Distribution of Distal Radius Fracture Lines Revealed by 3D Fracture Mapping

Distribution of Distal Radius Fracture Lines Revealed by 3D Fracture Mapping | 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 Research Article Distribution of Distal Radius Fracture Lines Revealed by 3D Fracture Mapping Hexin Zhang, Zhenbao Lu, Lei Wang, Weizhong Guo, Yu Su, Shenshen Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9010937/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Background: Distal radius fractures are among the most common clinical fractures. In this study, we mapped fracture lines associated with distal radius injuries and converted these mappings into heat maps. This method allowed us to assess the distribution of fracture lines in the distal radius that involve the radiocarpal joint and investigate the correlation between the positions of these fracture lines and the regions of comminution. Methods: A retrospective study analyzed 111 instances of distal radius fractures involving the radiocarpal joint. The E-3D 21.10 software from Central South University in Changsha, China, was used to generate three-dimensional models of the radius and each fracture segment. This extraction process included rotation, translation, and separation to reconstruct the three-dimensional model. After importing the model into the E-3D 21.10 software for registration, fracture lines were marked on the three-dimensional surface image of the radius template. These fracture lines were then combined to form a comprehensive fracture line map, which was later transformed into a heat map. Results: Both Frykman type III and type IV fractures show a pronounced concentration of fracture lines in the volar sections of the scaphoid and lunate fossae, resulting in a red appearance on the heat map. In contrast, fracture lines on the articular surface of the radial styloid process are less frequent, appearing blue on the heat map. Similarly, fractures classified as Frykman type VII and type VIII demonstrate a significant accumulation of fracture lines in the volar areas of both the lunate and scaphoid fossae, indicated in red on the heat map. Meanwhile, fracture lines on the articular surfaces of the radial styloid process, dorsal medial region, and dorsal ulnar notch are notably less concentrated, reflected in blue on the heat map. Conclusions: The findings of this research indicate that the volar regions of the scaphoid and lunate fossae pose a significant risk for distal radius fractures involving the radiocarpal articular surface. In contrast, fractures involving the radial styloid articular surface are comparatively less common. This study provides physicians with a better understanding of the characteristics of distal radius fractures, which will help them select the most suitable surgical techniques for various fracture types. distal radius fracture fracture line Frykman classification heat map Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Fractures of the distal radius (DRFs) are among the most common fracture types seen in clinical settings [ 1 ], with about 50% of these being intra-articular fractures [ 2 ].As the population ages and the incidence of high-energy injuries continues to rise, the frequency of these fractures is also increasing [ 3 – 4 ].Various classification systems, such as Frykman, AO, and Fernandez, are commonly employed to categorize distal radius fractures and guide treatment selection [ 5 – 7 ].Notably, the Frykman classification is more concise and accessible, making it particularly suitable for academic discussions. This system effectively differentiates between distal radius fractures and associated joint injuries, while also providing indirect insights into joint stability and partial damage. Therefore, this study selected the Frykman classification as the grouping criterion to thoroughly investigate distal radius fractures involving the radiocarpal joint. Because injuries to the radiocarpal joint surface are more common in clinical practice and are associated with poor outcomes, this study focused on Frykman types III, IV, VII, and VIII fractures. However, with the ongoing advancements in smart medical technology, traditional classification methods may exhibit limitations and fail to deliver accurate assessments of actual fracture morphology. Fracture mapping intuitively illustrates the distribution of fracture lines and their central tendency [ 8 – 9 ].This approach allows doctors to achieve a more comprehensive and three-dimensional understanding of particular types of fractures, thereby facilitating interpretation of fracture-line distribution. In the present study, CT scan images were used to create fracture maps for patients with intra-articular fractures of the distal radius, and the distribution patterns of these intra-articular fracture lines were subsequently analyzed. Materials and methods Subjects From January 2019 to December 2023, Mindong Hospital, affiliated with Fujian Medical University, enrolled a total of 258 individuals with distal radius fractures. The inclusion criteria were: (1) age ≥ 18 years; (2) availability of complete CT data; (3) closed intra-articular distal radius fractures; and (4) distal radius fractures classified as Frykman types III, IV, VII, or VIII. The exclusion criteria were: (1) poor CT image quality with slice thickness > 3 mm; (2) pathological fractures; and (3) a history of wrist deformity or wrist surgery. Ultimately, 111 patients with distal radius fractures met the eligibility criteria and were included in this study. Among the included patients, there were 65 females and 46 males, with ages ranging from 23 to 93 years and a mean age of 56.0 years. Of these cases, 53 were left-sided and 58 were right-sided. Using the Frykman classification system, 26 fractures were classified as type III, 27 as type IV, 29 as type VII, and 29 as type VIII. This retrospective study received approval from the Ethics Committee of Mindong Hospital, affiliated with Fujian Medical University (Approval No. K2024092304). The construction of fracture maps 3D reconstruction The patient’s computed tomography (CT) data (DICOM 3.0) were imported into the E-3D 21.10 software (Central South University, Changsha, China). A sequence with higher resolution and thinner slices was selected, in which the radius was clearly identifiable and the scanning range was comprehensive. The “New Threshold” tool was used to filter out surrounding muscle and other soft tissues of relatively higher density, thereby retaining only the required bone regions. The “Mass Separation” function was then used to label the radius and its fracture fragments with different colors to distinguish them from other bone regions. “Execute Separation” was applied to calculate and generate the masks of the radius and its fracture fragments. Subsequently, the “Solid Modeling” module was used to reconstruct 3D surfaces from the processed masks. Upon completion, three-dimensional models of the radius and its corresponding fracture fragments were generated. Fracture reduction In the surgical planning menu of the E-3D 21.10 software, the fracture fragments that needed to be reduced were selected, and reduction of all fracture fragments was completed through operations such as rotation and translation. Subsequently, the radius model and all reduced fracture-fragment models were selected, and “Combine and Split” was applied to generate an overall reduction model that included all reduced fracture fragments. In the