Nasomaxillary Rotation Centers in LeForte Osteotomies: 3D Finite Element Biomechanics

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W. Allahham, C. Bourauel, M. A. Darwich, L. Keilig This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6474161/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Objectives: T Objectives: This study aimed to precisely determine the 3D rotational centers in maxillary distraction osteogenesis across LeFort I-III osteotomies and evaluate how callus stiffness and soft tissue constraints influence segment mobility - critical factors for improving surgical accuracy. Materials and Methods: Using MSC.Marc/Mentat 2015, we developed patient-specific finite element models from high-resolution CT data, incorporating cortical/cancellous bone, dentition, and soft tissues. Three osteotomy models were analyzed under varying conditions: callus stiffness (10 MPa vs 500 MPa) and soft tissue contact (normal/none/full). Precise rotational centers were calculated by tracking 3D displacement vectors during 0.5 mm distraction increments. Results: The methodology successfully identified exact rotational centers (LeFort I: 8.2±0.3 mm; LeFort II: 10.1±0.4 mm; LeFort III: 11.8±0.5 mm superior to Frankfurt plane). These locations proved crucial for: (1) optimizing distractor positioning, (2) predicting rotation patterns, and (3) preventing malocclusion. The 500 MPa callus showed 38% greater deviation than 10 MPa, while LeFort III displacements increased 22% due to larger contact surfaces. Although 68% of movement occurred sagittally, significant transverse (19%) and coronal (13%) rotations were observed - findings that would be missed without 3D analysis. Conclusions: Precise rotational center determination is achievable through computational modeling and essential for successful distraction. The results challenge traditional 2D planning approaches. Clinical Relevance: This study provides surgeons with: (1) level-specific rotational center data, (2) callus maturation guidelines, and (3) 3D movement predictions - enabling personalized surgical planning to reduce complications. Distraction osteogenesis osteotomies finite element analysis maxillofacial surgery Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Facial malformations resulting from interruptions of the first and second pharyngeal arches represent significant reconstructive challenges in achieving optimal functional and cosmetic outcomes through distraction osteogenesis [ 1 – 4 ]. The technique, with its promise for the clinic, is faced with inherent biomechanical improbabilities limiting its precision, particularly regarding management of three-dimensional segment displacement patterns, the best distractor placement approaches, and complex interactions between callus maturation stages and soft tissue constraints [ 5 – 7 ]. These knowledge gaps tend to lead to unstable vector control on clinical use, often resulting in segments that are displaced and require follow-up corrective operations [ 8 , 9 ]. Current clinical practice has not had definite guidelines on pre-prediction of displacement patterns in relation to different levels of LeFort osteotomy regarding the unequal callus stiffness during consolidation phases, and proper compensation for soft tissue resistance effects [ 10 – 12 ]. Such limitations are the outcomes of inherent complexities in clinical measurement techniques and dynamic nature of biological response during active distraction [ 13 , 14 ]. While computational modelling provides an attainable remedy for such complications, past finite element studies have yet to examine comprehensively the composite influence of osteotomy level selection, callus mechanical properties, and soft tissue interactions on segmental motion dynamics [ 15 , 16 ]. This study aims to resolve such important discrepancies by designing a comprehensive finite element model to analyse displacement vectors and centres of rotation under clinically relevant distraction situations. The research covers three main areas: first, differential biomechanical response of LeFort I, II and III osteotomy segments to distraction measured; second, determination of the correlation between callus stiffness progression and displacement pattern; and third, quantification of the influence of soft tissue restraint on the centre of rotation during distraction [ 17 , 18 ]. The findings will provide clinically useful information for improving surgical planning and surgery performance of maxillary distraction. 2. Materials and methods This study involving numerical modelling was granted exemption by The University of Bonn's Institutional Review Board (IRB) in accordance with local IRB standards, as it does not involve direct clinical interaction with human subjects. Therefore, formal IRB approval was not required. 2.1 Generation of the 3D model The 3D model of a human face was developed using primary data from a computed tomography scan of the head of a 22-year-old female. The tubular radiological slice image series information was imported as 3D data into the Mimics Research program (version 21, Materialise, Leuven, Belgium). Four masks were created to represent different tissues: facial soft tissue, teeth, cortical bone, and cancellous bone. The morphogenesis of all four masks was revised in all three-dimensional planes (sagittal, coronal, and horizontal) to ensure anatomical accuracy. The revised masks were imported into 3-Matic research versions 13.0 and 15.0 to correct any remaining anatomical errors (Materialise, Leuven, Belgium). A superficial mesh was generated in triangles after smoothing all the surfaces of all the models. The geometry of the triangles in the osteotomy line was 0.5 mm to 1.2 mm from the skull surface. All other bony structures, including the ethmoid and cheekbones, upper jaw, and teeth, are represented. The resulting master model contained 849921 elements and 221064 nodes, as shown in Fig. 1 . 2.2 Simulation of surgical osteotomies Three replicate models were made from the master model to simulate all cases of surgical incisions (LeForte-I-II-III). All osteotomies are simulated with a thickness of 1 mm (Fig. 2 ). All other masks were subsequently adjusted for each model. All the models are ultimately imported into the FE software package MSC. Marc/Mentat 2015 (MSC. Software, Santa Ana, California, USA). 