Objective Analysis of Orbital Rim Fracture CT Images Using Curve and Area Measurement

Objective Analysis of Orbital Rim Fracture CT Images Using Curve and Area Measurement | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Objective Analysis of Orbital Rim Fracture CT Images Using Curve and Area Measurement Myungchul Lee, Junghwan Yoo, Jeenam Kim, Hyungon Choi, Donghyeok Shin, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4553660/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract The orbital bone presents a closed curve, and fracture results in disfigurement. An image analysis procedure was developed to examine before and after corrective surgery. An ellipse and circumscribed contour embodied the closed curve. Three-dimensional (3D) computed tomography (CT) images of were collected from 25 patients. Orbital rim data were generated, and binary images were created to facilitate closed curve analysis. Various indices, including the solidity value (closed curve area/convex hull area) and ellipse distance (discrepancy between the closed curve and the ellipse traversing the curve), were utilized. The ratios of various indices—including the number of vertices, solidity value, and ellipse distance—between the affected and unaffected sides showed postoperative values that were closer to 1, which would indicate perfect symmetry, than the preoperative measurements ( P < 0.05). The solidity value increased, while both the ellipse distance and curvature values decreased, reflecting the transformation of bends into smooth contours following reduction surgery ( P < 0.05). Significant correlations were observed between 1-solidity, ellipse distance, and curvature using the Pearson correlation test ( P < 0.05). This study validated postoperative changes in various indices and established correlations among multiple values, specifically solidity, ellipse distance, and curvature. Employing multiple indices with mutual complements has provided objective information confidently. Biological sciences/Computational biology and bioinformatics Physical sciences/Mathematics and computing orbital bone fracture computed tomography curve area Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 INTRODUCTION The orbital bone of the facial skeleton is composed of several bony segments that form a closed curve. An injury to this curve appears as a broken line, which can be identified in facial bone computed tomography (CT) images 1 . In contrast to the analysis of other parts of the facial skeleton, the closed curve shape and cup-shaped characteristic give the structure an additional opportunity for analysis. Numerous studies have focused on simplifying and standardizing spaces or structures and their relationships, employing methods such as Hamilton’s Ricci flow, geometrization, and vector calculus 2 – 5 . These theoretical approaches offer satisfactory solutions to complex structures and shapes that are difficult to grasp intuitively. Additionally, the formation of closed curves using approximate values presents an intriguing area of study when examining shapes in unidentified spaces 6 . Accurate measurement within this complex structure is challenging. The disruption caused by an injury alters a smooth curve, yet it still offers sufficient information prior to surgical correction 7 . Thus, CT studies are performed both before and after surgery to assess orbital fractures. These imaging studies are crucial for determining whether the fracture site has been adequately reduced 8 . It is necessary to check that the curve of the bone-to-bone contact area forms a smooth union. Biologic imaging techniques, such as CT scans, are employed in both static and dynamic modalities 6 , 9 . When natural alignment is disrupted, structural disfigurements become apparent. Conversely, the recovery of disarranged anatomical structures can be efficiently confirmed through postoperative morphometric evaluation. Additionally, the components of the orbital rim exhibit viscoelastic characteristics. Such unexpected alterations necessitate high-quality images to ensure adequate correction 10 . An image analysis procedure was developed to assess whether the orbital rim forms a smooth curve following corrective surgery. To analyze a specific area of interest in three-dimensional (3D) CT data, the image was segmented into a defined unit 11 . Subsequently, closed curves were generated and analyzed using ellipses and circles based on approximate values. Additionally, the curvature value was calculated on the closed curve, allowing for the determination of the average curvature. These various analytical methods yielded a set of results and demonstrated a correlation between the values. In this report, we describe the development of the analytical process and present the outcome measures. RESULTS The objective indices measured before and after surgery using the software were compared. The ratio between the affected and unaffected sides was figured out on each index. When symmetry between the affected and unaffected sides is achieved, the ratio approaches 1, as mentioned in the methods section. The ratio of vertices (number of vertices in the contour) before surgery was 0.9648 ± 0.1157, and after surgery, it was 1.0063 ± 0.0863, indicating a value closer to 1 ( P < 0.05). Similarly, the ratio of all points (number of pixels in the contour) before surgery was 0.9704 ± 0.1046, and after surgery, it was 1.0006 ± 0.0815, also indicating a value closer to 1 ( P < 0.05). The ratio of the solidity value (contour area/convex hull area) before surgery was 0.9923 ± 0.0292, and after surgery, it increased to 0.9965 ± 0.015, indicating a value closer to 1 ( P < 0.05). The ratio of the ellipse distance, which measures the discrepancy between the contour and the ellipse, was 1.4071 ± 0.8062 before surgery and decreased to 1.2661 ± 0.6218 after surgery ( P < 0.05) ( Table 1 , Fig. 1 ). Table 1 Pre- and post-operative comparison using ratios of affected and unaffected sides (unit: ratio). The ratios of vertices (number of vertices in the contour), all points (number of points [pixels] in the contour), solidity value (contour area divided by convex hull area), ellipse distance (discrepancy between contour and ellipse), and average curvature demonstrated postoperative changes converging towards 1 ( P < 0.05). A ratio of 1 indicates symmetry between the bilateral sides. PreOp., preoperative data; PostOp., postoperative data; SD, standard deviation Unit (ratio) Vertices All Points Solidity 1-Solidity Ellipse Distance Curvature PreOp. Average 0.9648 0.9704 0.9923 1.3978 1.4071 1.0458 SD 0.1157 0.1046 0.0292 0.7812 0.8062 0.0484 PostOp. Average 1.0063 1.0006 0.9965 1.1926 1.2661 1.0126 SD 0.0863 0.0815 0.015 0.4384 0.6218 0.0382 Furthermore, the values representing the discrepancy between smooth and irregular curves can be used in further analysis. When a smooth closed curve (yellow line) encircles an irregular curve (green line) with severe bends, the solidity value (contour area/convex hull area) of the affected side is significantly less than 1. Conversely, this value approaches 1 when the irregularity is corrected and the curve resembles a smooth contour. In this scenario, the affected side's ellipse distance, which measures the discrepancy between the contour (green line) and the ellipse (red line), is considerably greater than 0 before surgery. This distance will decrease towards zero as the curve smoothens postoperatively. Specifically, the affected side's solidity value before surgery was 0.9583 ± 0.0213, and after surgery, it improved to 0.9645 ± 0.0127, indicating a value close to 1 ( P < 0.05). The ellipse distance before surgery was 1.446 ± 0.681, and after surgery, it reduced to 1.1902 ± 0.4859, demonstrating a value nearing zero ( P < 0.05) ( Figs. 2 and 3 ) . The assessment process included analyzing the curvature of specific contours. The Fiji plugin calculates curvature values using B-splines 12 . The average curvature of the