further research, with various Angle classifications and other skeletal patterns, and with consideration of soft tissues, should be conducted. Moreover, other additional landmarks that are not located in the midline structure should be found for setting up the midsagittal reference plane. One example is the midsagittal plane that passes through 2 landmarks and runs perpendicular to the Frankfort horizontal plane. CONCLUSIONS
In scrutinizing the results of this study, we found that Na, ANS, and PNS are nearest to the symmetric midsagittal reference plane. These accordingly were used to establish a landmark-based midsagittal reference plane. Statistical shape analysis confirmed that this midsagittal reference plane is compatible with the symmetric midsagittal reference plane. Overall, the results indicated that a 3D midsagittal reference plane constructed of Na, ANS, and PNS could be a valuable tool for evaluation of patients with facial asymmetry. SUPPLEMENTARY DATA
Supplementary data related to this article can be found online at http://dx.doi.org/10.1016/j.ajodo.2016. 01.017. REFERENCES 1. Ahn JS, Hwang HS. Relationship between perception of facial asymmetry and postero-anterior cephalometric measurements. Korean J Orthod 2001;31:489-98. 2. Lee BR, Kang DK, Son WS, Park SB, Kim SS, Kim YI, et al. The relationship between condyle position, morphology and chin deviation in skeletal Class III patients with facial asymmetry using cone-beam CT. Korean J Orthod 2011;41:87-96. 3. Berssenbr€ ugge P, Berlin NF, Kebeck G, Runte C, Jung S, Kleinheinz J, et al. 2D and 3D analysis methods of facial asymmetry in comparison. J Craniomaxillofac Surg 2014;42:e327-34. 4. Kim JY, Jung HD, Jung YS, Hwang CJ, Park HS. A simple classification of facial asymmetry by TML system. J Craniomaxillofac Surg 2014;42:313-20.
August 2016 Vol 150 Issue 2
5. Hood CA, Bock M, Hosey MT, Bowman A, Ayoub AF. Facial asymmetry—3D assessment of infants with cleft lip & palate. Int J Paediatr Dent 2003;13:406-10. 6. Hwang HS, Hwang CH, Lee KH, Kang BC. Maxillofacial 3-dimensional image analysis for the diagnosis of facial asymmetry. Am J Orthod Dentofacial Orthop 2006;130:779-85. 7. Hajeer MY, Ayoub AF, Millett DT. Three-dimensional assessment of facial soft-tissue asymmetry before and after orthognathic surgery. Br J Oral Maxillofac Surg 2004;42:396-404. 8. Wong TY, Liu JK, Fang JJ, Wu TC, Tu YH. Use of the matching optimal symmetry plane method in planning surgical correction of facial asymmetry—a preliminary report of 20 patients. J Oral Maxillofac Surg 2014;72:1180.e1-13. 9. Mardia KV, Bookstein FL, Moreton IJ. Statistical assessment of bilateral symmetry of shapes. Biometrika 2000;2:285-300. 10. Grummons DC, Kappeyne van de Coppello MA. A frontal asymmetry analysis. J Clin Orthod 1987;21:448-65. 11. Jeon YN, Lee KH, Hwang HS. Validity of midsagittal reference planes constructed in 3D CT images. Korean J Orthod 2007;37:182-91. 12. Trpkova B, Prasad NG, Lam EW, Raboud D, Glover KE, Major PW. Assessment of facial asymmetries from posteranterior cephalograms: validity of reference lines. Am J Orthod Dentofacial Orthop 2003;123:512-20. 13. Peak SH, Ahn BK, Kim SH, Shon HB, Han HJ, Kang SM. A frontal cephalometric study on the reference lines to assess the craniomaxillofacial asymmetry. Korean J Orthod 1993;23:1-15. 14. Pelo S, Deli R, Correra P, Boniello R, Gasparini G, Moro A. Evaluation of 2 different reference planes used for the study of asymmetric facial malformations. J Craniofac Surg 2009;20:41-5. 15. Baek SH, Cho IS, Chang YI, Kim MJ. Skeletodental factors affecting chin point deviation in female patients with class III malocclusion and facial asymmetry: a three-dimensional analysis using computed tomography. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2007;104:628-39. ~ez-Vico RM, Iglesias-Linares A, Torres-Lagares D, Gutierrez16. Yan Perez JL, Solano-Reina E. Three-dimensional evaluation of craniofacial asymmetry: an analysis using computed tomography. Clin Oral Investig 2011;15:729-36. 17. Kwon TG, Park HS, Ryoo HM, Lee SH. A comparison of craniofacial morphology in patients with and without facial asymmetry—a three-dimensional analysis with computed tomography. Int J Oral Maxillofac Surg 2006;35:43-8. 18. Damstra J, Oosterkamp BC, Jansma J, Ren Y. Combined 3-dimensional and mirror-image analysis for the diagnosis for asymmetry. Am J Orthod Dentofacial Orthop 2011;140:886-94. 19. Ferrario VF, Sforza C, Poggio CE, Tartaglia G. Distance from symmetry: a three-dimensional evaluation of facial asymmetry. J Oral Maxillofac Surg 1994;52:1126-32. 20. McIntyre GT, Mossey PA. Size and shape measurement in contemporary cephalometrics. Eur J Orthod 2003;25:231-42. 21. Hartmann J, Meyer-Marcotty P, Benz M, Hausler G, StellzigEisenhauer A. Reliability of a method for computing facial symmetry plane and degree of asymmetry based on 3D-data. J Orofac Orthop 2007;68:477-90. 22. Meyer-Marcotty P, Alpers GW, Gerdes AB, Stellzig-Eisenhauer A. Impact of facial asymmetry in visual perception: a 3-dimensional data analysis. Am J Orthod Dentofacial Orthop 2010;137:168.e1-8. 23. Damstra J, Fourie Z, De Wit M, Ren Y. A three-dimensional comparison of a morphometric and conventional cephalometric midsagittal planes for craniofacial asymmetry. Clin Oral Investig 2012;16:285-94. 24. Richardson A. A comparison of traditional and computerized methods of cephalometric analysis. Eur J Orthod 1981;3:15-20.
