Sixty-three CT images were reviewed for this study. The CT scans had been obtained from the patients with mandibular prognathism who were older than 18 years old and received orthodontic and orthognathic surgical treatments at Chonnam National University Hospital from 2002 to 2007.

The symmetric and asymmetric groups were classified according to the chin deviation. Chin deviation was defined by the angle between the midsagittal reference plane and the projected line of line ANS-Me onto coronal reference plane on reconstructed CT scans. The patients with angles less than 2° were considered as the symmetric group (average chin deviation 1.42±0.53°; average ANB -4.54±2.09°; 8 males and 11 females; average age of 23.6±2.7 years), and those with the angle of 4° and greater than 4° as the asymmetric group (average chin deviation 7.13±2.60°; average ANB -3.40±2.75°; 18 males and 10 females; average age of 22.6±4.0 years).3,9 Those with the angle 2° and more and the angle less than 4°(2°≤angle<4°) were considered to be mildly asymmetrical (16 cases) and had been excluded from this study, thus this study consisted of 47 CT images.

CT scans were obtained by using a spiral CT scanner (Light Speed QX/I, GE Medical Systems, Milwaukee, WI, USA) with 512×512 matrix, 120 kV, 200 mA and gantry angle 0°. The axial image thickness was 2.5 mm, the table speed was 3 mm per second, and the scanning time was 0.8 second. Digital imaging and communication in medicine (DICOM) images were created in 1.0 mm slice thickness. The acquired DICOM data were input into a personal computer. Using the CT data, the 3D images were reconstructed by software, Vworks+Vsurgery (Cybermed, Seoul, Korea). A multiplanar reformatted image, a volumetric model and a surface-rendered model of a CT scan which were completely interfaced on the software were constructed. The landmarks were defined on the volumetric model with the guidance of the multiplanar reformatted image. Three orthogonal reference planes were established: the midsagittal reference plane (yz plane) was made of Cg, ANS and Op;9 the horizontal reference plane (xy plane) was formed perpendicular to the midsagittal reference plane to pass through right Or and left Po;9 the coronal reference plane (zx plane) was made with Dent7 to be perpendicular to both the midsagittal and the horizontal reference planes. Condylar landmarks, gonial landmarks, and menton were identified. The condylar landmarks were the most superior (Cd_sup), lateral (Cd_lat) and posterior (Cd_post) points of the condylar head. The gonial landmarks were the most inferior (Go_inf), lateral (Go_lat) and posterior (Go_post) points of the gonion area. Menton (Me) was the most inferior point on the mandibular symphysis. The lines, longitude of ramus (LR: Cd_sup-Go_inf), ramus lateral (RL: Cd_lat-Go_lat), ramus posterior (RP: Cd_post-Go_post) and mandibular body (MB: Go_post-Me) were established with connecting each landmark. The rectangular coordinates (|x|, y, z) were obtained by the measurement tool. |x| was the distance from the midsagittal reference plane, y was the distance from coronal plane, and z was the distance from the horizontal reference plane; |x| was set to an absolute value for our purpose of comparing differences of the deviated side and the opposite side (Table 1, Fig. 1).

An alternate spherical coordinate system was developed from the geographic coordinate system for 3D evaluation of the facial lines and facial asymmetry.15

Figure 2 shows the definition of the alternate spherical coordinate system (v, θ, φ) of LR as an example. The three orthogonal axes were drawn, centered at the landmark, Go_inf. LR was identified as a vector and its length v was measured. The angle between the midsagittal reference plane and the vector were identified as midsagittal inclination angle, θ. The angle between the coronal plane and the projection line of the vector onto the midsagittal reference plane was identified as coronal inclination angle, φ. The alternate spherical coordinates (v, θ, φ) of other facial lines were made in the same way. The line LR (Cd_sup-Go_inf) was formed as (x_cd-x_go, y_cd-y_go, z_cd-z_go), where (x_cd, y_cd, z_cd) is for Cd_sup and (x_go, y_go, z_go) is for Go_inf. If x=x_cd-x_go, y=y_cd-y_go, and z=z_cd-z_go, the alternate spherical coordinates (v, θ, φ) were obtained from the formulae as below: then θ, φ in radian measure were converted into θ, φ in angle (θ_rad=θ°×π/180; φ_rad=φ°×π/180).

The bilateral differences of the alternate spherical coordinates (dv, dθ, dφ) between the deviated side and the opposite side was obtained (Fig. 2).

Because the bilateral facial lines have different starting points on the three-dimensional space, it was also necessary to describe the starting point for a definite representation of the vectors. The bilateral difference (dx, dy, dz) of the starting points, Go_inf, Go_lat, Go_post were obtained.

The bilateral differences of the spherical polar coordinates of each line (dv, dθ, dφ) were compared between the groups by Mann-Whitney U test. The correlation with chin deviation was statistically analyzed by Spearman's test. The bilateral differences of the landmarks (dx, dy, dz) were statistically compared by Mann-Whitney U test. SPSS 18.0 (SPSS Inc, Chicago, IL, USA) was used for the statistic analysis.

The bilateral differences of lengths of LR, RL, RP and MB were -1.62±3.61 mm, -1.13±6.29 mm, 0.06±4.04 mm and -0.83±2.38 mm in the symmetric group, and -3.45±4.59 mm, -3.12±5.23 mm, -3.26±4.53 mm and -3.15±2.92 mm in the asymmetric group; the facial lines of the deviated side were generally shorter than those of the opposite side. The bilateral differences of lengths of RL and MB were significantly different between the groups (p<0.05). The bilateral differences of midsagittal inclination angles of LR, RL, RP and MB were -1.41±2.46°, -1.48±2.6°, -2.25 ±3.32° and 0.24±2.57° in the symmetric group, and -4.36±3.86°, -4.99±4.15°, -3.84±5.06° and -0.15±2.96° in the asymmetric group; the facial lines of the deviated side were generally more inclined toward the midsagittal plane than those of the opposite side. The bilateral differences of the midsagittal inclination angles of LR, RL, RP and MB were significantly different between the groups (p<0.05). The bilateral differences of coronal inclination angles of LR, RL, RP and MB were -0.42±3.29°, 1.56±10.93°, -0.23±3.98°, -1.65±1.74° in the symmetric group, and -1.28±3.78°, -2.34±11.69°, -3.49±4.03° and -8.06±3.84° in the asymmetric group. The facial lines of the deviated side were generally more inclined toward the coronal plane than those of the opposite side; however, there was no significant difference between the two groups in the bilateral differences of coronal inclination angle of the facial lines.

The differences of the length and midsagittal inclination of LR and MB were significantly correlated with chin deviation (p<0.05). The differences of the midsagittal inclinations of all the lines had significant correlations with chin deviation (p<0.05). The difference of the midsagittal inclination of the MB had a fairly high negative correlation with chin deviation (r=-0.829, p<0.05). LR and RL showed a relatively high negative correlation with chin deviation in the difference of midsagittal inclination (r=-.619, -.674, p<.05). As menton was deviated from the midsagittal reference plane, the bilateral differences of the midsagittal inclinations of LR, RL, RP and MB were negatively increased. The lines of the deviated side were more inclined to the midsagittal reference plane than those of the opposite side. There was no significant correlation of the coronal inclinations to the chin deviation (Table 2).

The bilateral differences dx and dz of the landmarks Go_inf, Go_lat and Go_post were significantly different between the two groups (p<0.05). The landmarks of deviated side were significantly more laterally and superiorly to the opposite side in the asymmetric group than in the symmetric group (Table 3).