orbital rim before surgery was 0.2853 ± 0.0078, while the post-surgery value was 0.2747 ± 0.0088. A comparison of these average values revealed a significant decrease in curvature for the orbital rim after surgery ( P < 0.05) (Table 2 ). Table 2 The solidity, ellipse distance, and curvature change when the bent unit is reduced, showing a smooth curve. Specifically, the affected side’s solidity value changed to a postoperative measurement closer to 1 ( P < 0.05). The ellipse distance and curvature value changed to postoperative measurement closer to 0 ( P < 0.05). PreOp., preoperative data; PostOp., postoperative data; SD, standard deviation Solidity (ratio) 1-Solidity (ratio) Ellipse Distance (mm) Curvature (µm − 1 ) PreOp. Average 0.9583 0.0417 1.446 0.2853 SD 0.0213 0.0213 0.681 0.0078 PostOp. Average 0.9645 0.0355 1.1902 0.2747 SD 0.0127 0.0127 0.4859 0.0088 Pearson correlation coefficients were calculated for the following values: solidity, ellipse distance, and curvature. After surgery, there was an increase in solidity, while both ellipse distance and curvature decreased. To assess the positive correlations among these values, 1-solidity, ellipse distance, and curvature were used in the analysis. The solidity is the ratio of pixels in the subject to pixels of the convex hull image. In this context, 1-solidity represents the rest of the convex hull image excluding the subject, and decrement can be assumed when irregular boundaries are reduced after surgery. The results showed a significant correlation between these values in both preoperative and postoperative measurements ( P < 0.05) ( Table 3 , Fig. 4 ). The raw dataset is presented as a supplementary file (supplement 1). Table 3 Pearson correlation test. Pre- and postoperative values of 1-solidity, ellipse distance, and curvature values were utilized for the analysis. The values presented significant correlations ( P < 0.05). R-value t value P -value Preoperative 1-Solidity vs. Ellipse distance 0.726 5.069 < 0.001 Ellipse distance vs. Curvature 0.731 5.133 < 0.001 Curvature vs. 1-Solidity 0.873 8.592 < 0.001 Postoperative 1-Solidity vs. Ellipse distance 0.728 5.089 < 0.001 Ellipse distance vs. Curvature 0.726 5.065 < 0.001 Curvature vs. 1-Solidity 0.845 7.576 < 0.001 DISCUSSION The orbital rim, composed of the frontal bone, zygomatic bone, and maxilla, forms a closed curve. This innate characteristic provides various analytic indices, such as height, width, curvature, and continuity. The curve can be analyzed by comparing it with circumscribing circles or tangent lines 13 . Anatomic structures like orbital fissures, the lacrimal fossa, and muscle attachments contribute to the irregularity of the orbital rim, preventing it from forming a perfect circle in its physiological state 14 . Rubin et al. described ancestral variations in the shape of the orbital rim, noting that European orbits exhibit more pronounced folding than either African or Asian orbits. Conversely, the lateral margin of African orbits is positioned more posteriorly relative to the medial margin compared to Asian orbits 15 . These findings indicate that curvilinear relationships are the most informative aspect of the shape of the orbital rim. Li et al. presented a study using deep learning-based CT radiomics to represent features of Asian bony orbits, analyzing them in relation to age and sex 16 . They found that during aging, the bony orbital area increased in males but decreased in women, with the area being consistently larger in men than in women. This difference may be attributed to variations in the position and degree of orbital bone resorption between men and women as they age. Bony structures can be analyzed using various formulas and geometry. Narra et al. introduced a method involving Ricci flow-based conformal mapping of the femur bone to examine the effects of exercise loading 2 . This approach allows the exploration of the causal relationship between habitual loading and the adaptive response in bone morphology through the spatial distribution of mechanically relevant features. The Ricci-flow based conformal mapping procedure demonstrated correspondence among the periosteal surfaces, enhancing the visualization of surface features. This, in turn, enabled the study of the group-wise distribution of mechanically relevant features. By using group-wise and composite-group maps, the bony surfaces impacted by specific loading were pinpointed with a high degree of spatial localization. Singh et al. studied orbital morphometry based on CT analysis 10 . Although variations in orbital depths exist between genders, no significant differences were observed in all parameters between the right and left orbits, confirming the symmetry of both orbits in the same individual. Fractures involving the orbital rims must be anatomically reduced before addressing other structures 7 . The symmetry between bilateral sides is crucial for orbital reconstruction, as it allows the standard orbit to serve as a benchmark guide. In our research, we examined the following indices: 1) vertices (number of vertices in the contour), 2) all points (number of contour points), 3) solidity (contour area [green] / convex hull area [yellow]), 4) ellipse distance (distance between shapes [contour: green, ellipse: red]), and 5) average curvature. These indices showed greater discrepancies preoperatively than in postoperative measurements. The consistent changes across multiple indices confirmed symmetric correction following surgical procedures. This study confirmed positive correlations between several values; 1-solidity, ellipse distance, and curvature with statistical significance ( P < 0.05). A closed curve with an irregular margin cannot be described by a single formula. In this context, multiple indices, specifically 1-solidity, ellipse distance, and curvature, were employed for interdisciplinary research. These three indices, when used together, can provide comprehensive information for both medical practitioners and patients. The analytic strategy of defining closed curves has been a significant area of research. Dallaston et al. developed strategies to describe a closed embedded plane curve using both formal asymptotic and numerical techniques 17 . Li et al. suggested a morphometric strategy for shape analysis and introduced three types of segments to classify components in the chain 18 . These include a mean segment (M-segment) characterized by a consistent shape and size, a circular helical segment (C-segment) defined by constant curvature, and a growth segment (G-segment) which maintains a consistent shape but varies in size. These segments were used to delineate the structure and construction of forms. Stepwise discriminant analysis was employed to define the shapes of anatomical structures, including the facial skeleton. The orbital rim consists of multiple segments, marked by ridges and grooves, giving it a complex shape even in the absence of any fractures. In this context, various strategies and formulas aimed at simplifying the orbital rim can facilitate effective evaluation. We employed methods based on the ellipse and convex hull area, using approximate values. These served as numerical evidence for assessing the deflections and bends in the structure. Posttraumatic disfigurement of the orbital rim is influenced by several factors. Choi et al. explored the relationship between the negative vector of the eye globe and the location of the fracture 19 . The term "negative orbit vector" describes a situation where the anterior portion of the globe protrudes beyond the soft tissue of the malar eminence. They focused on eyes that were prone to specific traumas. Their findings indicated that the negative orbit vector was more associated with fractures of the orbital floor than with those of the medial wall. Jacobs et al. analyzed CT images of patients with orbital fractures and determined that reduced preorbital and intraorbital soft tissue volumes are linked to these