mesh processing menu, “Execute Smoothing” was selected and performed repeatedly until the fracture gaps became clearly visible. Finally, the processed model was exported for subsequent use. Draw the fracture line A new project file was created using the radius from a healthy subject as the standard model. When importing the post-reduction models for all patients, each model was registered to the standard model. Using translation and rotation operations, the post-reduction models were accurately aligned to the corresponding spatial positions of the standard model. At this stage, slight gaps remained on the surfaces of the fracture fragments. The curve function was used to draw lines along these gaps on the fracture surfaces, ultimately forming the fracture line map. Generate a statistical analysis heatmap of fracture lines Within the fracture line mapping module of the E-3D 21.10 software, the standard template model was used, and the curves designated for analysis were selected, after which “Statistical Analysis” was applied to generate a fracture-line heat map. In the 3D view, blue represents areas with no curves, whereas red indicates regions with the highest curve density. Statistical analysis Statistical analyses were performed with SPSS (version 27.0). Continuous variables are expressed as the mean ± standard deviation (SD), and categorical variables are presented as frequency and percentage. To assess differences between groups, the chi-square test was used. A p value < 0.05 was considered statistically significant. Results Patient demographics and fracture characteristics As outlined in Table 1 , this research included a total of 111 individuals with distal radius fractures involving the radiocarpal joint. The study group included 65 females and 46 males, with ages ranging from 23 to 93 years and a mean age of 56.0 years. Within this population, 58 cases were classified as right-sided, while 53 were left-sided. Based on the Frykman classification system, the distribution of cases was 26 type III, 27 type IV, 29 type VII, and 29 type VIII. The baseline characteristics, including age and sex, did not show any statistically significant differences (P > 0.05) among patients categorized into different Frykman types. 3D map features In Frykman type III (Fig. 1 , Fig. 2 ), fracture lines are primarily located on the volar aspect of the lunate and scaphoid fossae, as indicated by intense red regions on the heat map. The articular surface of the radial styloid process is rarely affected, as reflected by blue areas on the heat map. For Frykman type IV, fracture lines are mainly distributed on the volar aspect of the scaphoid and lunate fossae, appearing as prominent red regions. The radial styloid articular surface is infrequently involved, as indicated by blue areas. In Frykman type VII, fracture lines are predominantly observed on the volar aspect of the lunate and scaphoid fossae, with prominent red regions on the heat map. In contrast, the dorsal medial articular surface and the radial styloid articular surface show very few fracture lines, depicted in blue. At the ulnar notch, fracture lines are largely concentrated on the volar region, while those on the dorsal aspect are relatively less frequent. For Frykman type VIII, fracture lines are widely distributed across the lunate fossa and scaphoid fossa, again highlighted by prominent red regions on the heat map. The dorsal medial articular surface and the radial styloid articular surface show a low occurrence of fracture lines, as indicated by blue areas. In the ulnar notch region, fracture lines are mainly present on the volar aspect, with a relatively sparse distribution on the dorsal side. 3D reconstruction map features In Frykman type III (Fig. 3 , Fig. 4 ), the fracture line extends from the volar aspect of the lunate fossa to its dorsal aspect. Although the fracture line involves the radiocarpal articular surface, the relative position between the distal radius articular surface and the carpus remains intact. In Frykman type IV, the fracture line extends from the volar aspect of the scaphoid fossa to the dorsal articular surface. This fracture line also crosses the radiocarpal articular surface but does not involve the distal radioulnar articular surface. Additionally, the relative positioning of the articular surface of the distal radius with respect to the carpus is preserved. In Frykman type VII, the fracture line extends from the volar aspect of the scaphoid fossa to the volar aspect of the lunate fossa, ultimately reaching the ulnar notch. This fracture line involves both the radiocarpal articular surface and the distal radioulnar articular surface, thereby altering the relative positions between the radiocarpal articular surface and the carpus. In Frykman type VIII, the fracture line extends from the volar aspect of the scaphoid fossa to the dorsal side of the scaphoid fossa and the base of the radial styloid process. This fracture line also affects the radiocarpal articular surface as well as the distal radioulnar articular surface, causing a shift in the relative positioning of the distal radius articular surface and the carpus. Distribution of fracture lines in scaphoid fossa and lunate fossa As detailed in Table 2 , the proportions of Frykman types III, IV, VII, and VIII involving the scaphoid fossa were 69.2%, 74.1%, 72.4%, and 79.3%, respectively, with no statistically significant differences among the four groups. Likewise, the proportions of Frykman types III, IV, VII, and VIII involving the lunate fossa were 80.8%, 70.4%, 75.9%, and 65.5%, respectively; again, no statistically significant differences were observed among the four groups. Table 2 Fracture line distribution in the lunate fossae and scaphoid fossae of patients with different Frykman subtypes(N = 111) Area Scaphoid fossae Lunate fossae III(n = 26)[n(%)] 18(69.2%) 21(80.8%) IV(n = 27)[n(%)] 20(74.1%) 19(70.4%) VII(n = 29)[n(%)] 21(72.4%) 22(75.9%) VIII(n = 29)[n(%)] 23(79.3%) 19(65.5%) P value III/IV 0.696 0.379 III/VII 0.795 0.660 III/VIII 0.392 0.205 IV/VII 0.889 0.643 IV/VIII 0.643 0.698 VII/VIII 0.539 0.387 Discussion With the advancement of technology and the ongoing dissemination of medical concepts, smart healthcare has gradually emerged as a prominent research field. In orthopedics, the application of smart healthcare primarily relies on various digital technologies to achieve a more systematic and standardized approach to orthopedic care, ensuring accurate positioning. This, in turn, better addresses the individual needs of patients, assists clinicians in enhancing treatment outcomes, and improves work efficiency.As the emphasis on big data analysis continues to grow, fracture heat maps based on three-dimensional CT have gained widespread adoption in orthopedic practice [10].The concept of the fracture heat map was first introduced in 2009, aiming to superimpose fracture lines from numerous cases and present them in the form of heat maps, thereby facilitating the study of the direction and distribution of fracture lines in specific regions [11-13]. Historically, Armitage and his team [14]were pioneers in proposing the concept of fracture heat maps in 2009, which contributed to the subsequent development of fracture mapping research. Over the past decade, fracture heat maps have been utilized to describe fractures in various locations, including the scapula, humerus, femur, and tibia. Additionally, some researchers have refined and extended fracture mapping