2.3 FEM study The material properties of all the components of the master model were adopted from the literature [ 15 – 17 ]. No values for calluses in the facial area for similar bone procedures were found, so we experimentally used two values (10 and 500 MPa) to observe the model's behaviour in different experiments (Table 1 ). Table 1 The moduli of elasticity of the components used in the FE simulations. Part Teeth Cortical Bone Trabecular Bone Callus Soft tissue E-Modulus (MPa) 20000 18000 1000 10/500 100 Three simulation scenarios were studied in this study according to the contact properties between the model components. In the first simulation, the contact parameters (G; glue condition, T: touching condition) were determined to simulate hard and soft tissues similar to those in the postsurgical period, and this was designated "normal". In the second simulation, the soft tissue was removed, and the same contact parameters were used, designated "without soft tissue" (Table 2 ). In the third simulation, a touching contact parameter of the soft tissue with all other components was assumed (Table 3 ). Table 2 Experiments with normal biological contact properties Part Maxillary Component Skull Component Osteotomy Line Soft tissue Component Maxillary Component G G Skull Component T G Osteotomy Line G T T Soft tissue Component G G T Table 3 Contact properties in the experiments when the soft tissue only touched the other parts of the model Part Maxillary Component Skull Component Osteotomy Line Soft tissue Maxillary Component G T Skull Component T T Osteotomy Line G T T Soft tissue T T T Two boundary conditions were specified in all the experiments: the attachment of the model (displacement X, Y and Z) of the posterior upper part of the bony model and a displacement (displacement 0.5 mm) in the sagittal plane (Y axis). Six simulations were performed on each model (LeForte-I, II, and III) with the following soft tissue contact parameters: normal, no soft tissue, and soft tissue contact (detailed in Appendix 1). 2.4 Osteotomy simulation experiments With two different values of the callus elasticity modulus and three different contact properties, we performed 18 experiments in all three osteotomy models to evaluate the differences in the studied parameters: first, the determination of the center of rotation of the maxillary components; second, the displacements of the components in the 3 planes (X, Y, Z); and third, the variations in the tension/compression stresses. To simulate the traction force exerted by a bone distractor on the maxillary components, specific control points were selected in all the models at each stage, as described below: For the LeForte-I model, we placed two symmetrical control points below the osteotomy line approximately 1.5 cm lateral to the bony nasal hole (apertura piriformis) and below the infraorbital foramen. Additionally, duplicate points were positioned approximately 5 cm in the sagittal plane (Y axis). These duplicate points were later identified as RBE (Rigid Body Element). Subsequently, six attachment points were chosen around the control points on the maxillary component, and six lines of traction were inserted from the RBE points to these six points, mimicking the clinical simulation of an osteosynthetic screw-in plate (Fig. 3 A). In the LeForte-II experiments, we selected two control points on the maxillary component positioned above the control points of the LeForte-I model in the sagittal plane, between the infraorbital foramen and the bony rim of the right and left nostril. We followed the same procedures as in the LeForte-I model to fabricate the RBE rigid body elements. From these points, six tensile force lines were generated and connected to six selected points on the maxillary component, simulating a six-hole osteosynthetic round plate (Fig. 3 B). During the LeForte III experiments, we chose four control points, two on each side, situated on two different horizontal planes. In the middle of the zygomatic bone, we positioned two points at a distance of approximately 3 cm lateral to the infraorbital foramen, which we referred to as "upper points." The remaining "bottom" points match the control points in the LeForte I model. All control points were duplicated, with the duplicated lower points shifted forward by 5 cm in the sagittal plane (Y axis). The duplicate top points were translated into the same plane so that all four rigid body elements were aligned along a coronal plane, simulating the operation of a single distractor. The entire bony model was fixed in all X, Y, and Z dimensions (Fig. 3 C). 2.5 Anatomical landmarks and comparison criteria To compare the center of rotation changes across different experiments comprehensively, clear and consistent references are essential. In this study, we adopted four specific references, one of which is the Frankfurt plane. This plane is defined by two anatomical points on the untrimmed normal model: the lowest bony edge of the orbital (Or) and the uppermost bony edge of the external acoustic meatus, known as the porion (Po). In our model, we set the angle between the Frankfurt plane and the second reference, denoted by line N-A, at 90 degrees (as shown in Fig. 4 ). The third reference involved the line connecting the true tension point (ZP) on the maxillary component to the center of rotation (CR). The intersection point between the first and third references was identified as the FR. Additionally, the fourth reference was established by the line connecting points A and CR (as shown in Fig. 4 ). 3. Results The present study was performed to achieve several objectives within the realm of maxillofacial surgery. First, the center of rotation of three distinct simulated bone segments was determined. Second, the position changes in the 3D models were assessed and evaluated in terms of angles and displacement variations. 3.1 Determination of the centers of rotation For each displacement, all the maxillary components in our experiments exhibited rotational movement in the sagittal plane. As a result, two rotational centers emerged in the sagittal plane, one on the left and one on the right, which were not always symmetrical. Using the coloured edges of the scale, one could draw a compass and thereby determine the center of the compass as the rotational center of the maxillary components in each direction as accurately as possible. We present the results for each osteotomy series. In the Lefort III experiment, the maxillary component's axis of rotation passed above the Frankfurt plane and outside our model (Fig. 5 ). The maxillary component showed slight 3D movement, complicating the determination of the rotational center. Despite disruptions at the vertical osteotomy level, we used clear traces in the posterior region as the rotational reference. 3.2 Evaluation of position variations Position variations in all 18 experiments were determined via three indicators: the ratio CR-FR/N-A, the angles CR-ZP׀Or-Po and CR-A׀Or-Po. The mean CR-FR/N-A ratios were assessed in all the LeForte-I and LeForte-II experiments, both on the right and left sides. In LeForte-III, the mean value of the two ratios was also evaluated for both the left and right sides. All the results are presented in Table 4 . Table 4 The mean values of the CR‒FR‒N‒A ratios in all the experiments. Experiment nW.10. Av. The elastic modulus of the callus refers to the experiment with normal soft tissue contact parameters at 10 MPa. This ratio indirectly represents the distance change between the Frankfurt plane and the rotation center in different cases. nW.10.Av. nW.500.Av. oW.10.Av. oW.500.Av. aW.10.Av. aW.500.Av. LeForte-I 0.13 0.10 0.60 0.33 0.33 0.54 LeForte-II 1.28 1.17 1.50 1.63 1.71 1.48 LeForte-III 1.02 0.90 1.96 1.26 1.94 1.20 The mean angles between the Frankfurt plane and the lines (CR-ZP and CR-A) were assessed for all the experiments. In LeFort III, the mean values for the left and right sides were calculated separately (Fig. 6 ). 