injuries 8 . The surrounding soft tissues dissipate impacts on the anterior orbital rim and within the orbit. Additionally, the orbital shape and its mechanical response to stress and force play roles in the extent and nature of disfigurement. Deserno demonstrated morphological alterations in cellular lipid membranes using differential geometry and curvature stresses 20 . The following principles were suggested to predict the effects: the force exerted is influenced by the surface geometry and local curvature, and the resultant force is not tangential to the surface when the curvature varies. Multiple causative factors influence the morphologic outcomes following physical impacts. Research conducted at both large-scale and microscopic levels helps elucidate these processes and their consequences. The human orbital bone features delicate anatomical structures that respond characteristically to physical stimuli. Orbital morphometry, which utilizes measurements and imaging studies, offers objective information. Our study revealed postoperative changes using various references, including vertices, circumscribed curves, and traversing ellipses. Additionally, positive correlations were confirmed among 1-solidity, ellipse distance, and curvature. A closed curve displaying irregularity cannot be described by a single formula. These three indices provided sufficient information for objective analysis and had complementary characteristics. METHODS Patients and Data Acquisition Three-dimensional (3D) CT images of facial bones were obtained from 25 patients with unilateral orbital rim fractures (14 males, aged 19–73 years, and 11 females, aged 25–68 years) who underwent reduction surgery to treat their fractures between March 2017 and February 2020. The study adhered to the ethical standards set forth in the 1964 Declaration of Helsinki and its subsequent amendments. Written informed consent was obtained from all patients. The institutional review board of Konkuk University Medical Center approved the study (approval number: KUMC 2022-03-013). An orbital rim fracture was diagnosed based on the patient's symptoms and an analysis of facial bone CT images; a 3D CT of the facial bones was utilized as it provides suitable views for assessing both preoperative displacement and postoperative correction. The CT images were acquired using a standard CT scanner (GoldSeal™ Optima™ CT660, General Electric Company, Boston, MA, USA) with consistent data acquisition settings. Orbital Rim Contour Data Generation The following method was used to generate orbital rim contour data (Fig. 5 ): Facial bone CT image preprocessing: Since the amount of data in facial bone CT images is usually too extensive for processing, only the region around the orbits is retained while the rest is deleted using standard software (Blender version 3.5; Blender Foundation, Amsterdam, the Netherlands). Cube generation and intersection calculation: A cube is generated to overlap with the CT image, and the intersecting surfaces are calculated. To ensure data consistency, the CT image is gradually advanced from the cube's center, and the first surface where the orbital rim contour is closed is used as the reference. Binary image creation: Noise is removed, and the inside of the contour is filled with 1 (white) and the outside with 0 (black) to create a binary image. Objective Indices for Analysis (Fig. 6 ) Vertices = Number of vertices in contour All Points = Number of points (pixels) in contour Solidity * = Contour area (green) / Convex hull area (yellow) Ellipse Distance † = Average distance between the contour (green) and ellipse (red) * Solidity is defined as the ratio of pixels in the subject to the pixels in the convex hull image, representing the subject's density. A value of 1 indicates a solid subject, whereas a value below 1 suggests a subject with irregular boundaries. This method was adopted from "Shape Analysis and Measurement" by Michael A. Wirth 21 . † Ellipse Drawing The ellipses are drawn using the fit-ellipse function in the open computer vision library. This function determines the best-fitting ellipse for a given set of 2D points. It employs the first algorithm outlined by Fitzgibbon et al. 22 . The above index values serve as a foundational basis for analysis. The ratio between the affected and unaffected sides was determined based on these values. This ratio was analyzed both before and after surgery. When symmetry between the affected and unaffected sides is achieved, the ratio approaches 1. $$\text{R}\text{a}\text{t}\text{i}\text{o} = \frac{Objective index of affected side}{Objective index of unaffected side} \cong 1 if symmetry$$ Facial Bone CT Analysis Using the Software Indices that indicate surgical outcomes can enhance comprehension for both patients and researchers. It is assumed that fractured areas are present before surgery; therefore, the values will be distributed heterogeneously compared to those obtained postoperatively. Index values measured before and after surgery were illustrated in a graph to demonstrate the outcomes. If the average value shows excessive dispersion, the graph can briefly and clearly display the outcomes for easier understanding. Statistical Analysis The paired t-test was employed to compare preoperative and postoperative measurements across various indices: vertices, all points, solidity, ellipse distance, and curvature values. Pearson's correlation test was used to assess the strength of the linear association between variables, specifically 1-solidity, ellipse distance, and curvature values. The analysis incorporated a 95% confidence interval. Standard software (SPSS for Windows version 25.0; IBM Corp., Armonk, NY, USA) was utilized for the statistical analysis. A P -value of less than 0.05 was deemed statistically significant. Declarations Conflict of interest The authors have no conflicting or vested interest whatsoever with respect to this research. Financial disclosure None of the authors has a financial interest in any of the products, devices, or drugs mentioned in this manuscript. Author Contribution Author contributions: M.L. and J.Y. designed the research. J.K. collected data. H.C. and D.S. analyzed the data. H.L. wrote the manuscript. All the authors read and approved the manuscript. Acknowledgments: This work was not supported by the research grant. Data Availability All data generated or analyzed during this study are included in this article and its supplementary information file. References Turvey, T. A. & Golden, B. A. Orbital anatomy for the surgeon. Oral Maxillofac Surg Clin North Am 24, 525–536, doi: 10.1016/j.coms.2012.08.003 (2012). Narra, N. et al. 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Additional Declarations No competing interests reported. Supplementary Files Supplement1.RawData.xlsx Cite Share Download PDF Status: Published Journal Publication published 13 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 04 Oct, 2024 Reviews received at journal 03 Oct, 2024 Reviewers agreed at journal 01 Oct, 2024 Reviews received at journal 12 Sep, 2024 Reviewers agreed at journal 05 Sep, 2024 Reviewers agreed at journal 03 Sep, 2024 Reviewers invited by journal 03 Sep, 2024 Editor assigned by journal 30 Aug, 2024 Editor invited by journal 12 Jun, 2024 Submission checks completed at journal 10 Jun, 2024 First submitted to journal 09 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4553660","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":319022283,"identity":"49ff700b-e784-48cb-a833-74f79f4f173c","order_by":0,"name":"Myungchul Lee","email":"","orcid":"","institution":"Konkuk University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Myungchul","middleName":"","lastName":"Lee","suffix":""},{"id":319022284,"identity":"cf7b26f5-6ef0-4f62-b186-f01d6855e1bf","order_by":1,"name":"Junghwan Yoo","email":"","orcid":"","institution":"Konkuk