methods, further advancing this field [15-17]. Distal radius fractures are among the most prevalent types of fractures encountered in clinical practice. The management of this injury is crucial, as the overall functionality of the wrist joint significantly relies on the stability of the distal radius and its ability to withstand axial loads [18-19]. As a result, accurately reconstructing the joint surface and ensuring stable fixation of the primary fracture segments are essential for reducing the likelihood of traumatic osteoarthritis and promoting functional recovery. In recent years, advancements in fixation technology have enabled effective stabilization of most distal radius fractures using volar locking plates [20]. This approach is especially recognized for its precision in positioning the distal locking screw correctly at the desired depth. Furthermore, effective management of intra-articular fractures of the distal radius necessitates that the surgeon possesses a comprehensive understanding of fracture types along with meticulous preoperative planning. Consequently, it is essential for the surgeon to promptly assess the configuration of the distal radius articular surface prior to the operation. Currently, multiple classification systems exist for distal radius fractures, and the Frykman classification stands out as especially beneficial for academic discussions because of its simplicity and clarity. Therefore, this study selected the Frykman classification as the framework for grouping and analysis. Given the high incidence of radiocarpal articular surface injuries and their relatively poor prognosis in clinical practice, this study focuses specifically on Frykman types III, IV, VII, and VIII. The findings of this study indicate that in Frykman type III fractures, the fracture line is primarily located in the volar region of both the scaphoid fossa and lunate fossa, whereas the radial styloid articular surface is rarely involved. Similarly, in Frykman type IV fractures, fracture lines tend to concentrate on the volar aspect of the scaphoid fossa and lunate fossa, with the radial styloid articular surface also rarely affected. Although bone loss may occur in Frykman type III and IV fractures, the spatial relationship between the carpus and the distal radius articular surface remains preserved. Therefore, a volar approach for reconstruction of the lunate and scaphoid fossae may be sufficient, potentially obviating the need for bone grafting. Fracture lines associated with Frykman type VII fractures mainly appear on the volar aspect of the lunate fossa and scaphoid fossa, whereas they are infrequently found on the dorsal medial articular surface and the radial styloid articular surface. In the area of the ulnar notch, these fracture lines predominantly concentrate on the volar aspect. For fractures classified as Frykman type VIII, fracture lines are primarily distributed across the lunate fossa and scaphoid fossa. As with type VII fractures, the dorsal medial articular surface and radial styloid articular surface show relatively few fracture lines, while the ulnar notch region also shows a marked concentration on the volar aspect. Both fracture types are considered severe intra-articular fractures that involve considerable bone loss and free bone fragments. During surgery, may be considered to utilize both volar and dorsal approaches in conjunction with bone grafting. Additionally, since Frykman types VII and VIII fractures involve the ulnar notch, careful evaluation of the triangular fibrocartilage complex (TFCC) is essential when reconstructing the distal radioulnar and radiocarpal articular surfaces. The TFCC contributes substantially to the stability of the distal radioulnar joint, making its restoration critical for the wrist joint’s overall functional recovery[21]. Another important finding of this study is that, in the majority of cases involving distal radius articular surface fractures, the radial styloid articular surface remains intact, with only a few instances of isolated fractures in this region. This finding indicates that the radial styloid process is not a standalone articular surface of the distal radius; instead, it is a crucial region made up of dense trabecular bone tissue[22]. This provides strong support for the rationality and safety of radial styloid screw fixation.In addition to the radial styloid region, the dorsal medial articular surface exhibited a lower fracture rate, indicating that this area may also serve as an additional entry point for screws. Therefore, may be considered to insert a screw from the dorsomedial toward the volar direction to more effectively stabilize the volar comminution site.Nevertheless, it is important to recognize that, given the current lack of accurate intraoperative tools for evaluating screw trajectory and depth, this technique continues to depend on the surgeon's expertise and proficiency to ensure precise screw placement and thereby minimize the risk of tendon damage and other procedure-related complications. This study offers several notable advantages. First, three-dimensional fracture mapping substantially improves visualization of the complex anatomy of the distal radius articular surface. Because fracture lines often traverse multiple articular regions, this approach enables more comprehensive characterization of fracture patterns, thereby reducing the risk of diagnostic errors. Second, this study focuses on Frykman types III, IV, VII, and VIII distal radius fractures and successfully constructs corresponding three-dimensional fracture maps, providing an intuitive 3D perspective for understanding the characteristics and injury mechanisms of fractures involving the radiocarpal articular surface. Finally, by integrating fracture line maps with heat maps, we found that fracture line maps are advantageous for depicting fracture direction and fine details, whereas heat maps more effectively convey overall patterns and fracture-line density. This combined analytical strategy provides a new perspective for comprehensively interpreting fracture characteristics. This study also has several limitations that warrant attention. First, because the reductions were performed virtually, the current mapping approach can depict only the distribution of fracture lines on the radial surface and cannot accurately represent displacement or compression of the fracture fragments. Second, generating fracture line maps requires relatively complex processing of the original images and substantial manual effort. Future work is therefore needed to improve both the functionality and efficiency of the software. Finally, this study did not establish a novel classification system based on distal radius articular-surface fracture maps. Future research should further integrate anatomical and biomechanical perspectives to ensure that any resulting clinical guidance is scientific and rigorous. In conclusion, three-dimensional fracture mapping clearly depicts the orientation and distribution of fracture lines on the radiocarpal articular surface of the radius. This study employed two complementary visualization techniques—line mapping and heat mapping—each with distinct advantages. By integrating these approaches, fracture-line morphology and spatial concentration can be presented more comprehensively. These findings provide a valuable reference for refined characterization of the distal radius articular surface, optimization of screw placement strategies, and the development of internal fixation designs. Declarations Authors’ contributions Hexin Zhang and Zhenbao Lu contributed equally to this work. The authors read and approved the final manuscript Funding The study did not receive funding. Data availability The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request. Ethics approval and consent to participate This study was approved by the Ethics Committee of the hospital where the research was conducted (Ethics approval number: K2024092304). 