# Condylar Changes Following Mandibular Setback Using Manual Guidance
## 2 Materials and Methods
Comparative studies of the changes in the condylar position were performed by superimposing CT data through voxel-based registration (Invivo5; Anatomage Inc., Santa Clara, CA, USA) at three time points: T0 (before surgery), T1 (within 1 week after surgery), and T2 (6 months after surgery). A comparative analysis was performed according to patient age, sex, the type of orthognathic surgery, the extent of mandibular setback, and the degree of asymmetry. Originally, a negative value on the \(x\)-axis indicated rightward movement and a positive value indicated leftward movement. Therefore, the sign of the x-coordinate values was reversed in the left and right condyles, leading to the mean of change in both condylar positions on the \(x\)-axis being offset. To overcome this issue, the sign of the x-coordinate values for the right condyle was reversed such that a negative value indicated medial movement and a positive value indicated lateral movement. This allowed consistency in that the same sign indicated movement in the same direction for both condyles. In contrast, on the \(y\)-axis, a negative value represented downward movement, while a positive value \begin{table}
\begin{tabular}{c c c c} \hline
**Patient** & **Age (Years)/** & \multirow{2}{*}{**Surgery Type**} & **Right Mandibular** & **Left Mandibular** \\
**(No.)** & **Sex** & & **Setback (mm)** & **Setback (mm)** \\ \hline
19 & 20/F & Mandibular surgery & 9 & 4 \\
20 & 23/F & Bimaxillary surgery & 3 & 4 \\
21 & 21/F & Bimaxillary surgery & 2 & 8 \\
22 & 20/M & Bimaxillary surgery & 8 & 12 \\
23 & 20/F & Bimaxillary surgery & 12 & 12 \\
24 & 20/F & Bimaxillary surgery & 9 & 7 \\
25 & 23/M & Bimaxillary surgery & 10 & 12 \\
26 & 17/F & Bimaxillary surgery & 9 & 11 \\
27 & 17/F & Mandibular surgery & 10 & 9 \\
28 & 23/M & Bimaxillary surgery & 14 & 14 \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. represented upward movement; on the \(z\)-axis, a negative value indicated advance, while a positive value indicated setback. Coordinate values were compared not only to the extent of movement along the x, y, and z axes but also to the linear distances in the coordinate space using the following formula, which helps calculate the distance between two points, A (x1, y1, and z1) and B (x2, y2, and z2) in the coordinate space (Figure 1c). \[\overline{\text{AB}}=\sqrt{\left(\text{x}_{2}-\text{x}_{1}\right)^{2}+\left( \text{y}_{2}-\text{x}_{1}\right)^{2}+\left(\text{z}_{2}-\text{z}_{1}\right)^{2}}\]  
After testing for normality using the Kolmogorov-Smirnov test, the change of condylar position between observational points was analyzed with a one-sample test (SPSS Inc., Chicago, IL, USA). In the one-sample \(t\)-test, it was assumed that there were no changes in the observational period and that the standard deviation in the mother group was the same as that in the observed samples. The change in condylar position before and after a specific surgical protocol was assessed using a dependent samples \(t\)-test to analyze within-subject effects. For comparisons between two different surgical protocols, an independent samples \(t\)-test was employed to evaluate differences in condylar positional changes. To analyze the effects of varying setback amounts on condylar positional changes, an independent samples \(t\)-test was utilized. Similarly, to compare the condylar positional changes associated with different levels of asymmetry, an independent samples \(t\)-test was conducted. The significance level was set at \(p<0.05\). Figure 1: (a) A model drawing depicting each measurement axis in 3D analysis. The nasion serves as the central point for all axes, with the Frankfort horizontal plane (FH plane) as the reference plane. The \(x\)-axis is a straight line that runs parallel to the line connecting the FH planes and Orbitale. The \(y\)-axis is a straight line that passes through the nasion and is perpendicular to the FH plane.