University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Junghwan","middleName":"","lastName":"Yoo","suffix":""},{"id":319022285,"identity":"d4beebfe-9789-4add-b364-5e238e736a69","order_by":2,"name":"Jeenam Kim","email":"","orcid":"","institution":"Konkuk University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jeenam","middleName":"","lastName":"Kim","suffix":""},{"id":319022286,"identity":"3a8f08c5-11aa-40af-9576-3eeedcbdb1d4","order_by":3,"name":"Hyungon Choi","email":"","orcid":"","institution":"Konkuk University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hyungon","middleName":"","lastName":"Choi","suffix":""},{"id":319022287,"identity":"66f5010e-3f29-491e-a703-b0d930097455","order_by":4,"name":"Donghyeok Shin","email":"","orcid":"","institution":"Konkuk University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Donghyeok","middleName":"","lastName":"Shin","suffix":""},{"id":319022288,"identity":"47121511-d668-4087-b80c-561de1f63ec4","order_by":5,"name":"Hasup Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYBACAwhlA6TZGBgbQGwe4rSkka7lMAlazNmPP5Mu+HPemF+6LU1yBoOdPAPP2Qd4tVj25JhJz2y7bSY559gxyQ0MyYYNvO0G+B12IIdNmrfhto3BjfQ2yQcMzAkM/GwE/HL++TNpnj/nYFrqidByI8FMmoftgJnBjTSQww4nMPC2EdLyxth6ZluyseSMtGTLGQbHDdt4jhFyWPrD2wV/7Az7JdIMb/ZUVMvz86Th1wICzEgmgKKHCMBMWMkoGAWjYBSMaAAALic+S9RwDLwAAAAASUVORK5CYII=","orcid":"","institution":"Konkuk University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Hasup","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2024-06-09 11:54:00","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4553660/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4553660/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-76818-8","type":"published","date":"2024-11-13T15:57:51+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":59605985,"identity":"4464f743-a669-4dbf-9608-c84ddab62397","added_by":"auto","created_at":"2024-07-03 18:50:54","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":113707,"visible":true,"origin":"","legend":"\u003cp\u003ePre- and post-operative comparison of the ratios of affected and unaffected sides. The ratios of vertices (number of vertices in the contour), all points (number of points [pixels] in the contour), solidity value (contour area divided by convex hull area), ellipse distance (average distance between contour and ellipse), and average curvature demonstrated postoperative changes converging towards 1 (P\u0026lt;0.05). A ratio of 1 indicates symmetry between the bilateral sides.\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/f931ef35e6847e2631253ea4.jpg"},{"id":59605981,"identity":"79718279-99b2-4124-9280-5be76efeceb1","added_by":"auto","created_at":"2024-07-03 18:50:54","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":153120,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of the right orbital rim. (a) The fractured right orbit showed a prominent groove on the inferior rim preoperatively. The solidity value (green contour area divided by yellow convex hull area) was 0.9709, the ellipse distance (discrepancy between green contour and red ellipse) was 1.482, and the average curvature was 0.2819 preoperatively. (b) The displacement was reduced postoperatively. The three values changed to 0.9796, 0.786, and 0.2641, respectively. The alteration represents convergence to the circumscribing smooth contour and traversing ellipse.\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/9c78be4cd504669eedc11ec5.jpg"},{"id":59605987,"identity":"f4a746ea-d034-495e-aae0-07896f91b223","added_by":"auto","created_at":"2024-07-03 18:50:54","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":150381,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of the left orbital rim. (a) The fractured left orbit showed a disfigurement on the inferior medial rim preoperatively. The solidity value (green contour area divided by yellow convex hull area) was 0.9399, the ellipse distance (discrepancy between green contour and red ellipse) was 1.393, and the average curvature was 0.2869 preoperatively. (b) The displacement was reduced postoperatively. The three values changed to 0.9738, 1.077, and 0.2674, respectively. The alteration represents convergence to the circumscribing smooth contour and traversing ellipse.\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/0d4337bd0363c05f3e323d61.jpg"},{"id":59606958,"identity":"78697a2d-2801-4c54-9a28-24256fd511c0","added_by":"auto","created_at":"2024-07-03 18:58:54","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":142095,"visible":true,"origin":"","legend":"\u003cp\u003ePre- and postoperative correlation measurements: 1-solidity, ellipse distance, and curvature were utilized for the analysis. The values presented significant correlations (\u003cem\u003eP\u003c/em\u003e\u0026lt;0.05).\u003c/p\u003e","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/2a0459c2553979f7731908d7.jpg"},{"id":59607614,"identity":"47e19373-1bad-4466-8a7d-48ae4c026d36","added_by":"auto","created_at":"2024-07-03 19:06:54","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":200848,"visible":true,"origin":"","legend":"\u003cp\u003eGeneration of orbital rim contour data. Facial bone CT image processing: The region of interest around the orbits is retained, while the rest of the unit is deleted (a, b). Cube generation and intersection calculation: A cube is generated to overlap with the CT image, and the intersecting surfaces are calculated (c). To ensure data consistency, the CT image is gradually advanced from the cube's center, and the first surface where the orbital rim contour is closed is used as the reference (d, e). Binary image creation: Noise is removed, and the inside of the contour is filled with 1 (white) and the outside with 0 (black) to create a binary image (f).\u003c/p\u003e","description":"","filename":"Figure5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/0a47104261dbbd7799d59034.jpg"},{"id":59606955,"identity":"c6ebad68-2521-4bad-8775-820644a76f1b","added_by":"auto","created_at":"2024-07-03 18:58:54","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":160233,"visible":true,"origin":"","legend":"\u003cp\u003eObjective indices for analysis are created at the preoperative (a) and postoperative (b) stages. Vertices (number of vertices in contour) and all points (number of points (pixels) in contour) are figured out on the green contour. The solidity is measured by the green contour area among the yellow convex hull area. A value of 1 corresponds to a solid object, while a value below 1 implies an object with irregular boundaries. The ellipse distance is measured by the average distance between the green contour and the red ellipse. The ellipses are drawn with the fit-ellipse function in the open computer vision library. The function calculates the ellipse that best fits a set of 2D points.\u003c/p\u003e","description":"","filename":"Figure6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/77881bb40df10d671b58ac72.jpg"},{"id":69285781,"identity":"2d50129a-e5a8-44c6-96ce-7b44998edaa3","added_by":"auto","created_at":"2024-11-18 19:28:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1396177,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/cb9fb9c3-4f87-4496-8002-5ed0a1e9e1bb.pdf"},{"id":59606956,"identity":"37a277d8-550b-4526-9071-54e4fabf794e","added_by":"auto","created_at":"2024-07-03 18:58:54","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":94975,"visible":true,"origin":"","legend":"","description":"","filename":"Supplement1.RawData.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-4553660/v1/402f4023dc8cb3e4280f2aa1.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Objective Analysis of Orbital Rim Fracture CT Images Using Curve and Area Measurement","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eThe orbital bone of the facial skeleton is composed of several bony segments that form a closed curve. An injury to this curve appears as a broken line, which can be identified in facial bone computed tomography (CT) images\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. In contrast to the analysis of other parts of the facial skeleton, the closed curve shape and cup-shaped characteristic give the structure an additional opportunity for analysis.