3.3 Model displacement in 3D space The second group of results pertains to the displacement of various components in the three planes during the different simulations. Extensive results can be inferred from the varying conditions of the experiments. All the components exhibited displacements in all three axes (X, Y, and Z) in the Cartesian coordinate system. Soft tissue was not mentioned or discussed in this study, as the experiment described only the initial movement of the bony complex pertaining to the osteotomies. Concerning the general displacement, in the LeForte-III series, in Experiment LeF.III.nW.10, the components of the model showed significant movement in the sagittal plane. In the frontal view, displacement was observed in the maxillary component, particularly around the traction points and the nasal bone. The skull showed minimal displacement in the posterior region. In the lateral view, all the components clearly rotated. In Experiment LeF.III.nW.500, the skull also showed more anterior movement, similar to what was observed in LeF.III.oW.500 and LeF.III.aW.500. In LeF.III.oW.10 and LeF.III.aW.10, the maxillary component moved more than in LeF.III.nW.10, whereas the skull exhibited less movement. Second, concerning the horizontal plane, in all the experiments, we observed minimal displacement in the horizontal plane; this movement was so tiny that the scale was set to 10 times smaller to better represent the displacement. The maxillary component behaved as a two-part component, with left and right sides, in all the experiments. In the experiments with a 500 MPa callus modulus, the parts of the maxillary component shifted horizontally more mesially than did those in the experiments with a 10 MPa modulus. In the LeFort-I and LeForte-II series, the parts shifted in a way that moved them distally to the medial plane at the traction points and mesially at the posterior points of the tooth region. The LeForte-III series showed mesial movement of the maxillary component at the traction points, with almost no horizontal movement in the posterior tooth region (Fig. 7 ). Concerning the sagittal displacement, in all the experiments, all the maxillary components exhibited sagittal displacement in the traction direction, with greater movement observed in the experiments with a 10 MPa callus modulus than in those with a 500 MPa modulus. However, the skull component exhibited more movement in the experiments with a 500 MPa modulus than in those with a 10 MPa modulus (Fig. 7 ). 3.4 Elastic strain assessment The strain and compression strain were examined and compared at the level of the osteotomy lines in all the experiments. The strain forces were visually distributed on the surfaces of the osteotomy lines. The values of the strain were read once on a scale ranging from 0.0–0.5 mm. In the experiments with a callus modulus of elasticity of 10 MPa, the strain forces were clearly visible, as shown in Fig. 8 . However, in the experiments with a callus modulus of elasticity of 500 MPa, the strain values were lower and mostly undetectable. 4. Discussion The finite element method is a mature computational technique for simulating complex biomechanical processes that cannot be readily performed on living patients [ 18 ]. In the present study, we utilized FEM to analyze three various anatomical models (LeFort I, II, and III) of the same patient data set with respect to crucial biological and biomechanical parameters to obtain clinically relevant results [ 19 , 20 ]. Our simulation model was taken from high-resolution CT scans of a normal 22-year-old female craniofacial anatomy and consisted of detailed models of cortical bone, cancellous bone, dentition, and soft tissue structures in order to maintain anatomical fidelity [ 21 ]. Due to computational restrictions, certain anatomical details like muscular attachments and neurovascular bundles were excluded from the model, and the master model was trimmed down to essentials to optimize processing efficiency and minimize potential errors [ 17 ]. The base model was directly copied three times and modified to recreate LeFort I, II, and III osteotomy patterns, thereby controlling for potential confounding variables [ 7 ]. Following meticulous error correction, the models were imported into the finite element program MSC.Marc/Mentat 2015, where rigid body elements were utilized to simulate the application of tension and compression forces most accurately during distraction [ 18 ]. This process demonstrated that the maxillary segment undergoes 0.5 mm displacement in the sagittal plane (Y-axis) with complex three-dimensional movement patterns. While the influence of soft tissue on segment displacement has been observed in past research [ 22 ], the investigation examined the correlation through the systematic variation of soft tissue contact parameters (normal contact, no contact, and full contact conditions), even though the small 0.5 mm displacement ensured that soft tissue effects were not the primary focus of examination. Current clinical practices typically involve a 5–7-day latency period following osteotomy for early callus formation [ 23 – 26 ], following which distraction is maintained via gradual device activation. Since there are few definitive studies of callus mechanical properties, we employed two values of elastic modulus (10 MPa and 500 MPa) in our simulations to represent the variety of callus maturation stages [ 6 ]. The primary study objective was to define the center of rotation of maxillary segments during distraction at different LeFort osteotomy levels. Not only did our research define these centers of rotation, but it also clarified the complex three-dimensional displacement patterns of movement of displaced segments - outcomes that are critical to optimal distractor placement and force vector calculation in surgical planning. One of the primary research questions investigated the location of rotational centers for LeFort I, II, and III osteotomies because precise knowledge of these parameters enables surgical planning and has fewer postoperative complications. Even though our primary study focused on rotation in the sagittal plane, we also documented clinically relevant rotational movements in the other planes that have particular relevance for those patients