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Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 15 Apr, 2026 Reviews received at journal 01 Apr, 2026 Reviewers agreed at journal 30 Mar, 2026 Reviewers agreed at journal 28 Mar, 2026 Reviewers invited by journal 13 Mar, 2026 Editor invited by journal 03 Mar, 2026 Editor assigned by journal 03 Mar, 2026 Submission checks completed at journal 03 Mar, 2026 First submitted to journal 02 Mar, 2026 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-9010937","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606331676,"identity":"46e89be2-8202-4fc3-94a4-1979c1a0d834","order_by":0,"name":"Hexin Zhang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Hexin","middleName":"","lastName":"Zhang","suffix":""},{"id":606331677,"identity":"9e9f8941-e614-4371-a214-c5a805a7f79f","order_by":1,"name":"Zhenbao 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Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyklEQVRIiWNgGAWjYBCDBDYGBsYHDAwHSNPCbECaFiBmkyBKi3z/AebPvDvq8vikm49V/qi4k9jAfvjoBnxaDG4ksEnznjlczCZzLO02z5lniQ08aWk38GqRYGBj5m07kNgmkWN2m7HtcGKDBI8ZXi0Qh7XVAbXkfyv8SYwWhgMJDNK8bcwgW9gYeInRAvKL5FygyjaJNGNpnjOHjdsI+QXksA9vgQ6bPyP54ccfFYdl+9kPH8PvMAb+D6h8NvzKR8EoGAWjYBQQAwAlhkpxPaXh9QAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Shenshen","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-03-02 13:53:39","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9010937/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9010937/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104874771,"identity":"0d6e0586-7983-4715-b00a-6c666e2d0964","added_by":"auto","created_at":"2026-03-18 08:33:12","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":443652,"visible":true,"origin":"","legend":"\u003cp\u003eFracture-line heat maps for Frykman types III, IV, VII, and VIII distal radius fractures (E-3D 21.10).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9010937/v1/e656e0344f3bd7130256e68c.png"},{"id":104874773,"identity":"2612da59-c0c8-4667-8ac8-b84c001c0118","added_by":"auto","created_at":"2026-03-18 08:33:12","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":389711,"visible":true,"origin":"","legend":"\u003cp\u003eFracture-line distribution maps for Frykman types III, IV, VII, and VIII distal radius fractures (E-3D 21.10).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9010937/v1/d92a52d91aa83c3f99b4ea0a.png"},{"id":104874772,"identity":"ac77659b-1347-42c4-b8c5-eb87b1988914","added_by":"auto","created_at":"2026-03-18 08:33:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":519104,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentative 3D solid models of Frykman types III, IV, VII, and VIII distal radius fractures (E-3D 21.10).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9010937/v1/be0ad49fa4f7a7b422d6647a.png"},{"id":105034257,"identity":"80070ffa-57fe-4c29-b06c-479b1206bf11","added_by":"auto","created_at":"2026-03-20 07:22:57","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":192403,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentative CT images of Frykman types III, IV, VII, and VIII distal radius fractures (E-3D 21.10).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9010937/v1/3d3b062bdf37d4fbd21a8200.png"},{"id":105751848,"identity":"2879f8e4-900f-4859-b871-a2e0fe2fd823","added_by":"auto","created_at":"2026-03-30 15:47:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2345089,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9010937/v1/f2e864b8-c7b2-4c46-b331-e5b3299b212f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Distribution of Distal Radius Fracture Lines Revealed by 3D Fracture Mapping","fulltext":[{"header":"Introduction","content":"\u003cp\u003eFractures of the distal radius (DRFs) are among the most common fracture types seen in clinical settings [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], with about 50% of these being intra-articular fractures [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].As the population ages and the incidence of high-energy injuries continues to rise, the frequency of these fractures is also increasing [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].Various classification systems, such as Frykman, AO, and Fernandez, are commonly employed to categorize distal radius fractures and guide treatment selection [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].Notably, the Frykman classification is more concise and accessible, making it particularly suitable for academic discussions. This system effectively differentiates between distal radius fractures and associated joint injuries, while also providing indirect insights into joint stability and partial damage. Therefore, this study selected the Frykman classification as the grouping criterion to thoroughly investigate distal radius fractures involving the radiocarpal joint. Because injuries to the radiocarpal joint surface are more common in clinical practice and are associated with poor outcomes, this study focused on Frykman types III, IV, VII, and VIII fractures. However, with the ongoing advancements in smart medical technology, traditional classification methods may exhibit limitations and fail to deliver accurate assessments of actual fracture morphology.\u003c/p\u003e \u003cp\u003eFracture mapping intuitively illustrates the distribution of fracture lines and their central tendency [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].This approach allows doctors to achieve a more comprehensive and three-dimensional understanding of particular types of fractures, thereby facilitating interpretation of fracture-line distribution. In the present study, CT scan images were used to create fracture maps for patients with intra-articular fractures of the distal radius, and the distribution patterns of these intra-articular fracture lines were subsequently analyzed.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSubjects\u003c/h2\u003e \u003cp\u003eFrom January 2019 to December 2023, Mindong Hospital, affiliated with Fujian Medical University, enrolled a total of 258 individuals with distal radius fractures. The inclusion criteria were: (1) age\u0026thinsp;\u0026ge;\u0026thinsp;18 years; (2) availability of complete CT data; (3) closed intra-articular distal radius fractures; and (4) distal radius fractures classified as Frykman types III, IV, VII, or VIII. The exclusion criteria were: (1) poor CT image quality with slice thickness\u0026thinsp;\u0026gt;\u0026thinsp;3 mm; (2) pathological fractures; and (3) a history of wrist deformity or wrist surgery. Ultimately, 111 patients with distal radius fractures met the eligibility criteria and were included in this study. Among the included patients, there were 65 females and 46 males, with ages ranging from 23 to 93 years and a mean age of 56.0 years. Of these cases, 53 were left-sided and 58 were right-sided. Using the Frykman classification system, 26 fractures were classified as type III, 27 as type IV, 29 as type VII, and 29 as type VIII. This retrospective study received approval from the Ethics Committee of Mindong Hospital, affiliated with Fujian Medical University (Approval No. K2024092304).