\u003c/p\u003e \u003cp\u003eNumerous studies have focused on simplifying and standardizing spaces or structures and their relationships, employing methods such as Hamilton\u0026rsquo;s Ricci flow, geometrization, and vector calculus\u003csup\u003e\u003cspan additionalcitationids=\"CR3 CR4\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. These theoretical approaches offer satisfactory solutions to complex structures and shapes that are difficult to grasp intuitively. Additionally, the formation of closed curves using approximate values presents an intriguing area of study when examining shapes in unidentified spaces\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAccurate measurement within this complex structure is challenging. The disruption caused by an injury alters a smooth curve, yet it still offers sufficient information prior to surgical correction\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Thus, CT studies are performed both before and after surgery to assess orbital fractures. These imaging studies are crucial for determining whether the fracture site has been adequately reduced\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. It is necessary to check that the curve of the bone-to-bone contact area forms a smooth union.\u003c/p\u003e \u003cp\u003eBiologic imaging techniques, such as CT scans, are employed in both static and dynamic modalities\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. When natural alignment is disrupted, structural disfigurements become apparent. Conversely, the recovery of disarranged anatomical structures can be efficiently confirmed through postoperative morphometric evaluation. Additionally, the components of the orbital rim exhibit viscoelastic characteristics. Such unexpected alterations necessitate high-quality images to ensure adequate correction\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAn image analysis procedure was developed to assess whether the orbital rim forms a smooth curve following corrective surgery. To analyze a specific area of interest in three-dimensional (3D) CT data, the image was segmented into a defined unit\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. Subsequently, closed curves were generated and analyzed using ellipses and circles based on approximate values. Additionally, the curvature value was calculated on the closed curve, allowing for the determination of the average curvature. These various analytical methods yielded a set of results and demonstrated a correlation between the values. In this report, we describe the development of the analytical process and present the outcome measures.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eThe objective indices measured before and after surgery using the software were compared. The ratio between the affected and unaffected sides was figured out on each index. When symmetry between the affected and unaffected sides is achieved, the ratio approaches 1, as mentioned in the \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003emethods\u003c/span\u003e section. The ratio of vertices (number of vertices in the contour) before surgery was 0.9648\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1157, and after surgery, it was 1.0063\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0863, indicating a value closer to 1 (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). Similarly, the ratio of all points (number of pixels in the contour) before surgery was 0.9704\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1046, and after surgery, it was 1.0006\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0815, also indicating a value closer to 1 (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e \u003cp\u003eThe ratio of the solidity value (contour area/convex hull area) before surgery was 0.9923\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0292, and after surgery, it increased to 0.9965\u0026thinsp;\u0026plusmn;\u0026thinsp;0.015, indicating a value closer to 1 (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). The ratio of the ellipse distance, which measures the discrepancy between the contour and the ellipse, was 1.4071\u0026thinsp;\u0026plusmn;\u0026thinsp;0.8062 before surgery and decreased to 1.2661\u0026thinsp;\u0026plusmn;\u0026thinsp;0.6218 after surgery (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e).\u003c/b\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePre- and post-operative comparison using ratios of affected and unaffected sides (unit: ratio). The ratios of vertices (number of vertices in the contour), all points (number of points [pixels] in the contour), solidity value (contour area divided by convex hull area), ellipse distance (discrepancy between contour and ellipse), and average curvature demonstrated postoperative changes converging towards 1 (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). A ratio of 1 indicates symmetry between the bilateral sides. PreOp., preoperative data; PostOp., postoperative data; SD, standard deviation\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003cp\u003e(ratio)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVertices\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAll Points\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSolidity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1-Solidity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEllipse Distance\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCurvature\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePreOp.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9648\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9704\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9923\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.3978\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.4071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1.0458\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.1157\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.7812\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.8062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0484\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePostOp.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.0006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9965\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.1926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.2661\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e1.0126\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0863\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0815\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.4384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.6218\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0382\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFurthermore, the values representing the discrepancy between smooth and irregular curves can be used in further analysis. When a smooth closed curve (yellow line) encircles an irregular curve (green line) with severe bends, the solidity value (contour area/convex hull area) of the affected side is significantly less than 1. Conversely, this value approaches 1 when the irregularity is corrected and the curve resembles a smooth contour. In this scenario, the affected side's ellipse distance, which measures the discrepancy between the contour (green line) and the ellipse (red line), is considerably greater than 0 before surgery. This distance will decrease towards zero as the curve smoothens postoperatively. Specifically, the affected side's solidity value before surgery was 0.9583\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0213, and after surgery, it improved to 0.9645\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0127, indicating a value close to 1 (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). The