American Journal of Orthodontics and Dentofacial Orthopedics
Statistical shape analysis-based determination of optimal midsagittal reference plane for evaluation of facial asymmetry Sang Min Shin,a You-Min Kim,b Na-Ri Kim,c Yong-Seok Choi,d Soo-Byung Park,e and Yong-Il Kimf Busan and Yangsan, South Korea
Introduction: The purpose of this study was to determine, by statistical shape analysis of original and mirrored skeletal landmarks, the optimal landmark-based midsagittal reference plane for evaluation of facial asymmetry. Methods: The study sample comprised 69 patients with facial asymmetry (36 men, 33 women; mean age, 23.0 6 4.1 years). All landmarks were obtained with cone-beam computed tomography using a 3-dimensional coordinate system. For identifying the landmark-based midsagittal reference plane, the 3 landmarks nearest to the symmetric midsagittal reference plane were selected by ordinary and generalized Procrustes analyses. To verify the 3-landmark-based midsagittal reference plane's compatibility with the symmetric midsagittal reference plane, asymmetry measurements were calculated and tested for each. Results: The 3 nearest landmarks (nasion, anterior nasal spine, and posterior nasal spine) were selected for the 3-landmark-based midsagittal reference plane. The averages of the sums of the squared Euclidean distance and the squared Procrustes distance differences between the 2 configurations and shapes fabricated by the symmetric and landmark-based midsagittal reference planes, respectively, were calculated as 0.121 6 0.241 mm and 1.69 3 106 6 3.25 3 106. The testing results for the symmetric and landmarkbased midsagittal reference planes were almost the same. Conclusion: The results indicated that a 3dimensional midsagittal reference plane constructed of nasion, anterior nasal spine, and posterior nasal spine could be a valuable tool for the evaluation of patients with facial asymmetry. (Am J Orthod Dentofacial Orthop 2016;150:252-60)
a Researcher, Department of Orthodontics, School of Dentistry, Pusan National University, Busan, South Korea; researcher, Department of Statistics, College of Nature, Pusan National University, Busan, South Korea. b Resident, Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. c Postgraduate student, Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. d Professor, Department of Statistics, College of Nature, Pusan National University, Busan, South Korea. e Professor, Department of Orthodontics, Dental Research Institute, Pusan National University Dental Hospital, Yangsan, South Korea. f Assistant professor, Department of Orthodontics, Institute of Translational Dental Sciences, School of Dentistry, Pusan National University, Yangsan, South Korea; assistant professor, Biomedical Research Institute, Pusan National University Hospital, Busan, South Korea. All authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest, and none were reported. Supported by the National Research Foundation of Korea grant funded by the Korean government (MSIP) (2015R1C1A1A01051832) and by the Research Fund Program of Research Institute for Basic Sciences, Pusan National University, Korea, 2014, Project No. RIBS-PNU-2014-109. Address correspondence to: Yong-Il Kim, Dental Research Institute, Pusan National University Dental Hospital, Geumoro 20, Mulgeumeup, Yangsan, South Korea 626-787; e-mail, [email protected]. Submitted, May 2015; revised and accepted, January 2016. 0889-5406/$36.00 Ó 2016 by the American Association of Orthodontists. All rights reserved. http://dx.doi.org/10.1016/j.ajodo.2016.01.017
252
I
n the past, most patients with facial asymmetry who underwent orthognathic surgery had severe maxillofacial deformities, but lately, amid improved socioeconomic conditions and with the increased interest in appearance, many people are eager to correct even a slight facial asymmetry.1 The need for accurate analysis of facial asymmetry has increased concomitantly and now includes the factors that directly contribute to asymmetry and determine its treatment.2 Unfortunately, a perfectly symmetric face is rare. Bilateral landmarks tend to show the asymmetric positions from the skull base to the chin area. This means that reference planes constructed with such craniofacial structural landmarks could be used for a uniquely effective assessment of facial asymmetry. The reference plane setup, therefore, is the most important step in treatment planning for facial asymmetry. Most studies on facial asymmetry have been based on 2-dimensional imaging methods such as clinical photography and posteroanterior cephalography.3,4
Shin et al
These methods, however, cannot account for the 3-dimensional (3D) nature of the face. In response to this problem, various 3D imaging techniques have been developed.5 Hwang et al6 proposed a facial asymmetry analysis method that uses computed tomography and offers, as reference planes, the Frankfort horizontal plane and the midsagittal plane composed of 3 landmarks: opisthion, crista galli, and anterior nasal spine (ANS). Hajeer et al7 established an alternative, softtissue reference plane using an individual symmetric configuration that was computed according to the average of the original and mirror images in 3D stereophotogrammetry. They used that reference plane to assess facial asymmetry before and after orthognathic surgery. Wong et al8 proposed, for evaluation of facial asymmetry, a voxel-based matching optimal symmetry plane method that automatically overlaps with an optimized algorithm and can set up a midsagittal plane without a landmark. For effective correction of facial asymmetry, accurate evaluation is essential, for which it is necessary to set up the midsagittal