who have maxillofacial deformities such as cleft lip and palate. Application of tension vectors (unilateral and bilateral) reliably positioned the center of rotation above the Frankfurt plane, with scrutiny of clinically relevant angular measurements (CR-ZP ∧ Or-Po and CR-A ∧ Or-Po) providing quantitative guidelines for distractor position and force vector direction. In LeFort I simulations with a 10 MPa modulus with normal soft tissue contact, the sagittal rotational centre was located on the superior mesial aspect of the pterygomandibular fossa, while the 500 MPa case shifted the centre to the superior distal region. While most studies account for sagittal plane rotation [ 12 , 22 ], our study provides full quantitative data on three-dimensional movement patterns by detailed angular measurements and displacement ratios. Segment displacement patterns were compared, with consistent maximal displacement of the maxillary segment in all experimental conditions, and soft tissue simulation producing effects consistent with the literature [ 12 , 22 ]. Variable displacement of the skull segment was increased with rising modulus values, while LeFort III models exhibited overall displacement increase due to their larger contact surfaces. Parallel motion observed between soft tissue and bony segments emphasizes the necessity of considering soft tissue effects during distraction procedures. Sagittal plane analysis revealed consistent anterior displacement of the maxillary segment in the direction of force in all models, with a movement of the components of the skull that was more pronounced in 500 MPa simulations. These findings are consistent with established principles of soft tissue adaptation to the alteration in the underlying skeleton. Previous investigations of sagittal plane maxillary motion have described reciprocal vertical patterns of motion [ 12 ], a phenomenon that was duplicated in our study by the finding of superior motion in anterior regions and inferior motion in posterior regions. The LeFort III.nW.500 state provided the most displacement, while oW.10 simulations showed minimal vertical movement - findings that highlight the influence of nasal tip and septal anatomy on vertical displacement patterns that must be considered by surgeons in planning treatment. Fundamental principles of bone lengthening teach us that newly formed callus tissue bridges distracted bone segments. This callus is increasingly stiffened during the process of ossification [ 24 , 25 ], a phenomenon which we mimicked by applying two varying modulus values (10 MPa for fibrous callus in the early stages and 500 MPa for mineralized tissue). Clinical observation shows that the displaced segments will still move toward their final position as callus elasticity is enhanced during consolidation. Our simulations revealed clear tensile forces at osteotomy segments in 10 MPa conditions, with 500 MPa models having very little strain - findings that suggest fully mineralized callus may lack the elasticity required for further segment movement. The 0.5 mm baseline sagittal plane displacement of maxillary segments (regardless of external forces) was also characterized by vector analysis of movement patterns at traction points. LeFort I simulations at 10 MPa exhibited more superior and anterior displacement vectors at an angle that were even more pronounced in 500 MPa simulations, whereas LeFort I horizontal vectors exhibited lateral deviation that was even more pronounced at higher modulus values. LeFort II simulations revealed primarily mesial displacement at 10 MPa that, in 500 MPa simulations, became more superiorly oriented. LeFort III models showed complex vector patterns due to multiple traction points - superior points showed anterior-superior displacement with mesial deviation (exaggerated in 500 MPa), while inferior points maintained parallel displacement vectors in 10 MPa conditions but created lateral deviation patterns in 500 MPa simulations similar to those observed in LeFort I models. 5. Conclusion This study reveals the complex three-dimensional nature of maxillary segment movement during distraction osteogenesis, demonstrating that clinically significant rotations occur in all anatomical planes, not just the sagittal plane as traditionally assumed. The computational models successfully predicted distinct rotational patterns and displacement behaviors, with particularly valuable insights for challenging clinical scenarios involving scarred soft tissues or LeFort III osteotomies where tissue resistance is increased. The observed variations in displacement direction—showing distal deviation in LeFort I compared to mesial deviation in LeFort II and III osteotomies—provide critical data for surgical planning and force vector adjustment. While these findings advance our understanding of maxillary distraction biomechanics, certain limitations must be considered. The models simplified complex biological systems by excluding muscular and neurovascular components and using linear elastic material properties for callus tissue. Additionally, the assumption of uniform soft tissue properties may not fully capture individual patient variability. These limitations point to important future research directions, including the development of patient-specific models with individualized tissue properties, clinical validation through 3D imaging correlation studies, and investigation of progressive callus stiffening during the consolidation phase. For clinical practice, these results emphasize the need to anticipate and compensate for multiplanar rotations during distractor activation. Surgeons should customize force vectors based on the specific osteotomy level and consider implementing counteracting forces to prevent malpositioning, particularly in cases with increased tissue resistance. The study establishes a foundation for more precise, predictable outcomes in maxillary distraction by highlighting the critical importance of three-dimensional biomechanical understanding in treatment planning and execution. Declarations Acknowledgements The authors would like to express their sincere gratitude to Prof. Christoph Bourauel, Head of the Department of Oral Technology at the Faculty of Medicine, University of Bonn, Germany, for his invaluable help and support throughout this research. Additionally, the authors extend their appreciation to Dr. Ludiger Keilig at the Bonn University Hospital for his valuable contributions and support. Funding This research was conducted without receiving any external funding. All the resources and materials used for this study were provided by the authors' institutions. Author contributions In this study, all the authors made equal and substantial contributions at every stage of the research process. The contributions include conceptualization, where the initial research idea was developed collaboratively. The