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eThe construction of fracture maps\u003c/h3\u003e\n\u003cp\u003e \u003cb\u003e3D reconstruction\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe patient\u0026rsquo;s computed tomography (CT) data (DICOM 3.0) were imported into the E-3D 21.10 software (Central South University, Changsha, China). A sequence with higher resolution and thinner slices was selected, in which the radius was clearly identifiable and the scanning range was comprehensive. The \u0026ldquo;New Threshold\u0026rdquo; tool was used to filter out surrounding muscle and other soft tissues of relatively higher density, thereby retaining only the required bone regions. The \u0026ldquo;Mass Separation\u0026rdquo; function was then used to label the radius and its fracture fragments with different colors to distinguish them from other bone regions. \u0026ldquo;Execute Separation\u0026rdquo; was applied to calculate and generate the masks of the radius and its fracture fragments. Subsequently, the \u0026ldquo;Solid Modeling\u0026rdquo; module was used to reconstruct 3D surfaces from the processed masks. Upon completion, three-dimensional models of the radius and its corresponding fracture fragments were generated.\u003c/p\u003e\n\u003ch3\u003eFracture reduction\u003c/h3\u003e\n\u003cp\u003eIn the surgical planning menu of the E-3D 21.10 software, the fracture fragments that needed to be reduced were selected, and reduction of all fracture fragments was completed through operations such as rotation and translation. Subsequently, the radius model and all reduced fracture-fragment models were selected, and \u0026ldquo;Combine and Split\u0026rdquo; was applied to generate an overall reduction model that included all reduced fracture fragments. In the mesh processing menu, \u0026ldquo;Execute Smoothing\u0026rdquo; was selected and performed repeatedly until the fracture gaps became clearly visible. Finally, the processed model was exported for subsequent use.\u003c/p\u003e\n\u003ch3\u003eDraw the fracture line\u003c/h3\u003e\n\u003cp\u003eA new project file was created using the radius from a healthy subject as the standard model. When importing the post-reduction models for all patients, each model was registered to the standard model. Using translation and rotation operations, the post-reduction models were accurately aligned to the corresponding spatial positions of the standard model. At this stage, slight gaps remained on the surfaces of the fracture fragments. The curve function was used to draw lines along these gaps on the fracture surfaces, ultimately forming the fracture line map.\u003c/p\u003e\n\u003ch3\u003eGenerate a statistical analysis heatmap of fracture lines\u003c/h3\u003e\n\u003cp\u003eWithin the fracture line mapping module of the E-3D 21.10 software, the standard template model was used, and the curves designated for analysis were selected, after which \u0026ldquo;Statistical Analysis\u0026rdquo; was applied to generate a fracture-line heat map. In the 3D view, blue represents areas with no curves, whereas red indicates regions with the highest curve density.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eStatistical analysis\u003c/h2\u003e \u003cp\u003eStatistical analyses were performed with SPSS (version 27.0). Continuous variables are expressed as the mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation (SD), and categorical variables are presented as frequency and percentage. To assess differences between groups, the chi-square test was used. A p value\u0026thinsp;\u0026lt;\u0026thinsp;0.05 was considered statistically significant.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003ePatient demographics and fracture characteristics\u003c/h2\u003e\n \u003cp\u003eAs outlined in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, this research included a total of 111 individuals with distal radius fractures involving the radiocarpal joint. The study group included 65 females and 46 males, with ages ranging from 23 to 93 years and a mean age of 56.0 years. Within this population, 58 cases were classified as right-sided, while 53 were left-sided. Based on the Frykman classification system, the distribution of cases was 26 type III, 27 type IV, 29 type VII, and 29 type VIII. The baseline characteristics, including age and sex, did not show any statistically significant differences (P\u0026thinsp;\u0026gt;\u0026thinsp;0.05) among patients categorized into different Frykman types.\u003c/p\u003e\n \u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cstrong\u003e3D map features\u003c/strong\u003e\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn Frykman type III (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), fracture lines are primarily located on the volar aspect of the lunate and scaphoid fossae, as indicated by intense red regions on the heat map. The articular surface of the radial styloid process is rarely affected, as reflected by blue areas on the heat map. For Frykman type IV, fracture lines are mainly distributed on the volar aspect of the scaphoid and lunate fossae, appearing as prominent red regions. The radial styloid articular surface is infrequently involved, as indicated by blue areas. In Frykman type VII, fracture lines are predominantly observed on the volar aspect of the lunate and scaphoid fossae, with prominent red regions on the heat map. In contrast, the dorsal medial articular surface and the radial styloid articular surface show very few fracture lines, depicted in blue. At the ulnar notch, fracture lines are largely concentrated on the volar region, while those on the dorsal aspect are relatively less frequent. For Frykman type VIII, fracture lines are widely distributed across the lunate fossa and scaphoid fossa, again highlighted by prominent red regions on the heat map. The dorsal medial articular surface and the radial styloid articular surface show a low occurrence of fracture lines, as indicated by blue areas. In the ulnar notch region, fracture lines are mainly present on the volar aspect, with a relatively sparse distribution on the dorsal side.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e3D reconstruction map features\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eIn Frykman type III (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e), the fracture line extends from the volar aspect of the lunate fossa to its dorsal aspect. Although the fracture line involves the radiocarpal articular surface, the relative position between the distal radius articular surface and the carpus remains intact. In Frykman type IV, the fracture line extends from the volar aspect of the scaphoid fossa to the dorsal articular surface. This fracture line also crosses the radiocarpal articular surface but does not involve the distal radioulnar articular surface. Additionally, the relative positioning of the articular surface of the distal radius with respect to the carpus is preserved. In Frykman type VII, the fracture line extends from the volar aspect of the scaphoid fossa to the volar aspect of the lunate fossa, ultimately reaching the ulnar notch. This fracture line involves both the radiocarpal articular surface and the distal radioulnar articular surface, thereby altering the relative positions between the radiocarpal articular surface and the carpus. In Frykman type VIII, the fracture line extends from the volar aspect of the scaphoid fossa to the dorsal side of the scaphoid fossa and the base of the radial styloid process. This fracture line also affects the radiocarpal articular surface as well as the distal radioulnar articular surface, causing a shift in the relative positioning of the distal radius articular surface and the carpus.