ellipse distance before surgery was 1.446\u0026thinsp;\u0026plusmn;\u0026thinsp;0.681, and after surgery, it reduced to 1.1902\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4859, demonstrating a value nearing zero (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) \u003cb\u003e(\u003c/b\u003eFigs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe assessment process included analyzing the curvature of specific contours. The Fiji plugin calculates curvature values using B-splines\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. The average curvature of the orbital rim before surgery was 0.2853\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0078, while the post-surgery value was 0.2747\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0088. A comparison of these average values revealed a significant decrease in curvature for the orbital rim after surgery (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe solidity, ellipse distance, and curvature change when the bent unit is reduced, showing a smooth curve. Specifically, the affected side\u0026rsquo;s solidity value changed to a postoperative measurement closer to 1 (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). The ellipse distance and curvature value changed to postoperative measurement closer to 0 (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). PreOp., preoperative data; PostOp., postoperative data; SD, standard deviation\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSolidity\u003c/p\u003e \u003cp\u003e(ratio)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1-Solidity (ratio)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEllipse Distance (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCurvature\u003c/p\u003e \u003cp\u003e(\u0026micro;m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePreOp.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9583\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.446\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.2853\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.681\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0078\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePostOp.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.1902\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.2747\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0127\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0127\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.4859\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0088\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ePearson correlation coefficients were calculated for the following values: solidity, ellipse distance, and curvature. After surgery, there was an increase in solidity, while both ellipse distance and curvature decreased. To assess the positive correlations among these values, 1-solidity, ellipse distance, and curvature were used in the analysis. The solidity is the ratio of pixels in the subject to pixels of the convex hull image. In this context, 1-solidity represents the rest of the convex hull image excluding the subject, and decrement can be assumed when irregular boundaries are reduced after surgery. The results showed a significant correlation between these values in both preoperative and postoperative measurements (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e).\u003c/b\u003e The raw dataset is presented as a supplementary file (supplement 1).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePearson correlation test. Pre- and postoperative values of 1-solidity, ellipse distance, and curvature values were utilized for the analysis. The values presented significant correlations (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003et value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e-value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePreoperative\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1-Solidity vs. Ellipse distance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.726\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEllipse distance vs. Curvature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.731\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.133\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCurvature vs. 1-Solidity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.873\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.592\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePostoperative\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1-Solidity vs. Ellipse distance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.089\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEllipse distance vs. Curvature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.726\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCurvature vs. 1-Solidity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.845\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.576\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eThe orbital rim, composed of the frontal bone, zygomatic bone, and maxilla, forms a closed curve. This innate characteristic provides various analytic indices, such as height, width, curvature, and continuity. The curve can be analyzed by comparing it with circumscribing circles or tangent lines\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Anatomic structures like orbital fissures, the lacrimal fossa, and muscle attachments contribute to the irregularity of the orbital rim, preventing it from forming a perfect circle in its physiological state\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. Rubin et al. described ancestral variations in the shape of the orbital rim, noting that European orbits exhibit more pronounced folding than either African or Asian orbits. Conversely, the lateral margin of African orbits is positioned more posteriorly relative to the medial margin compared to Asian orbits\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. These findings indicate that curvilinear relationships are the most informative aspect of the shape of the orbital rim.\u003c/p\u003e \u003cp\u003eLi et al. presented a study using deep learning-based CT radiomics to represent features of Asian bony orbits, analyzing them in relation to age and sex\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. They found that during aging, the bony orbital area increased in males but decreased in women, with the area being consistently larger in men than in women. This difference may be attributed to variations in the position and degree of orbital bone resorption between men and women as they age.\u003c/p\u003e \u003cp\u003eBony structures can be analyzed using various formulas and geometry. Narra et al. introduced a method involving Ricci flow-based conformal mapping of the femur bone to examine the effects of exercise loading\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. This approach allows the exploration of the causal relationship between habitual loading and the adaptive response in bone morphology through the spatial distribution of mechanically relevant features. The Ricci-flow based conformal mapping procedure demonstrated correspondence among the periosteal surfaces, enhancing the visualization of surface features. This, in turn, enabled the study of the group-wise distribution of mechanically relevant features. By using group-wise and composite-group maps, the bony surfaces impacted by specific loading were pinpointed with a high degree of spatial localization.