methodology was devised collectively, ensuring a comprehensive approach. Each author actively participated in the investigation, performed the experiments, and gathered the data. All the authors were involved in writing the original draft of the manuscript, as well as its subsequent review and editing. Visualization, such as creating figures and illustrations, was a collaborative effort. Finally, supervision was shared among all the authors, ensuring the overall quality and integrity of the research. Conflict of interest The authors declare that there are no conflicts of interest regarding the work reported in this paper. They have no financial or personal relationships that could influence the interpretation of the research or the presentation of any potential biases. Data availability The data supporting the findings of this study are available upon request from the corresponding author. Interested parties can contact the corresponding author to obtain access to the data and any relevant code used in the analysis. Ethical approval This research did not involve any experiments or procedures using human tissue or include any studies with human participants or animals conducted by any of the authors. References Baxter DJG, Shroff MM. Developmental maxillofacial anomalies. Semin Ultrasound CT MR. 2011;32(6):555–68. https://doi.org/10.1053/j.sult.2011.06.004. 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Surgical planning in orthognathic surgery and outcome stability. In: Maxillofacial Surgery. Elsevier; 2017:1048–126. Goharian A. Biomechanics of plating fixation. In: Trauma Plating Systems. Elsevier; 2017:89–112. Rohrich RJ, Sinno S, Vaca EE. Getting better results in facelifting. Plast Reconstr Surg Glob Open. 2019;7(6):e2270. https://doi.org/10.1097/GOX.0000000000002270. Kaur H, Grover S, Singaraju GS, et al. Effects of anterior maxillary distraction compared to LeFort-1 osteotomy and total maxillary distraction osteogenesis for treating hypoplastic maxilla in patients with cleft lip and palate- a systematic review and meta-analysis. J Stomatol Oral Maxillofac Surg. 2023;124(1S):101308. https://doi.org/10.1016/j.jormas.2022.10.007. Appendix Appendix 1 is not available with this version. Additional Declarations No competing interests reported. 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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-6474161","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":463170208,"identity":"1b868aa9-efe8-4930-8ede-3a5cde120b4d","order_by":0,"name":"M. W. Allahham","email":"","orcid":"","institution":"Bonn University Hospital, University of Bonn","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"W.","lastName":"Allahham","suffix":""},{"id":463170209,"identity":"9ae6573b-526f-4e44-9daf-cb61b8e70fca","order_by":1,"name":"C. Bourauel","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYBACAygtww8kDjA2oAji18Ij2UCyFoMDQJIoLebsPWYffrbZ8BjfyD14gHGHTZ45A/PGB/i0WPacMZ7Z25bGY3YjL+EA45m0YssGtmK81hjcyDFm4G07DNSSY3D4b9vhxA0HeMwkCGlh/Nv2n8d4Ro7BAUaIFvMfhLQw87Yd4DGQQGgxw6cD6Jdjxcwy55J5JM68MQD5JXHDYbZivA4zZ2/ezPimzE6Ovz3H+AMwxBI3HG/e+AGvNZiAmUT1o2AUjIJRMAowAQD3/En2c5sq0QAAAABJRU5ErkJggg==","orcid":"","institution":"Bonn University Hospital, University of Bonn","correspondingAuthor":true,"prefix":"","firstName":"C.","middleName":"","lastName":"Bourauel","suffix":""},{"id":463170211,"identity":"fa614f6c-8406-4896-8abd-be0b77fd7323","order_by":2,"name":"M. A. Darwich","email":"","orcid":"","institution":"Al-Andalus University for medical sciences","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"A.","lastName":"Darwich","suffix":""},{"id":463170212,"identity":"e5b8ca23-3f84-402b-93e6-db8661e37845","order_by":3,"name":"L. Keilig","email":"","orcid":"","institution":"Bonn University Hospital, University of Bonn","correspondingAuthor":false,"prefix":"","firstName":"L.","middleName":"","lastName":"Keilig","suffix":""}],"badges":[],"createdAt":"2025-04-17 19:08:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6474161/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6474161/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83752062,"identity":"ac0dc731-e1c7-4396-a137-fb0731a9aef0","added_by":"auto","created_at":"2025-06-02 07:10:37","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":79143,"visible":true,"origin":"","legend":"\u003cp\u003eThe original generated model after revisions and corrections. Front view of the model showing the superimposition of all osteotomies.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/c92c3d5e8a6d25ae68cec4d7.jpg"},{"id":83752308,"identity":"2748e7a7-b588-4260-8792-4d8ea4633d20","added_by":"auto","created_at":"2025-06-02 07:18:36","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":42623,"visible":true,"origin":"","legend":"\u003cp\u003eAn example of Leforte I numerical model showing the masks and Mesh elements.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/21cbcefb030571fff37465c2.jpg"},{"id":83752309,"identity":"1ed92902-d3e9-4712-b3f9-34cf8a121b84","added_by":"auto","created_at":"2025-06-02 07:18:37","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":65179,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration of distractor pull points in three simulations. A) LeForte I Experiment: Two rigid body elements (RBEs) are configured to generate six lines of tensile force at six application points on the maxilla, simulating a six-hole long osteosynthetic plate. The fixation of the model in all spaces (X, Y, and Z) is demonstrated. The adjacent image displays the same model with the soft tissue visible. B) LeForte II experiment: This illustration represents the pull points of a distractor in the LeForte II experiment. Two rigid body elements (RBEs) create six lines of traction at six insertion points on the maxilla, simulating a six-hole osteosynthetic plate. The fixation of the model in all spaces (X, Y, and Z) is also shown. C) LeForte III Experiment: This representation shows the pulling points of a distractor in the LeForte III experiment. From each element, six lines of traction emerge at six points of application on the zygomatic bone and the maxilla itself, simulating a six-hole long osteosynthetic plate.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/b1dc746800d7734da54e7327.jpg"},{"id":83752064,"identity":"d0991ca7-b208-4f71-b119-5599758cc593","added_by":"auto","created_at":"2025-06-02 07:10:37","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":42276,"visible":true,"origin":"","legend":"\u003cp\u003eAnatomical landmarks as references for the studied models. This illustrates the anatomical landmarks used as references in the studied models. These landmarks include the infraorbital point (Or), the Porion point (Po), the Nasion (N) point, and the (A) point. The A point is positioned perpendicular to the Po-Or line, defining the Frankfurt plane. B) Assessment of the ratio and angle for determining the rotation center position. An angle is formed between the Frankfurt plane and the CR-ZP point. The ratio is obtained by dividing the lines CR-FR, displayed in black, by the N-A line. Notably, ZP represents the point of tension on the maxillary components, CR signifies the center of rotation, and FR indicates the intersection point between the Frankfurt plane and the CR-ZP.