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003eDistribution of fracture lines in scaphoid fossa and lunate fossa\u003c/h2\u003e\n \u003cp\u003eAs detailed in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the proportions of Frykman types III, IV, VII, and VIII involving the scaphoid fossa were 69.2%, 74.1%, 72.4%, and 79.3%, respectively, with no statistically significant differences among the four groups. Likewise, the proportions of Frykman types III, IV, VII, and VIII involving the lunate fossa were 80.8%, 70.4%, 75.9%, and 65.5%, respectively; again, no statistically significant differences were observed among the four groups.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFracture line distribution in the lunate fossae and scaphoid fossae of patients with different Frykman subtypes(N\u0026thinsp;=\u0026thinsp;111)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eArea\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eScaphoid fossae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLunate fossae\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eIII(n\u0026thinsp;=\u0026thinsp;26)[n(%)]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18(69.2%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21(80.8%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eIV(n\u0026thinsp;=\u0026thinsp;27)[n(%)]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20(74.1%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19(70.4%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eVII(n\u0026thinsp;=\u0026thinsp;29)[n(%)]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21(72.4%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e22(75.9%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eVIII(n\u0026thinsp;=\u0026thinsp;29)[n(%)]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23(79.3%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19(65.5%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eP value\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII/IV\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.696\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.379\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII/VII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.795\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.660\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII/VIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.392\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.205\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIV/VII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.643\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIV/VIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.643\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.698\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVII/VIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.539\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.387\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eWith the advancement of technology and the ongoing dissemination of medical concepts, smart healthcare has gradually emerged as a prominent research field. In orthopedics, the application of smart healthcare primarily relies on various digital technologies to achieve a more systematic and standardized approach to orthopedic care, ensuring accurate positioning. This, in turn, better addresses the individual needs of patients, assists clinicians in enhancing treatment outcomes, and improves work efficiency.As the emphasis on big data analysis continues to grow, fracture heat maps based on three-dimensional CT have gained widespread adoption in orthopedic practice [10].The concept of the fracture heat map was first introduced in 2009, aiming to superimpose fracture lines from numerous cases and present them in the form of heat maps, thereby facilitating the study of the direction and distribution of fracture lines in specific regions [11-13]. Historically, Armitage and his team [14]were pioneers in proposing the concept of fracture heat maps in 2009, which contributed to the subsequent development of fracture mapping research. Over the past decade, fracture heat maps have been utilized to describe fractures in various locations, including the scapula, humerus, femur, and tibia. Additionally, some researchers have refined and extended fracture mapping methods, further advancing this field [15-17].\u003c/p\u003e\n\u003cp\u003eDistal radius fractures are among the most prevalent types of fractures encountered in clinical practice. The management of this injury is crucial, as the overall functionality of the wrist joint significantly relies on the stability of the distal radius and its ability to withstand axial loads [18-19]. As a result, accurately reconstructing the joint surface and ensuring stable fixation of the primary fracture segments are essential for reducing the likelihood of traumatic osteoarthritis and promoting functional recovery. In recent years, advancements in fixation technology have enabled effective stabilization of most distal radius fractures using volar locking plates [20]. This approach is especially recognized for its precision in positioning the distal locking screw correctly at the desired depth. Furthermore, effective management of intra-articular fractures of the distal radius necessitates that the surgeon possesses a comprehensive understanding of fracture types along with meticulous preoperative planning. Consequently, it is essential for the surgeon to promptly assess the configuration of the distal radius articular surface prior to the operation. Currently, multiple classification systems exist for distal radius fractures, and the Frykman classification stands out as especially beneficial for academic discussions because of its simplicity and clarity. Therefore, this study selected the Frykman classification as the framework for grouping and analysis. Given the high incidence of radiocarpal articular surface injuries and their relatively poor prognosis in clinical practice, this study focuses specifically on Frykman types III, IV, VII, and VIII.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; The findings of this study indicate that in Frykman type III fractures, the fracture line is primarily located in the volar region of both the scaphoid fossa and lunate fossa, whereas the radial styloid articular surface is rarely involved. Similarly, in Frykman type IV fractures, fracture lines tend to concentrate on the volar aspect of the scaphoid fossa and lunate fossa, with the radial styloid articular surface also rarely affected. Although bone loss may occur in Frykman type III and IV fractures, the spatial relationship between the carpus and the distal radius articular surface remains preserved. Therefore, a volar approach for reconstruction of the lunate and scaphoid fossae may be sufficient, potentially obviating the need for bone grafting.