reference plane. Previous studies, for the purposes of accurate analysis, determined the reference plane with superimposition between the original and mirror images.6,7 These reference planes were individualized without specific cephalometric landmarks. However, cephalometric landmark-based reference planes should be easier to use and, thus, preferable to orthodontic practitioners. The aim of this study, therefore, was to find, using ordinary Procrustes analysis from original and mirror skeletal landmarks, the optimal landmark-based midsagittal reference plane for evaluation of facial asymmetry. Our specific aims were (1) to establish the symmetric midsagittal reference plane from the bilateral skeletal landmarks of the original shape and its mirrored shape with the ordinary Procrustes analysis superimposition method, and (2) to propose a clinically useful landmark-based midsagittal reference plane composed of the existing cephalometric landmarks nearest to the symmetric midsagittal reference plane. MATERIAL AND METHODS
This was a retrospective study. The study group comprised 69 patients with facial asymmetry (36 men, 33 women; mean ages: women, 23.0 6 4.2 years; men, 22.9 6 4.1 years; total, 23.0 6 4.1 years) undergoing treatment at the Department of Orthodontics, Pusan National University Dental Hospital, Yangsan, South Korea. The Angle classifications of patients were as follows: Class I, 10 patients; Class II, 12 patients; Class III, 47 patients (Table I). All had a mildly to moderately
253
Table I. Demographic data for subjects (means and standard deviations) Class I (n 5 10) 6/4
Class II (n 5 12) 7/5
Sex (female/ male) Age (y) 21.23 6 3.35 24.25 6 3.41 SNA ( ) 80.26 6 2.25 81.84 6 2.60 SNB ( ) 79.16 6 2.32a 77.81 6 2.93a ANB ( ) 1.11 6 0.45a 4.02 6 1.34b
Class III (n 5 47) 23/24
P value 0.524
23.18 6 4.14 80.02 6 2.60 82.86 6 3.14b -2.84 6 2.06c
0.217 0.108 0.000 0.000
Chi-square and ANOVA tests were used for group comparisons; the same superscript letter means no statistical significance.
deviated menton (mean deviation, 3.6 6 2.3 mm) on posteroanterior cephalography regardless of the Angle classification. The exclusion criteria were cleft lip or palate, craniofacial syndrome, and facial trauma. This study was reviewed and approved by the institutional review board of Pusan National University Dental Hospital (PNUDH-2015-003). The landmarks were acquired from cone-beam computed tomography (CBCT) images. The skeletal landmarks were obtained on 3D CBCT images. The CBCT scanner (Zenith3D; Vatech, Seoul, Korea) was set to a 90-kVp tube voltage, a 4-mA tube current, 0.3-mm voxel size, and a 24-second scan time, with the Frankfort horizontal plane parallel to the floor. The CBCT data thus acquired were processed in 3D x-, y-, z-coordinate images by Ondemand3D software (Cybermed, Seoul, Korea). The axes were defined as follows. The x-axis, determined first, included nasion (Na) and ran between the right and left orbitales. The y-axis included Na and ran perpendicular to the x-axis on the Frankfort horizontal plane. The z-axis included Na and ran perpendicular to the x-axis and y-axis. The common origin (0, 0, 0) of the 3 axes was Na. The landmarks were as follows (Table II). The bilateral landmarks were the foramen ovale, foramen rotundum, foramen spinosum, hypoglossal canal, internal acoustic meatus, jugular foramen, orbitale, infraorbitale, supraorbitale, porion, and greater palatine canal, as well as the most inferior points of the frontozygomatic and zygomaticomaxillary sutures. The landmarks on the midline were Na, sella, basion, opisthion, A-point, anterior nasal spine (ANS), posterior nasal spine (PNS), and nasopalatine canal. All landmark positions were recorded in their x, y, z coordinates. The individual symmetric midsagittal reference planes were each generated in the following steps (Figs 1-3): (1) establishing the center of the original configuration as the origin, (2) obtaining the mirrored
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
254
Table II. Definitions of landmarks Landmark Bilateral landmarks (right and left) Foramen ovale Foramen rotundum Foramen spinosum Frontozygomatic suture Greater palatine canal Hypoglossal canal Infraorbitale Orbitale Porion Supraorbitale Zygomaticomaxillary suture Landmarks on midline structure A-point ANS Basion Inferior nasopalatine canal Nasion Nasopalatine canal Opisthion PNS Sella B-point Menton Genial tubercle
Definition Center of the foramen ovale Center of the foramen rotundum Center of the foramen spinosum Medial point of the orbital rim of the zygomaticofrontal suture Center of the opening of the greater palatine canal Center of the right hypoglossal canal Center of the opening of the greater palatine canal Lowest point in the inferior margin of the orbit Superior point of the upper contour of the external auditory meatus Center of the supraorbital foramen Superior medial point of the zygomaticomaxillary suture Deepest point on the innermost curvature from the maxillary ANS to the crest of the maxillary alveolar process Tip of the bony ANS Mid-dorsal point of the anterior margin of the foramen magnum Most inferior point of the posterior border of the nasopalatine canal Most anterior point of the frontonasal suture on the median plane Lowest point of the opening of the nasopalatine canal Middle point on the posterior margin of the foramen magnum, opposite the basion Tip of the bony PNS Center of the hypophyseal fossa (sella turcica) Deepest point between the chin and the mandibular incisors Most inferior point on the chin in the lateral view Most posterior point of the genial tubercle
Fig 1. A, Original configuration and B, its mirrored configuration.