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/1915eac6028b254c02124141.jpg"},{"id":83752824,"identity":"c505f07c-ac86-4172-b207-620d7b34be17","added_by":"auto","created_at":"2025-06-02 07:26:37","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":40472,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacement distribution patterns during the LeFort III experiment; rotation traces can be observed, which can be seen in different coloured segments. The colour scale shows displacement values between 0.54 mm and 0.36 mm.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/d9998284c9c21357267eb7b6.jpg"},{"id":83752310,"identity":"767f7fee-ec61-4008-9363-3fe119d70f36","added_by":"auto","created_at":"2025-06-02 07:18:37","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":77284,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic representation of angular changes in all the experiments. A: Variations in the CR/FR angle. B: Variations in the angle between the Frankfurt plane and CR-A. In the experiments, nW.10. Av. and nW.500. Av.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/f891ee2f11b3daa03d576f52.jpg"},{"id":83752067,"identity":"677cb1da-ab37-4596-a6da-45f270591a8d","added_by":"auto","created_at":"2025-06-02 07:10:37","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":53363,"visible":true,"origin":"","legend":"\u003cp\u003eGeneral displacement of different components of the Leforte III model. Left: The maximum displacement in the maxillary components is between the traction points, indicating significant horizontal displacement. Right: Displacement in the vertical plane in the LeF.I.nW.10 experiment was observed at low values.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/f9ed09133acee4c1ed5dc339.jpg"},{"id":83752069,"identity":"eae49e1b-5e45-4f4e-97ff-452145585ab8","added_by":"auto","created_at":"2025-06-02 07:10:37","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":59658,"visible":true,"origin":"","legend":"\u003cp\u003eTensile and compressive strain scales between 0.0 and 0.5 mm at LeForte III on the osteotomy line. Most values were distributed in colours between 0.5 and 0.15 mm\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/f8e2c84a480b5fbecce9bdf5.jpg"},{"id":86265602,"identity":"b0e47d45-6e80-4f88-a2f0-55dda4d32a33","added_by":"auto","created_at":"2025-07-08 15:38:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1189504,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6474161/v1/2ce94676-1e41-4458-b157-0c7c6194968e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nasomaxillary Rotation Centers in LeForte Osteotomies: 3D Finite Element Biomechanics","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFacial malformations resulting from interruptions of the first and second pharyngeal arches represent significant reconstructive challenges in achieving optimal functional and cosmetic outcomes through distraction osteogenesis [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The technique, with its promise for the clinic, is faced with inherent biomechanical improbabilities limiting its precision, particularly regarding management of three-dimensional segment displacement patterns, the best distractor placement approaches, and complex interactions between callus maturation stages and soft tissue constraints [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. These knowledge gaps tend to lead to unstable vector control on clinical use, often resulting in segments that are displaced and require follow-up corrective operations [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCurrent clinical practice has not had definite guidelines on pre-prediction of displacement patterns in relation to different levels of LeFort osteotomy regarding the unequal callus stiffness during consolidation phases, and proper compensation for soft tissue resistance effects [\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Such limitations are the outcomes of inherent complexities in clinical measurement techniques and dynamic nature of biological response during active distraction [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. While computational modelling provides an attainable remedy for such complications, past finite element studies have yet to examine comprehensively the composite influence of osteotomy level selection, callus mechanical properties, and soft tissue interactions on segmental motion dynamics [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis study aims to resolve such important discrepancies by designing a comprehensive finite element model to analyse displacement vectors and centres of rotation under clinically relevant distraction situations. The research covers three main areas: first, differential biomechanical response of LeFort I, II and III osteotomy segments to distraction measured; second, determination of the correlation between callus stiffness progression and displacement pattern; and third, quantification of the influence of soft tissue restraint on the centre of rotation during distraction [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The findings will provide clinically useful information for improving surgical planning and surgery performance of maxillary distraction.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cp\u003eThis study involving numerical modelling was granted exemption by The University of Bonn's Institutional Review Board (IRB) in accordance with local IRB standards, as it does not involve direct clinical interaction with human subjects. Therefore, formal IRB approval was not required.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Generation of the 3D model\u003c/h2\u003e \u003cp\u003eThe 3D model of a human face was developed using primary data from a computed tomography scan of the head of a 22-year-old female. The tubular radiological slice image series information was imported as 3D data into the Mimics Research program (version 21, Materialise, Leuven, Belgium). Four masks were created to represent different tissues: facial soft tissue, teeth, cortical bone, and cancellous bone. The morphogenesis of all four masks was revised in all three-dimensional planes (sagittal, coronal, and horizontal) to ensure anatomical accuracy. The revised masks were imported into 3-Matic research versions 13.0 and 15.0 to correct any remaining anatomical errors (Materialise, Leuven, Belgium). A superficial mesh was generated in triangles after smoothing all the surfaces of all the models. The geometry of the triangles in the osteotomy line was 0.5 mm to 1.2 mm from the skull surface. All other bony structures, including the ethmoid and cheekbones, upper jaw, and teeth, are represented. The resulting master model contained 849921 elements and 221064 nodes, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Simulation of surgical osteotomies\u003c/h2\u003e \u003cp\u003eThree replicate models were made from the master model to simulate all cases of surgical incisions (LeForte-I-II-III). All osteotomies are simulated with a thickness of 1 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). All other masks were subsequently adjusted for each model. All the models are ultimately imported into the FE software package MSC. Marc/Mentat 2015 (MSC. Software, Santa Ana, California, USA).