Facial bone is composed of a collection of thin segments and contains hollow structures (i.e., foramens and sinuses), which distinguishes it from long bones. Because of this difference, analysis software is an essential component for facial bone studies and image assessment4,10. Therefore, clinical physicians with experience with facial bone images and computer scientists who can develop image analysis software conducted a joint study.
Computational biology is a research field that focuses on data analysis and validation of theoretical methods in biological interactions. Adequate analytic software is crucial because non-invasive evaluation and preliminary studies are required. This type of analysis is particularly important in biomechanical sciences11. Many studies have been performed using analytic software to detect and estimate subtle changes. Ylitalo et al. quantified the surface of degenerated cartilage using micro-CT image stacks12. Surface continuity, fibrillation, and fissures were examined to evaluate osteoarthritis on articular surfaces. This method could provide an additional type of reference methodology for diagnostic imaging. In addition, Salfer et al. estimated the curvature of cell membranes using cryo-electron tomography images13. An estimation algorithm was introduced to differentiate reliable signals in noisy image data. The analytic strategy was also applied to the surface of embryonic cells and human brain hemispheres.
Our analytic software emphasized the need for an adequate algorithm to evaluate the degree of curvature that can provide straightforward visualization and data expression in understandable ways. A geometric algorithm was suggested based on the analytic strategy of clinicians. Accordingly, reasonable calculation formulas that could be understood by scientists from different research fields were necessary. Therefore, a triangular mesh model was adopted to analyze bent and curved surfaces. The initial medical images were stored in a DICOM file format and converted into OBJ files, which are versatile and can be utilized for 3D image assessment14. The OBJ image files contain multiple triangles sharing vertices and sides. These elements provide vectors and a reference plane. The average sin values of the angles between each vector and the reference plane were utilized to produce a discrete curvature approximation.
During the program development process, the range of the triangular mesh (triangular pyramid) that should be used to calculate the curvature was discussed. When the curvature is calculated by specifying a wide range based on one apex, irregularities can be more sensitively measured. Therefore, even small changes can result in a large value (i.e., close to 1). During the initial program development, the results were derived from a narrow range setting, and thus the difference between the fractured part and the normal part was not evident. To solve this problem, the range was gradually increased, and a range over which the results were valid was obtained.
The analytic software has user-friendly features for the image analysis stage. OBJ files are input into the software and evaluated by clinicians. The subdivisions among facial bone structures can be easily selected using a mouse cursor. Thereafter, a bar graph showing curvature ranges and the percentage of each curvature range is presented automatically. Numeric values (i.e., discrete curvature approximation) are also displayed in a different window. This simplicity added efficiency and accessibility to the analysis process.
Before surgery, both the inferior orbital rim and the anterior maxilla exhibited greater curvature values due to sharp bends. After surgery, a decrease in the curvature value occurred because of substantial changes after reduction (Figs. 1 and 2). In addition, when the fractured side and the unaffected side were compared with each other, greater similarity results were demonstrated after surgery using the BCSI (Figs. 3 and 4).
Because of their anatomical nature, neither the inferior orbital rim nor the anterior maxilla forms a perfect curve15,16. Therefore, an indicator is needed that can be used as a standard for analysis. Therefore, to increase the objectivity of measurements, comparisons were performed before and after surgery, followed by comparisons between the fractured side and the unaffected side. Facial bone curvature has been studied due to its complexity and regional shape changes during the aging process. Williams et al. performed a thorough analysis of the curvature of several landmarks17. Data were collected on the orbit, zygomatic arch, nasal bone aperture, and alveolar process of the maxilla. The configuration and vector plot of each structure provided useful information to perceive the curvature of facial bone.
The objective measurement of curvature has been utilized in the preoperative planning stage of various studies. Facciuto et al. generated a 3D skull model of a patient who underwent composite reconstruction of the frontal and superior orbital rim areas18. A xenohybrid bone substitute was used to supplement the defect, and a digital design of the curved surface was used to perform adequate reconstruction of the complicated architecture. Wang et al. designed a digital template to restore the orbital rim, orbital floor, and anterior maxilla of facial cleft patients19. The outer table of the cranial bone was used as a donor site, and accurate measurement of the shape and curvature was crucial. A computer-assisted rapid prototyping technique assisted in performing precise surgical procedures and anticipating the contour of recipient sites. Park et al. presented the anatomical characteristics of patients with orbital wall fracture20. Orbital CT images were analyzed according to the area and thickness of the orbital wall and the coefficient of curvature. The coefficient of curvature was measured on the inferior orbital wall (i.e., orbital floor), and the inferior wall fracture group had a greater curvature coefficient than the medial orbital fracture group.
The limitations of our study include discrepancies in outcomes depending on the image quality. The facial bone CT images were obtained using a 2-mm interval between consecutive sections. Reconstructed 3D CT images based on section slices cannot show a perfect curve, and the unintended flaws could affect the resulting values. Recent studies have presented curvature estimation and segmentation techniques to account for breaks in curves, and favorable results have been demonstrated2,10,13. Our group is planning to implement appropriate strategies to resolve this limitation. Furthermore, absorbable fixation plates and screws were visible on CT images, and these could be inevitable artifacts. Advanced methods to differentiate implants from natural bony components are necessary to achieve an accurate analysis.
Appropriate analytic software is an essential component for preoperative planning and postoperative analysis. This method has the advantage of allowing delicate and non-invasive assessments. Our newly developed analysis software was applied to differentiate between pre- and postoperative curvature values. Its capability was further validated with regard to the similarity between facial bones on both sides of patients. CT images can be processed and evaluated using discrete differential geometry methods. Modification of previous formulas will foster further precision and accuracy in various fields of computational biology.