configuration from the original configuration around the YZ plane, (3) superimposing the original on its mirrored configuration and the mirrored on the
August 2016 Vol 150 Issue 2
original configuration using partial ordinary Procrustes analysis, and (4) after aligning 2 superimposed configurations called Procrustes fits, creating the
American Journal of Orthodontics and Dentofacial Orthopedics
Shin et al
255
Fig 2. Superimpositions of the original on its mirrored configuration and of the mirrored on the original configuration using partial ordinary Procrustes analysis.
Table III. Mean distances between the symmetric
midsagittal reference plane and the landmarks on midline structures (n 5 67) Na ANS PNS NPC A-point Opisthion Sella Basion Mean 0.697 0.755 0.775 0.819 0.823 1.047 1.064 1.041 SD 0.542 0.527 0.723 0.681 0.570 0.869 0.999 1.071 NPC, Nasopalatine canal.
Fig 3. Symmetric configuration created according to the arithmetic mean of 2 Procrustes fits. The individual symmetric midsagittal reference plane was calculated on that basis.
individual symmetric configuration according to the arithmetic mean of those fits. The individual symmetric midsagittal reference plane was calculated on that basis.
For the purpose of identifying the landmark-based symmetric midsagittal reference planes, the cephalometric landmarks on the midline structure were tested to find those at the smallest distance from the symmetric midsagittal reference plane. To measure the distances between the individual symmetric midsagittal reference plane and the landmarks on the midline structure, all original and corresponding mirrored configurations were superimposed by full generalized Procrustes analysis, and the mean values were calculated (Table III). The 3 landmarks with the smallest distances were then used to draw the landmarks-based symmetric midsagittal reference plane. The 3-landmark-based plane's compatibility with the individual symmetric midsagittal reference plane was verified by measuring the asymmetry for each and testing it based on the study of Mardia et al.9 The asymmetry of the 3-landmark-based plane was measured as follows (Figs 4 and 5): (1) estimating the multiple
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
256
Fig 4. Landmark-based midsagittal reference plane with selected landmarks (Na, ANS, and PNS).
Fig 5. Asymmetry measurements for each configuration using the distance between the symmetric configuration and the ordinary Procrustes analysis fit onto the symmetric configuration.