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; Fracture lines associated with Frykman type VII fractures mainly appear on the volar aspect of the lunate fossa and scaphoid fossa, whereas they are infrequently found on the dorsal medial articular surface and the radial styloid articular surface. In the area of the ulnar notch, these fracture lines predominantly concentrate on the volar aspect. For fractures classified as Frykman type VIII, fracture lines are primarily distributed across the lunate fossa and scaphoid fossa. As with type VII fractures, the dorsal medial articular surface and radial styloid articular surface show relatively few fracture lines, while the ulnar notch region also shows a marked concentration on the volar aspect. Both fracture types are considered severe intra-articular fractures that involve considerable bone loss and free bone fragments. During surgery, may be considered to utilize both volar and dorsal approaches in conjunction with bone grafting. Additionally, since Frykman types VII and VIII fractures involve the ulnar notch, careful evaluation of the triangular fibrocartilage complex (TFCC) is essential when reconstructing the distal radioulnar and radiocarpal articular surfaces. The TFCC contributes substantially to the stability of the distal radioulnar joint, making its restoration critical for the wrist joint\u0026rsquo;s overall functional recovery[21].\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; Another important finding of this study is that, in the majority of cases involving distal radius articular surface fractures, the radial styloid articular surface remains intact, with only a few instances of isolated fractures in this region. This finding indicates that the radial styloid process is not a standalone articular surface of the distal radius; instead, it is a crucial region made up of dense trabecular bone tissue[22]. This provides strong support for the rationality and safety of radial styloid screw fixation.In addition to the radial styloid region, the dorsal medial articular surface exhibited a lower fracture rate, indicating that this area may also serve as an additional entry point for screws. Therefore, may be considered to insert a screw from the dorsomedial toward the volar direction to more effectively stabilize the volar comminution site.Nevertheless, it is important to recognize that, given the current lack of accurate intraoperative tools for evaluating screw trajectory and depth, this technique continues to depend on the surgeon\u0026apos;s expertise and proficiency to ensure precise screw placement and thereby minimize the risk of tendon damage and other procedure-related complications.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; This study offers several notable advantages. First, three-dimensional fracture mapping substantially improves visualization of the complex anatomy of the distal radius articular surface. Because fracture lines often traverse multiple articular regions, this approach enables more comprehensive characterization of fracture patterns, thereby reducing the risk of diagnostic errors. Second, this study focuses on Frykman types III, IV, VII, and VIII distal radius fractures and successfully constructs corresponding three-dimensional fracture maps, providing an intuitive 3D perspective for understanding the characteristics and injury mechanisms of fractures involving the radiocarpal articular surface. Finally, by integrating fracture line maps with heat maps, we found that fracture line maps are advantageous for depicting fracture direction and fine details, whereas heat maps more effectively convey overall patterns and fracture-line density. This combined analytical strategy provides a new perspective for comprehensively interpreting fracture characteristics.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; This study also has several limitations that warrant attention. First, because the reductions were performed virtually, the current mapping approach can depict only the distribution of fracture lines on the radial surface and cannot accurately represent displacement or compression of the fracture fragments. Second, generating fracture line maps requires relatively complex processing of the original images and substantial manual effort. Future work is therefore needed to improve both the functionality and efficiency of the software. Finally, this study did not establish a novel classification system based on distal radius articular-surface fracture maps. Future research should further integrate anatomical and biomechanical perspectives to ensure that any resulting clinical guidance is scientific and rigorous.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; In conclusion, three-dimensional fracture mapping clearly depicts the orientation and distribution of fracture lines on the radiocarpal articular surface of the radius. This study employed two complementary visualization techniques\u0026mdash;line mapping and heat mapping\u0026mdash;each with distinct advantages. By integrating these approaches, fracture-line morphology and spatial concentration can be presented more comprehensively. These findings provide a valuable reference for refined characterization of the distal radius articular surface, optimization of screw placement strategies, and the development of internal fixation designs.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHexin Zhang and Zhenbao Lu contributed equally to this work. The authors read and approved the final manuscript\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe study did not receive funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was approved by the Ethics Committee of the hospital where the research was conducted (Ethics approval \u0026nbsp; number: K2024092304).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor details\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMindong Hospital Affiliated to Fujian Medical University,Fuan355000,Fujian,China\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eHorst Taylor A,Jupiter Jesse B,Stabilisation of distal radius fractures: Lessons learned and future directions.[J] .Injury, 2016, 47: 313-9.DOI:10.1016/j.injury.2015.09.030\u003c/li\u003e\n \u003cli\u003eTeunis Teun,Bosma Niels H,Lubberts Bart et al. 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Significance of the Sparing Pronator Quadratus for Volar Plating of Distal Radius Fractures: A Prospective Study.[J] .Cureus, 2024, 16: 0.DOI:10.7759/cureus.74274\u003c/li\u003e\n \u003cli\u003eChenfei, Li,Jiaqing, Ye,Jian, Lu et al. Predictors of limited forearm rotation following conservative treatment of distal radius fractures: a retrospective comparative study.[J] .BMC Musculoskelet Disord, 2024, 25: 0.DOI:10.1186/s12891-024-08178-3\u003c/li\u003e\n \u003cli\u003eYao Xiang,Zhou Kaihua,Lv Bin et al. 3D mapping and classification of tibial plateau fractures.[J] .Bone Joint Res, 2020, 9: 258-267.DOI:10.1302/2046-3758.96.BJR-2019-0382.R2\u003c/li\u003e\n \u003cli\u003eXie Xuetao,Zhan Yu,Wang Yukai et al. Comparative Analysis of Mechanism-Associated 3-Dimensional Tibial Plateau Fracture Patterns.[J] .J Bone Joint Surg Am, 2020, 102: 410-418.DOI:10.2106/JBJS.19.00485\u003c/li\u003e\n \u003cli\u003ePeter A, Cole,Robert K, Mehrle,Mohit, Bhandari et al. The pilon map: fracture lines and comminution zones in OTA/AO type 43C3 pilon fractures.[J] .J Orthop Trauma, 2013, 27: 0.DOI:10.1097/BOT.0b013e318288a7e9\u003c/li\u003e\n \u003cli\u003eMcGonagle Lorcan,Cordier Tim,Link Bjorn C et al. Tibia plateau fracture mapping and its influence on fracture fixation.