\u003c/p\u003e \u003cp\u003eSingh et al. studied orbital morphometry based on CT analysis\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Although variations in orbital depths exist between genders, no significant differences were observed in all parameters between the right and left orbits, confirming the symmetry of both orbits in the same individual. Fractures involving the orbital rims must be anatomically reduced before addressing other structures\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. The symmetry between bilateral sides is crucial for orbital reconstruction, as it allows the standard orbit to serve as a benchmark guide. In our research, we examined the following indices: 1) vertices (number of vertices in the contour), 2) all points (number of contour points), 3) solidity (contour area [green] / convex hull area [yellow]), 4) ellipse distance (distance between shapes [contour: green, ellipse: red]), and 5) average curvature. These indices showed greater discrepancies preoperatively than in postoperative measurements. The consistent changes across multiple indices confirmed symmetric correction following surgical procedures.\u003c/p\u003e \u003cp\u003eThis study confirmed positive correlations between several values; 1-solidity, ellipse distance, and curvature with statistical significance (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). A closed curve with an irregular margin cannot be described by a single formula. In this context, multiple indices, specifically 1-solidity, ellipse distance, and curvature, were employed for interdisciplinary research. These three indices, when used together, can provide comprehensive information for both medical practitioners and patients.\u003c/p\u003e \u003cp\u003eThe analytic strategy of defining closed curves has been a significant area of research. Dallaston et al. developed strategies to describe a closed embedded plane curve using both formal asymptotic and numerical techniques\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Li et al. suggested a morphometric strategy for shape analysis and introduced three types of segments to classify components in the chain\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. These include a mean segment (M-segment) characterized by a consistent shape and size, a circular helical segment (C-segment) defined by constant curvature, and a growth segment (G-segment) which maintains a consistent shape but varies in size. These segments were used to delineate the structure and construction of forms. Stepwise discriminant analysis was employed to define the shapes of anatomical structures, including the facial skeleton. The orbital rim consists of multiple segments, marked by ridges and grooves, giving it a complex shape even in the absence of any fractures. In this context, various strategies and formulas aimed at simplifying the orbital rim can facilitate effective evaluation. We employed methods based on the ellipse and convex hull area, using approximate values. These served as numerical evidence for assessing the deflections and bends in the structure.\u003c/p\u003e \u003cp\u003ePosttraumatic disfigurement of the orbital rim is influenced by several factors. Choi et al. explored the relationship between the negative vector of the eye globe and the location of the fracture\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. The term \"negative orbit vector\" describes a situation where the anterior portion of the globe protrudes beyond the soft tissue of the malar eminence. They focused on eyes that were prone to specific traumas. Their findings indicated that the negative orbit vector was more associated with fractures of the orbital floor than with those of the medial wall. Jacobs et al. analyzed CT images of patients with orbital fractures and determined that reduced preorbital and intraorbital soft tissue volumes are linked to these injuries\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. The surrounding soft tissues dissipate impacts on the anterior orbital rim and within the orbit. Additionally, the orbital shape and its mechanical response to stress and force play roles in the extent and nature of disfigurement.\u003c/p\u003e \u003cp\u003eDeserno demonstrated morphological alterations in cellular lipid membranes using differential geometry and curvature stresses\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. The following principles were suggested to predict the effects: the force exerted is influenced by the surface geometry and local curvature, and the resultant force is not tangential to the surface when the curvature varies. Multiple causative factors influence the morphologic outcomes following physical impacts. Research conducted at both large-scale and microscopic levels helps elucidate these processes and their consequences.\u003c/p\u003e \u003cp\u003eThe human orbital bone features delicate anatomical structures that respond characteristically to physical stimuli. Orbital morphometry, which utilizes measurements and imaging studies, offers objective information. Our study revealed postoperative changes using various references, including vertices, circumscribed curves, and traversing ellipses. Additionally, positive correlations were confirmed among 1-solidity, ellipse distance, and curvature. A closed curve displaying irregularity cannot be described by a single formula. These three indices provided sufficient information for objective analysis and had complementary characteristics.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003ePatients and Data Acquisition\u003c/h2\u003e \u003cp\u003eThree-dimensional (3D) CT images of facial bones were obtained from 25 patients with unilateral orbital rim fractures (14 males, aged 19\u0026ndash;73 years, and 11 females, aged 25\u0026ndash;68 years) who underwent reduction surgery to treat their fractures between March 2017 and February 2020. The study adhered to the ethical standards set forth in the 1964 Declaration of Helsinki and its subsequent amendments. Written informed consent was obtained from all patients. The institutional review board of Konkuk University Medical Center approved the study (approval number: KUMC 2022-03-013).\u003c/p\u003e \u003cp\u003eAn orbital rim fracture was diagnosed based on the patient's symptoms and an analysis of facial bone CT images; a 3D CT of the facial bones was utilized as it provides suitable views for assessing both preoperative displacement and postoperative correction. The CT images were acquired using a standard CT scanner (GoldSeal\u0026trade; Optima\u0026trade; CT660, General Electric Company, Boston, MA, USA) with consistent data acquisition settings.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eOrbital Rim Contour Data Generation\u003c/h2\u003e \u003cp\u003eThe following method was used to generate orbital rim contour data (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eFacial bone CT image preprocessing: Since the amount of data in facial bone CT images is usually too extensive for processing, only the region around the orbits is retained while the rest is deleted using standard software (Blender version 3.5; Blender Foundation, Amsterdam, the Netherlands).\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCube generation and intersection calculation: A cube is generated to overlap with the CT image, and the intersecting surfaces are calculated. To ensure data consistency, the CT image is gradually advanced from the cube's center, and the first surface where the orbital rim contour is closed is used as the reference.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e Binary image creation: Noise is removed, and the inside of the contour is filled with 1 (white) and the outside with 0 (black) to create a binary image.