regression line of the 3-landmark coordinates for each centered original configuration (the response variable of the regression line is the x-axis coordinate), (2) obtaining Xi for i 5 1, ., n, which is the configuration of rotating the original configuration as the estimated regression line is perpendicular to the x-axis, (3) determining the mirrored configuration Yi from the rotated configuration Xi around the YZ plane, (4) calculating the individual symmetric configurations Si of the Procrustes fits by the interactive ordinary Procrustes analysis of the Xiand Yi, and (5) measuring the asymmetry for each configuration as follows (see the Supplemental Material for more details). Let Xi for i 5 1, ., n be the ith configuration, and let Si be the individual symmetric configuration of Xi and
August 2016 Vol 150 Issue 2
the mirrored configuration Yi of Xi. Then the sum of the squared Euclidean distances is defined as the sum of distances between the corresponding landmarks of Xi and Si. However, the sum of the squared Euclidean distances depends on location, scale, and rotational effects of Xi. So, we consider another measure to analyze asymmetry, the squared Procrustes distances of the shapes. Here, “shape” means all the geometric information that remains when location, scale, and rotational effects are filtered out from a configuration. Therefore, first we must obtain a centered configuration from Xi. Then to remove the scale effect from Xi, we divide the centered configuration to the centroid size of Xi, and we call it the centered preshape. Since the location and scale effects are filtered out, all centered preshapes
American Journal of Orthodontics and Dentofacial Orthopedics
Shin et al
have the same scale. Then the squared Procrustes distances can be obtained by matching the centered preshape of Xi for i 5 1,., n and that of Si as closely possible over rotations. It can be obtained by the ordinary Procrustes analysis solution. Hence, the squared Procrustes distance is a measure for the asymmetry that does not depend on location, scale, and rotational effects of the original configuration, Xi. Based on the same manner as the sum of the squared Euclidean distances and the squared Procrustes distances, the amount of asymmetry was calculated as follows: (1) by comparing landmark changes between the original and symmetric configurations and shapes for the 2 methods, respectively; and (2) by comparing the differences of the amount of asymmetry between the 2 configurations and 2 shapes produced by the 2 methods. We compared the total variations for asymmetry measurements according to 2 (symmetric and 3-landmark-based) midsagittal reference planes. Mardia et al9 proposed an object-symmetry testing procedure that uses the close approximation of the Euclidean metric in the tangent space to the true Procrustes distance. In this way, Procrustes tangent projections XiP and YiP can be obtained from Procrustes fits by the generalized Procrustes analysis of Xi and Yi with respect to the full Procrustes mean shape G. The Procrustes tangent projections XiP and YiP have the same meaning as the centered preshapes, and G is symmetric and has P P the same shape as the ordinary average 12 ðX 1Y Þ, P P P where X and Y are the arithmetic means of Xi and YiP , respectively. Accordingly, it is possible to decompose the asymmetry of all data as follows (see the Supplemental Material for more details). The total variations for the asymmetry of all data are defined as the sum of squares of the distances between the corresponding landmarks of XiP and YiP . The total variation of the asymmetry SST can be decomposed as the variations between mean shapes and the variations within subjects. The variation between mean shapes is defined as the sum of squares of the distances between P P the corresponding landmarks of X and Y ; it means the between-squares side, SSB, for asymmetry. The variations within subjects can be measured by the sum of squares of the distances between the corresponding P P landmarks of XiP X and YiP Y ; the variations can be denoted by the within-subjects sum of squares, SSW. Using this method, it is possible to test the asymmetry of the population in the same manner as 1-way analysis of variance (ANOVA). All landmarks were remeasured at 2-week intervals by 2 investigators (S.M.S., Y-M.K.). The systematic intraexaminer and interexaminer errors between the 2
257
measurements were determined with a paired t test. Also, the magnitudes of those errors were assessed by calculating the intraclass correlation coefficient (ICC). For statistical computation purposes, the language R (Vienna, Austria) was used. RESULTS
The intraexaminer and interexaminer reliabilities of the landmarks were very good. There were no statistically significant differences in landmark identifications. The mean intraexaminer ICC values for the x, y, and z coordinate system were 0.924 (SD, 0.078) for the x-axis, 0.941 (SD, 0.056) for the y-axis, and 0.940 (SD, 0.054) for the z-axis. The mean interexaminer ICC values were 0.811 (SD, 0.228) for the x-axis, 0.865 (SD, 0.277) for the y-axis, and 0.916 (SD, 0.070) for the z-axis. Then we selected the nearest landmarks to the symmetric midsagittal reference plane. After all original and their mirrored configurations were superimposed by full generalized Procrustes analysis, the mean distances between the symmetric midsagittal reference plane and all landmarks on the midline structure were calculated (Table III). The 3 nearest landmarks were, in order, Na (0.697 6 0.542 mm), ANS (0.755 6 0.527 mm), and PNS (0.775 6 0.723 mm). These accordingly were selected for the 3-landmark-based midsagittal reference plane. We compared the landmark changes between the original and symmetric configurations and shapes fabricated by 2 (symmetric and 3-landmark-based) midsagittal reference plane methods. As a means of identifying the extents to which the pairwise landmarks changed according to the 2 midsagittal reference planes, the differences between the original and the fabricated symmetric configurations and shapes were measured using the sum of the squared Euclidean distances of the configurations and the squared Procrustes distances of the shapes, respectively, for the asymmetry measurements. The results showed little difference in the asymmetry measurements (sum of the squared Euclidean distances and squared Procrustes distances) between the symmetry and 3-landmark-based midsagittal reference planes (Table IV). However, the asymmetry measurements (sum of the squared Euclidean distances) for each configuration also were measured using the average of the distances between the symmetric configuration and the ordinary Procrustes analysis fit of the original configuration on the symmetric configuration. The measured asymmetries (sum of the squared Euclidean distances) on the 3-landmark-based plane were somewhat greater than those on the symmetric midsagittal reference plane.
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
258
Table IV. Asymmetry measurements on the symmetric
midsagittal reference plane and the 3-landmark-based plane Average of SSED (mm) Average of SPD Symmetric plane 70.614 6 2.759 9.67 3 104 6 7.28 3 104 Landmark-based 70.655 6 52.770 9.68 3 104 6 7.28 3 104 plane SSED, Sum of the squared Euclidean distance; SPD, squared Procrustes distance.