[J] .J Orthop Traumatol, 2019, 20: 12.DOI:10.1186/s10195-019-0519-1\u003c/li\u003e\n \u003cli\u003eYu Tao,Zhang Yingqi,Zhou Haichao et al. Distribution of posterior malleolus fracture lines in ankle fracture of supination-external rotation.[J] .Orthop Traumatol Surg Res, 2021, 107: 103000.DOI:10.1016/j.otsr.2021.103000\u003c/li\u003e\n \u003cli\u003eMellema Jos J,Eygendaal Denise,van Dijk C Niek et al. Fracture mapping of displaced partial articular fractures of the radial head.[J] .J Shoulder Elbow Surg, 2016, 25: 1509-16.DOI:10.1016/j.jse.2016.01.030\u003c/li\u003e\n \u003cli\u003eBryan M, Armitage,Coen A, Wijdicks,Ivan S, Tarkin et al. Mapping of scapular fractures with three-dimensional computed tomography.[J] .J Bone Joint Surg Am, 2009, 91: 0.DOI:10.2106/JBJS.H.00881\u003c/li\u003e\n \u003cli\u003eWang Chao,Zhu Yong,Long Haitao et al. Three-dimensional mapping of distal humerus fracture.[J] .J Orthop Surg Res, 2021, 16: 545.DOI:10.1186/s13018-021-02691-0\u003c/li\u003e\n \u003cli\u003eZhang Yingqi,Sun Yeqing,Liao Shenghui et al. Three-Dimensional Mapping of Medial Wall in Unstable Pertrochanteric Fractures.[J] .Biomed Res Int, 2020, 2020: 8428407.DOI:10.1155/2020/8428407\u003c/li\u003e\n \u003cli\u003eFu Yucheng,Liu Rong,Liu Yang et al. Intertrochanteric fracture visualization and analysis using a map projection technique.[J] .Med Biol Eng Comput, 2019, 57: 633-642.DOI:10.1007/s11517-018-1905-1\u003c/li\u003e\n \u003cli\u003eCamps C,Durand A,Merle M,[Treatment of partial articular fractures of the distal radius in active young adults].[J] .Hand Surg Rehabil, 2016, null: S126-S132.DOI:10.1016/j.hansur.2016.07.008\u003c/li\u003e\n \u003cli\u003ePanu, H Nordback,Ellen Y, Lee,Jin Xi, Lim et al. Risk for Flexor Pollicis Longus Rupture after Volar Lock Plating for Distal Radius Fracture Lasts Over a Decade.[J] .Arch Bone Jt Surg, 2024, 12: 0.DOI:10.22038/ABJS.2024.77674.3587\u003c/li\u003e\n \u003cli\u003eUğur, Bezirgan,Erdin\u0026ccedil;, Acar,Yener, Yoğun et al. Treatment Effectiveness of Volar Plates in Distal Radius Dorsal Rim Fractures.[J] .Rev Bras Ortop (Sao Paulo), 2024, 59: 0.DOI:10.1055/s-0044-1790579\u003c/li\u003e\n \u003cli\u003eMak Michael Chu Kay,Ho Pak Cheong,Complications after arthroscopic triangular fibrocartilage complex (TFCC) surgery.[J] .J Hand Surg Eur Vol, 2024, 49: 149-157\u003c/li\u003e\n \u003cli\u003eHenri, Vasara,Antti, Stenroos,Petra, Tarkiainen et al. Incidence and risk factors of adverse events after distal radius fracture fixation with volar locking plates: retrospective analysis of 2,790 cases.[J] .Acta Orthop, 2024, 95: 645-653\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-musculoskeletal-disorders","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmsd","sideBox":"Learn more about [BMC Musculoskeletal Disorders](http://bmcmusculoskeletdisord.biomedcentral.com/)","snPcode":"","submissionUrl":"https://author-welcome.nature.com/12891","title":"BMC Musculoskeletal Disorders","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"distal radius fracture, fracture line, Frykman classification, heat map","lastPublishedDoi":"10.21203/rs.3.rs-9010937/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9010937/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground: \u003c/strong\u003eDistal radius fractures are among the most common clinical fractures. In this study, we mapped fracture lines associated with distal radius injuries and converted these mappings into heat maps. This method allowed us to assess the distribution of fracture lines in the distal radius that involve the radiocarpal joint and investigate the correlation between the positions of these fracture lines and the regions of comminution.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods: \u003c/strong\u003eA retrospective study analyzed 111 instances of distal radius fractures involving the radiocarpal joint. The E-3D 21.10 software from Central South University in Changsha, China, was used to generate three-dimensional models of the radius and each fracture segment. This extraction process included rotation, translation, and separation to reconstruct the three-dimensional model. After importing the model into the E-3D 21.10 software for registration, fracture lines were marked on the three-dimensional surface image of the radius template. These fracture lines were then combined to form a comprehensive fracture line map, which was later transformed into a heat map.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e Both Frykman type III and type IV fractures show a pronounced concentration of fracture lines in the volar sections of the scaphoid and lunate fossae, resulting in a red appearance on the heat map. In contrast, fracture lines on the articular surface of the radial styloid process are less frequent, appearing blue on the heat map. Similarly, fractures classified as Frykman type VII and type VIII demonstrate a significant accumulation of fracture lines in the volar areas of both the lunate and scaphoid fossae, indicated in red on the heat map. Meanwhile, fracture lines on the articular surfaces of the radial styloid process, dorsal medial region, and dorsal ulnar notch are notably less concentrated, reflected in blue on the heat map.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions: \u003c/strong\u003eThe findings of this research indicate that the volar regions of the scaphoid and lunate fossae pose a significant risk for distal radius fractures involving the radiocarpal articular surface. In contrast, fractures involving the radial styloid articular surface are comparatively less common. This study provides physicians with a better understanding of the characteristics of distal radius fractures, which will help them select the most suitable surgical techniques for various fracture types.\u003c/p\u003e","manuscriptTitle":"Distribution of Distal Radius Fracture Lines Revealed by 3D Fracture Mapping","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-18 08:33:07","doi":"10.21203/rs.3.rs-9010937/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-15T08:19:04+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-01T14:42:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"326033340711529036042958753069988609492","date":"2026-03-30T06:40:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"250595985994928490582959476187696942229","date":"2026-03-28T11:20:43+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-13T08:01:55+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-03-04T04:46:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-03T10:12:48+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-03T10:08:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Musculoskeletal Disorders","date":"2026-03-02T13:43:44+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-musculoskeletal-disorders","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmsd","sideBox":"Learn more about [BMC Musculoskeletal Disorders](http://bmcmusculoskeletdisord.biomedcentral.com/)","snPcode":"","submissionUrl":"https://author-welcome.nature.com/12891","title":"BMC Musculoskeletal Disorders","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"417730ea-6dc6-4f41-a29a-156a8eb759db","owner":[],"postedDate":"March 18th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-18T08:33:07+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-18 08:33:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9010937","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9010937","identity":"rs-9010937","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}