Challenges in measuring angles between craniofacial structures

Abstract Objective: Three-dimensional (3D) angular measurements between craniofacial planes pose challenges to quantify maxillary and mandibular skeletal discrepancies in surgical treatment planning. This study aims to compare the reproducibility and reliability of two modules to measure angles between planes or lines in 3D virtual surface models. Methodology: Twenty oriented 3D virtual surface models de-identified and constructed from CBCT scans were randomly selected. Three observers placed landmarks and oriented planes to determine angular measurements of pitch, roll and yaw using (1) 3D pre-existing planes, (2) 3D planes created from landmarks and (3) lines created from landmarks. Inter- and intra-observer reproducibility and repeatability were examined using the Intra-Class Correlation (ICC) test. One observer repeated the measurements with an interval of 15 days. ANOVA was applied to compare the 3 methods. Results: The three methods tested provided statistically similar, reproducible and reliable angular measurements of the facial structures. A strong ICC varying from 0.92 to 1.00 was found for the intra-observer agreement. The inter-observer ICC varied from 0.84 to 1.00. Conclusion: Measurements of 3D angles between facial planes in a common coordinate system are reproducible and repeatable either using 3D pre-existing planes, created based on landmarks or angles between lines created from landmarks.

axial, coronal and sagittal images, but also creating a 3D reformatted image. However, research purposes and surgery planning go beyond simple visualization, and therefore several 3D cephalometric tools have also been proposed to quantify linear and angular craniofacial measurements, transitioning from 2D to 3D analyses. [14][15][16][17][18][19][20] Most of these studies use CBCT to visualize a specific region, but still perform an overall overview of the patient using reformatted 2D images.
The use of 3D planes to quantify the craniofacial morphology proportions or measure angles between planes of anatomical structures pose mathematical challenges. It is important to understand that in 3D analysis a plane is defined by three points that may not lie at the same level; that the angle between two planes are determined by the normal vector of the planes; and  (Figure 3c and 3d).

Statistical analysis
To assess the reproducibility and reliability of the methods, three observers assessed the angles defined in the three spatial planes. To assess the repeatability of the method, one observer repeated the angular measurements with an interval of 15 days.

Correlation Coefficient (ICC) test.
To compare the three methods of measuring 3D angles while considering the normal distribution of the results, the ANOVA test was applied.   Table 1 shows the intra-and inter-rater correlations.

Results
For the measurements performed with 3D pre-existing planes adjusting the tangent to surfaces by utilizing the Angle Planes module, the smallest intra-observer ICC was 0.93 and the smallest inter-rater ICC was 0.84, For the measurements with "angles between lines from landmarks", utilizing the Q3DC module, the lowest intra-observer ICC was 0.92 and the lowest inter-rater ICC was 0.88. For the measurements performed with 3D planes created based on landmarks by utilizing the Angle Planes module landmarks option, the lowest intra-observer ICC was 0.94 and the lowest inter-rater ICC was 0.91.
Even though there were slight differences in the inter and intra-rater correlations using the three methods for angular measurements, the ANOVA test showed no significant difference between the three methods (Table 2).

Discussion
In the transition between 2D and 3D assessments of craniofacial structures, 2D images have been rendered from CBCT scans and conventional cephalometric analysis has been applied in a number of recent studies. The advantages of cephalometric analysis in images rendered from CBCT scans is the lack of magnification of the image and, in asymmetrical cases, the possibility to measure the right and the left sides separately. Previous studies have shown that 2D digital visual treatment objectives are similar to conventional assessment for the maxilla, but less for the mandible due to surgical mandibular changes being more complex than maxillary changes. 4    x-rays (condylar angle). Even though this study utilized measurements derived from known 2D cephalometry populational norms and standards, the 3D surface models constructed from CBCT images allow users to measure any other angles that may be helpful to evaluate complex skeletal discrepancies that were not previously possible to measure in 2D images. 6,[11][12][13] The two methods using landmarks were similar, and no significant challenges were noticed. The method of managing pre-existing planes, however, demanded more practice adjusting the planes towards the correct position during the calibration period. ANOVA results showed statistical similarity between the methods ( Table 2). The high intra-observer correlation found suggests that all methods are repeatable options for angular measurements of 3D surface models ( Table   1). The high inter-observer correlations suggest that all methods are also reproducible (Table 1). Therefore, users may use any tool they feel more comfortable with.
The greatest challenge in transitioning from 2D to 3D craniofacial measurements is how to interpret the data findings in a clinically meaningful