Differences between configurations and shapes were produced by the 2 (symmetric and 3-landmark-based) midsagittal reference plane methods. The average sum of the squared Euclidean distance and the squared Procrustes distance differences between the 2 configurations and the 2 shapes produced by the symmetric and landmark-based midsagittal reference planes were calculated as 0.121 6 0.241 mm and 1.69 3 106 6 3.25 3 106, respectively. Since the test data were almost identical, there were small differences between 2 plane methods. It meant that the 2 configurations and the 2 shapes produced by the symmetric and landmark-based midsagittal reference planes were similar. We compared the total variations of the asymmetry measurements according to 2 (symmetric and 3-landmark-based) midsagittal reference planes based on the method of Mardia et al.9 To verify the 3-landmark-based plane for compatibility with the symmetric midsagittal reference plane, asymmetry measurements were calculated for each plane and tested according to the method of Mardia et al. Using this method tested the total variation of asymmetry measurements in the same manner as 1-way ANOVA. The results showed Fy5:548 ðPy6:10631024 Þ on the 3-landmark-based midsagittal reference plane and Fy5:548 ðPy6:10631024 Þ on the symmetric midsagittal reference plane. As is apparent, the test data were almost identical; there was no significant difference between the planes. DISCUSSION
The posteroanterior cephalogram has been widely used for analysis of facial asymmetry. Traditionally, the midsagittal reference line has been defined using certain landmarks on 2-dimensional posteroanterior cephalograms: eg, vertical lines passing through Na and ANS, or through crista galli and ANS. Vertical planes passing through the midpoints of bilateral landmarks were used as well.10-13 Unfortunately, there are some limitations in clarifying cephalometric landmarks from overlapped
August 2016 Vol 150 Issue 2
structures using posteroanterior cephalograms. For this reason, facial asymmetry analysis should use 3D computed tomography or CBCT images. Hwang et al6 evaluated facial asymmetry using a midsagittal reference plane incorporating opisthion, crista galli, and ANS. Pelo et al14 emphasized the 3D computed tomography utility of a reference plane passing through the lateral semicircular canals. Meanwhile, Baek et al15 used, as their midsagittal reference, the plane including crista galli and the midpoint of the anterior clinoid processes and running perpendicular to the Frankfort horizontal plane. Authors of other studies have applied midsagittal reference planes incorporating sella, Na, menton, the midpoint of the 2 most lateral points of the foramen magnum, and the midpoint of the foramen spinosum.15-18 Notwithstanding all of the research devoted to this issue, the methods of landmark selection in the clinical field still have limitations. The method should use specific landmarks that are identifiable with good reproducibility. To overcome the possible limitations of setting up cephalometric midsagittal planes, the mirror image has been applied for facial asymmetry analysis.7,19-22 Damstra et al23 discovered that superimposition of mirror images could quantify the differences between anatomically correct anatomy and deformity. They insisted that a morphometrically determined midsagittal reference plane could eliminate the problems associated with anatomically determined planes. Wong et al,8 similarly, used a voxel-based median plane to assess facial bone asymmetry and reported that it was effective for subsequent treatment of patients. Symmetric midsagittal reference planes such as these suggested ones have been shown to produce accurate and reliable reference planes for comparative study.21,22 However, in clinical practice, it is difficult to find symmetric midsagittal reference planes without specific programs or a statistical package. Alternatively, the landmarkbased midsagittal reference plane can easily be applied in the clinical setting. In this study, to find the landmark-based midsagittal reference plane, we used full generalized Procrustes analysis-based superimposition of the original and its mirrored configuration and calculated the mean distances between the symmetric midsagittal reference plane and all landmarks on the midline structure (Table III). The 3 nearest landmarks on the midline structure were determined, in order, as follows: Na (0.697 6 0.542 mm), ANS (0.755 6 0.527 mm), and PNS (0.775 6 0.723 mm). These 3 landmarks, accordingly, were selected for the landmark-based midsagittal reference plane. The data indicated that these were close to the symmetric midsagittal reference plane: the mean differences were within 0.8 mm, and the standard
American Journal of Orthodontics and Dentofacial Orthopedics
Shin et al
deviations were within 0.7 mm. In this study, most of the tested landmarks were on the cranial base. Kwon et al17 reported that the degree of cranial base asymmetry did not differ between patients with asymmetry or symmetry and concluded that cranial base asymmetry severity is not a main factor in facial asymmetry. This suggests that landmarks on the cranial base can be used as reference points for construction of the midsagittal reference plane in patients with mild-to-moderate facial asymmetry. In this study, we selected 3 landmarks on the midline structure for the midsagittal reference plane. Several previous studies also have taken this approach. Trpkova et al,12 using 2-dimensional posteroanterior image analysis, found that vertical lines passing through the midpoints between the bilateral pairs of orbital landmarks are more accurate and valid for various asymmetries. Richardson24 observed that the midsagittal plane running perpendicular to the Frankfort horizontal plane and passing through Na and sella was the most similar to the symmetric midsagittal reference plane. On the other hand, Ferrario et al19 insisted that overall, the symmetric midsagittal reference plane did not include any facial midline landmarks. Our results, however, support the hypothesis that for patients with mild-to-moderate facial asymmetry, the symmetric midsagittal reference plane is almost on the midline. As a means of determining the optimal landmarkbased midsagittal reference plane for orthodontists and oral surgeons, the selected landmark-based midsagittal reference plane was tested with 2 comparisons. The first was for landmark changes between the original