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eObjective Indices for Analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e)\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eVertices\u0026thinsp;=\u0026thinsp;Number of vertices in contour\u003c/p\u003e \u003cp\u003eAll Points\u0026thinsp;=\u0026thinsp;Number of points (pixels) in contour\u003c/p\u003e \u003cp\u003eSolidity\u003csup\u003e*\u003c/sup\u003e = Contour area (green) / Convex hull area (yellow)\u003c/p\u003e \u003cp\u003eEllipse Distance\u003csup\u003e\u0026dagger;\u003c/sup\u003e = Average distance between the contour (green) and ellipse (red)\u003c/p\u003e \u003cp\u003e \u003csup\u003e*\u003c/sup\u003eSolidity is defined as the ratio of pixels in the subject to the pixels in the convex hull image, representing the subject's density. A value of 1 indicates a solid subject, whereas a value below 1 suggests a subject with irregular boundaries. This method was adopted from \"Shape Analysis and Measurement\" by Michael A. Wirth \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003csup\u003e\u0026dagger;\u003c/sup\u003eEllipse Drawing\u003c/p\u003e \u003cp\u003eThe ellipses are drawn using the fit-ellipse function in the open computer vision library. This function determines the best-fitting ellipse for a given set of 2D points. It employs the first algorithm outlined by Fitzgibbon et al. \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe above index values serve as a foundational basis for analysis. The ratio between the affected and unaffected sides was determined based on these values. This ratio was analyzed both before and after surgery. When symmetry between the affected and unaffected sides is achieved, the ratio approaches 1.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\text{R}\\text{a}\\text{t}\\text{i}\\text{o} = \\frac{Objective index of affected side}{Objective index of unaffected side} \\cong 1 if symmetry$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eFacial Bone CT Analysis Using the Software\u003c/h2\u003e \u003cp\u003eIndices that indicate surgical outcomes can enhance comprehension for both patients and researchers. It is assumed that fractured areas are present before surgery; therefore, the values will be distributed heterogeneously compared to those obtained postoperatively. Index values measured before and after surgery were illustrated in a graph to demonstrate the outcomes. If the average value shows excessive dispersion, the graph can briefly and clearly display the outcomes for easier understanding.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eStatistical Analysis\u003c/h2\u003e \u003cp\u003eThe paired t-test was employed to compare preoperative and postoperative measurements across various indices: vertices, all points, solidity, ellipse distance, and curvature values. Pearson's correlation test was used to assess the strength of the linear association between variables, specifically 1-solidity, ellipse distance, and curvature values. The analysis incorporated a 95% confidence interval.\u003c/p\u003e \u003cp\u003eStandard software (SPSS for Windows version 25.0; IBM Corp., Armonk, NY, USA) was utilized for the statistical analysis. A \u003cem\u003eP\u003c/em\u003e-value of less than 0.05 was deemed statistically significant.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eConflict of interest\u003c/h2\u003e\n\u003cp\u003eThe authors have no conflicting or vested interest whatsoever with respect to this research.\u003c/p\u003e\n\u003ch2\u003eFinancial disclosure\u003c/h2\u003e\n\u003cp\u003eNone of the authors has a financial interest in any of the products, devices, or drugs mentioned in this manuscript.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthor contributions: M.L. and J.Y. designed the research. J.K. collected data. H.C. and D.S. analyzed the data. H.L. wrote the manuscript. All the authors read and approved the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments:\u003c/h2\u003e \u003cp\u003eThis work was not supported by the research grant.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAll data generated or analyzed during this study are included in this article and its supplementary information file.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eTurvey, T. A. \u0026amp; Golden, B. A. Orbital anatomy for the surgeon. 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A Buyer's Guide to Conic Fitting. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.researchgate.net/publication/2237785\u003c/span\u003e\u003cspan address=\"https://www.researchgate.net/publication/2237785\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (1970).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"orbital bone, fracture, computed tomography, curve, area","lastPublishedDoi":"10.21203/rs.3.rs-4553660/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4553660/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe orbital bone presents a closed curve, and fracture results in disfigurement. An image analysis procedure was developed to examine before and after corrective surgery. An ellipse and circumscribed contour embodied the closed curve. Three-dimensional (3D) computed tomography (CT) images of were collected from 25 patients. Orbital rim data were generated, and binary images were created to facilitate closed curve analysis. Various indices, including the solidity value (closed curve area/convex hull area) and ellipse distance (discrepancy between the closed curve and the ellipse traversing the curve), were utilized. The ratios of various indices\u0026mdash;including the number of vertices, solidity value, and ellipse distance\u0026mdash;between the affected and unaffected sides showed postoperative values that were closer to 1, which would indicate perfect symmetry, than the preoperative measurements (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). The solidity value increased, while both the ellipse distance and curvature values decreased, reflecting the transformation of bends into smooth contours following reduction surgery (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). Significant correlations were observed between 1-solidity, ellipse distance, and curvature using the Pearson correlation test (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). This study validated postoperative changes in various indices and established correlations among multiple values, specifically solidity, ellipse distance, and curvature. Employing multiple indices with mutual complements has provided objective information confidently.\u003c/p\u003e","manuscriptTitle":"Objective Analysis of Orbital Rim Fracture CT Images Using Curve and Area Measurement","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-03 18:50:49","doi":"10.21203/rs.3.rs-4553660/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-04T04:51:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-04T00:24:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"136007722255369847902677423670730145188","date":"2024-10-01T15:35:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-12T10:46:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"125617576293052024239005582206512586053","date":"2024-09-06T00:03:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"131187485771387554840130695297108651250","date":"2024-09-04T02:14:55+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-03T14:21:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-08-30T19:54:15+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-06-12T09:59:07+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-11T02:56:17+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-06-09T11:52:33+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"017d11cb-2893-448b-9390-06c26688a9af","owner":[],"postedDate":"July 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":33734533,"name":"Biological sciences/Computational biology and bioinformatics"},{"id":33734534,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2024-11-18T19:23:28+00:00","versionOfRecord":{"articleIdentity":"rs-4553660","link":"https://doi.org/10.1038/s41598-024-76818-8","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-11-13 15:57:51","publishedOnDateReadable":"November 13th, 2024"},"versionCreatedAt":"2024-07-03 18:50:49","video":"","vorDoi":"10.1038/s41598-024-76818-8","vorDoiUrl":"https://doi.org/10.1038/s41598-024-76818-8","workflowStages":[]},"version":"v1","identity":"rs-4553660","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4553660","identity":"rs-4553660","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}