and symmetric configurations and shapes fabricated by the 2 (symmetric and 3-landmark-based) midsagittal reference plane methods. For the calculation of the landmark changes between the 2 configurations and the 2 shapes, respectively, the means of the sum of the squared Euclidean distances and the squared Procrustes distances were obtained. But before discussing the comparison results, we should distinguish an object's configuration from its shape. The configuration is the set of measured landmarks on a particular object; the shape is all geometric information on that object when location, scale, and rotational effects are filtered out. Two configurations' difference can be determined using the sum of the squared Euclidean distances between pairwise landmarks, but this might be inaccurate because the distance depends on the measured scale. Therefore, in statistical shape analysis, this difference is measured with reference to the squared Procrustes distances between 2 shapes, since the shape does not vary under translation and scaling of the configuration. In our study, to identify the extents to which the pairwise
259
landmarks changed according to the 2 midsagittal reference planes, the differences between the original and the 2 fabricated configurations or shapes were measured using the sum of the squared Euclidean distances or the squared Procrustes distances, respectively. The results of the comparisons of the landmark changes between the original and symmetric configurations and shapes fabricated by the 2 (symmetric and 3-landmark-based) midsagittal reference plane methods showed no significant differences (Table IV). The second comparison tested for its utility in determining the optimal landmark-based midsagittal reference plane was that between the 2 configurations and shapes produced by the 2 (symmetric and 3-landmarkbased) midsagittal reference plane methods. The asymmetries according to the 2 configurations differed slightly. Specifically, the asymmetries (sum of the squared Euclidean distances and the squared Procrustes distances) measured on the 3-landmark-based plane were somewhat greater than those on the symmetric midsagittal reference plane. On the other hand, comparisons of the landmark changes between the 2 configurations and shapes fabricated from the 2 midsagittal reference planes, respectively, were performed. The average sums of the squared Euclidean distances and squared Procrustes distances differences between the 2 configurations and shapes fabricated based on the symmetric and landmark-based midsagittal reference planes were calculated as 0.121 6 0.241 mm and 1.69 3 106 6 3.25 3 106, respectively. These are clinically acceptable differences. Based on the data obtained in this study, we can suggest 3 landmarks (Na, ANS, and PNS) for determination of the midsagittal reference plane in patients with mild-to-moderate facial asymmetry. Previous reports have introduced 3D image landmarks such as sella, the midpoint of the anterior clinoid process, the foramen spinosum midpoint, and the foramen magnum midpoint.6,15-17 However, finding these landmarks on 3D images is difficult without automatic software to define the midpoint between 2 specific pairwise landmarks. Hence, we endeavored to find the midline structural landmarks nearest to the midsagittal reference plane. Furthermore, the previous several midsagittal reference planes have not been compared for their accuracy. Among several midsagittal reference planes, the most accurate one would be a symmetric midsagittal reference plane. However, our suggested landmark-based midsagittal reference plane proved to be compatible with the symmetric one in this statistical study. Damstra et al23 claimed that use of this symmetric midsagittal reference plane for visually intact, asymmetry-unaffected regions of the skull might be
American Journal of Orthodontics and Dentofacial Orthopedics
August 2016 Vol 150 Issue 2
Shin et al
260
more valuable for diagnosis and treatment planning of craniofacial asymmetry. If this approach were to be individualized and automated, it could be useful for clinicians. This notwithstanding, the landmark-based midsagittal reference plane, alternatively, could be a helpful and easy method. In this study, we examined patients with mild-tomoderate facial asymmetry and a skewed distribution of Angle classifications. The utility of the suggested landmark-based midsagittal reference plane for other types of asymmetry has yet to be validated. Also, because soft tissues can offset facial skeletal asymmetry, the clinician should consider these midsagittal reference planes for skeletal and soft tissues differently. Therefore, further research, with various Angle classifications and other skeletal patterns, and with consideration of soft tissues, should be conducted. Moreover, other additional landmarks that are not located in the midline structure should be found for setting up the midsagittal reference plane. One example is the midsagittal plane that passes through 2 landmarks and runs perpendicular to the Frankfort horizontal plane. CONCLUSIONS
In scrutinizing the results of this study, we found that Na, ANS, and PNS are nearest to the symmetric midsagittal reference plane. These accordingly were used to establish a landmark-based midsagittal reference plane. Statistical shape analysis confirmed that this midsagittal reference plane is compatible with the symmetric midsagittal reference plane. Overall, the results indicated that a 3D midsagittal reference plane constructed of Na, ANS, and PNS could be a valuable tool for evaluation of patients with facial asymmetry. SUPPLEMENTARY DATA
Supplementary data related to this article can be found online at http://dx.doi.org/10.1016/j.ajodo.2016. 01.017. REFERENCES 1. Ahn JS, Hwang HS. Relationship between perception of facial asymmetry and postero-anterior cephalometric measurements. Korean J Orthod 2001;31:489-98. 2. Lee BR, Kang DK, Son WS, Park SB, Kim SS, Kim YI, et al. The relationship between condyle position, morphology and chin deviation in skeletal Class III patients with facial asymmetry using cone-beam CT. Korean J Orthod 2011;41:87-96. 3. Berssenbr€ ugge P, Berlin NF, Kebeck G, Runte C, Jung S, Kleinheinz J, et al. 2D and 3D analysis methods of facial asymmetry in comparison. J Craniomaxillofac Surg 2014;42:e327-34. 4. Kim JY, Jung HD, Jung YS, Hwang CJ, Park HS. A simple classification of facial asymmetry by TML system. J Craniomaxillofac Surg 2014;42:313-20.
August 2016 Vol 150 Issue 2
5. Hood CA, Bock M, Hosey MT, Bowman A, Ayoub AF. Facial asymmetry—3D assessment of infants with cleft lip & palate. Int J Paediatr Dent 2003;13:406-10. 6. Hwang HS, Hwang CH, Lee KH, Kang BC. Maxillofacial 3-dimensional image analysis for the diagnosis of facial asymmetry. Am J Orthod Dentofacial Orthop 2006;130:779-85. 7. Hajeer MY, Ayoub AF, Millett DT. Three-dimensional assessment of facial soft-tissue asymmetry before and after orthognathic surgery. Br J Oral Maxillofac Surg 2004;42:396-404. 8. Wong TY, Liu JK, Fang JJ, Wu TC, Tu YH. Use of the matching optimal symmetry plane method in planning surgical correction of facial asymmetry—a preliminary report of 20 patients. J Oral Maxillofac Surg 2014;72:1180.e1-13. 9. Mardia KV, Bookstein FL, Moreton IJ. Statistical assessment of bilateral symmetry of shapes. Biometrika 2000;2:285-300. 10. Grummons DC, Kappeyne van de Coppello MA. A frontal asymmetry analysis. J Clin Orthod 1987;21:448-65. 11. Jeon YN, Lee KH, Hwang HS. Validity of midsagittal reference planes constructed in 3D CT images. Korean J Orthod 2007;37:182-91. 12. Trpkova B, Prasad NG, Lam EW, Raboud D, Glover KE, Major PW. Assessment of facial asymmetries from posteranterior cephalograms: validity of reference lines. Am J Orthod Dentofacial Orthop 2003;123:512-20. 13. Peak SH, Ahn BK, Kim SH, Shon HB, Han HJ, Kang SM. A frontal cephalometric study on the reference lines to assess the craniomaxillofacial asymmetry. Korean J Orthod 1993;23:1-15. 14. Pelo S, Deli R, Correra P, Boniello R, Gasparini G, Moro A. Evaluation of 2 different reference planes used for the study of asymmetric facial malformations. J Craniofac Surg 2009;20:41-5. 15. Baek SH, Cho IS, Chang YI, Kim MJ. Skeletodental factors affecting chin point deviation in female patients with class III malocclusion and facial asymmetry: a three-dimensional analysis using computed tomography. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2007;104:628-39. ~ez-Vico RM, Iglesias-Linares A, Torres-Lagares D, Gutierrez16. Yan Perez JL, Solano-Reina E. Three-dimensional evaluation of craniofacial asymmetry: an analysis using computed tomography. Clin Oral Investig 2011;15:729-36. 17. Kwon TG, Park HS, Ryoo HM, Lee SH. A comparison of craniofacial morphology in patients with and without facial asymmetry—a three-dimensional analysis with computed tomography. Int J Oral Maxillofac Surg 2006;35:43-8. 18. Damstra J, Oosterkamp BC, Jansma J, Ren Y. Combined 3-dimensional and mirror-image analysis for the diagnosis for asymmetry. Am J Orthod Dentofacial Orthop 2011;140:886-94. 19. Ferrario VF, Sforza C, Poggio CE, Tartaglia G. Distance from symmetry: a three-dimensional evaluation of facial asymmetry. J Oral Maxillofac Surg 1994;52:1126-32. 20. McIntyre GT, Mossey PA. Size and shape measurement in contemporary cephalometrics. Eur J Orthod 2003;25:231-42. 21. Hartmann J, Meyer-Marcotty P, Benz M, Hausler G, StellzigEisenhauer A. Reliability of a method for computing facial symmetry plane and degree of asymmetry based on 3D-data. J Orofac Orthop 2007;68:477-90. 22. Meyer-Marcotty P, Alpers GW, Gerdes AB, Stellzig-Eisenhauer A. Impact of facial asymmetry in visual perception: a 3-dimensional data analysis. Am J Orthod Dentofacial Orthop 2010;137:168.e1-8. 23. Damstra J, Fourie Z, De Wit M, Ren Y. A three-dimensional comparison of a morphometric and conventional cephalometric midsagittal planes for craniofacial asymmetry. Clin Oral Investig 2012;16:285-94. 24. Richardson A. A comparison of traditional and computerized methods of cephalometric analysis. Eur J Orthod 1981;3:15-20.
American Journal of Orthodontics and Dentofacial Orthopedics