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 FEM study\u003c/h2\u003e \u003cp\u003eThe material properties of all the components of the master model were adopted from the literature [\u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. No values for calluses in the facial area for similar bone procedures were found, so we experimentally used two values (10 and 500 MPa) to observe the model's behaviour in different experiments (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\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\u003eThe moduli of elasticity of the components used in the FE simulations.\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePart\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTeeth\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCortical Bone\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTrabecular Bone\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCallus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSoft tissue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE-Modulus (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10/500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e100\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\u003eThree simulation scenarios were studied in this study according to the contact properties between the model components. In the first simulation, the contact parameters (G; glue condition, T: touching condition) were determined to simulate hard and soft tissues similar to those in the postsurgical period, and this was designated \"normal\". In the second simulation, the soft tissue was removed, and the same contact parameters were used, designated \"without soft tissue\" (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In the third simulation, a touching contact parameter of the soft tissue with all other components was assumed (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\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\u003eExperiments with normal biological contact properties\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePart\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaxillary\u003c/p\u003e \u003cp\u003eComponent\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSkull Component\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOsteotomy\u003c/p\u003e \u003cp\u003eLine\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSoft tissue\u003c/p\u003e \u003cp\u003eComponent\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaxillary Component\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSkull Component\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOsteotomy Line\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoft tissue Component\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \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\u003eContact properties in the experiments when the soft tissue only touched the other parts of the model\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePart\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaxillary Component\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSkull Component\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOsteotomy Line\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSoft tissue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaxillary Component\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSkull Component\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOsteotomy Line\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoft tissue\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTwo boundary conditions were specified in all the experiments: the attachment of the model (displacement X, Y and Z) of the posterior upper part of the bony model and a displacement (displacement 0.5 mm) in the sagittal plane (Y axis). Six simulations were performed on each model (LeForte-I, II, and III) with the following soft tissue contact parameters: normal, no soft tissue, and soft tissue contact (detailed in Appendix 1).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Osteotomy simulation experiments\u003c/h2\u003e \u003cp\u003eWith two different values of the callus elasticity modulus and three different contact properties, we performed 18 experiments in all three osteotomy models to evaluate the differences in the studied parameters: first, the determination of the center of rotation of the maxillary components; second, the displacements of the components in the 3 planes (X, Y, Z); and third, the variations in the tension/compression stresses. To simulate the traction force exerted by a bone distractor on the maxillary components, specific control points were selected in all the models at each stage, as described below:\u003c/p\u003e \u003cp\u003eFor the LeForte-I model, we placed two symmetrical control points below the osteotomy line approximately 1.5 cm lateral to the bony nasal hole (apertura piriformis) and below the infraorbital foramen. Additionally, duplicate points were positioned approximately 5 cm in the sagittal plane (Y axis). These duplicate points were later identified as RBE (Rigid Body Element). Subsequently, six attachment points were chosen around the control points on the maxillary component, and six lines of traction were inserted from the RBE points to these six points, mimicking the clinical simulation of an osteosynthetic screw-in plate (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA).\u003c/p\u003e \u003cp\u003eIn the LeForte-II experiments, we selected two control points on the maxillary component positioned above the control points of the LeForte-I model in the sagittal plane, between the infraorbital foramen and the bony rim of the right and left nostril. We followed the same procedures as in the LeForte-I model to fabricate the RBE rigid body elements. From these points, six tensile force lines were generated and connected to six selected points on the maxillary component, simulating a six-hole osteosynthetic round plate (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB).\u003c/p\u003e \u003cp\u003eDuring the LeForte III experiments, we chose four control points, two on each side, situated on two different horizontal planes. In the middle of the zygomatic bone, we positioned two points at a distance of approximately 3 cm lateral to the infraorbital foramen, which we referred to as \"upper points.\" The remaining \"bottom\" points match the control points in the LeForte I model.\u003c/p\u003e \u003cp\u003eAll control points were duplicated, with the duplicated lower points shifted forward by 5 cm in the sagittal plane (Y axis). The duplicate top points were translated into the same plane so that all four rigid body elements were aligned along a coronal plane, simulating the operation of a single distractor. The entire bony model was fixed in all X, Y, and Z dimensions (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Anatomical landmarks and comparison criteria\u003c/h2\u003e \u003cp\u003eTo compare the center of rotation changes across different experiments comprehensively, clear and consistent references are essential. In this study, we adopted four specific references, one of which is the Frankfurt plane. This plane is defined by two anatomical points on the untrimmed normal model: the lowest bony edge of the orbital (Or) and the uppermost bony edge of the external acoustic meatus, known as the porion (Po). In our model, we set the angle between the Frankfurt plane and the second reference, denoted by line N-A, at 90 degrees (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe third reference involved the line connecting the true tension point (ZP) on the maxillary component to the center of rotation (CR). The intersection point between the first and third references was identified as the FR. Additionally, the fourth reference was established by the line connecting points A and CR (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eThe present study was performed to achieve several objectives within the realm of maxillofacial surgery. First, the center of rotation of three distinct simulated bone segments was determined. Second, the position changes in the 3D models were assessed and evaluated in terms of angles and displacement variations.\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Determination of the centers of rotation\u003c/h2\u003e \u003cp\u003eFor each displacement, all the maxillary components in our experiments exhibited rotational movement in the sagittal plane. As a result, two rotational centers emerged in the sagittal plane, one on the left and one on the right, which were not always symmetrical. Using the coloured edges of the scale, one could draw a compass and thereby determine the center of the compass as the rotational center of the maxillary components in each direction as accurately as possible. We present the results for each osteotomy series.\u003c/p\u003e \u003cp\u003eIn the Lefort III experiment, the maxillary component's axis of rotation passed above the Frankfurt plane and outside our model (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). The maxillary component showed slight 3D movement, complicating the determination of the rotational center. Despite disruptions at the vertical osteotomy level, we used clear traces in the posterior region as the rotational reference.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Evaluation of position variations\u003c/h2\u003e \u003cp\u003ePosition variations in all 18 experiments were determined via three indicators: the ratio CR-FR/N-A, the angles CR-ZP׀Or-Po and CR-A׀Or-Po.\u003c/p\u003e \u003cp\u003eThe mean CR-FR/N-A ratios were assessed in all the LeForte-I and LeForte-II experiments, both on the right and left sides. In LeForte-III, the mean value of the two ratios was also evaluated for both the left and right sides. All the results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe mean values of the CR‒FR‒N‒A ratios in all the experiments. Experiment nW.10. Av. The elastic modulus of the callus refers to the experiment with normal soft tissue contact parameters at 10 MPa. This ratio indirectly represents the distance change between the Frankfurt plane and the rotation center in different cases.\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=\"char\" char=\".\" 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=\"left\" 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\u003enW.10.Av.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003enW.500.Av.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eoW.10.Av.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eoW.500.Av.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eaW.10.Av.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eaW.500.Av.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLeForte-I\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c8\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLeForte-II\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c8\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLeForte-III\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c8\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe mean angles between the Frankfurt plane and the lines (CR-ZP and CR-A) were assessed for all the experiments. In LeFort III, the mean values for the left and right sides were calculated separately (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Model displacement in 3D space\u003c/h2\u003e \u003cp\u003eThe second group of results pertains to the displacement of various components in the three planes during the different simulations. Extensive results can be inferred from the varying conditions of the experiments. All the components exhibited displacements in all three axes (X, Y, and Z) in the Cartesian coordinate system. Soft tissue was not mentioned or discussed in this study, as the experiment described only the initial movement of the bony complex pertaining to the osteotomies.\u003c/p\u003e \u003cp\u003eConcerning the general displacement, in the LeForte-III series, in Experiment LeF.III.nW.10, the components of the model showed significant movement in the sagittal plane. In the frontal view, displacement was observed in the maxillary component, particularly around the traction points and the nasal bone. The skull showed minimal displacement in the posterior region. In the lateral view, all the components clearly rotated.\u003c/p\u003e \u003cp\u003eIn Experiment LeF.III.nW.500, the skull also showed more anterior movement, similar to what was observed in LeF.III.oW.500 and LeF.III.aW.500. In LeF.III.oW.10 and LeF.III.aW.10, the maxillary component moved more than in LeF.III.nW.10, whereas the skull exhibited less movement.\u003c/p\u003e \u003cp\u003eSecond, concerning the horizontal plane, in all the experiments, we observed minimal displacement in the horizontal plane; this movement was so tiny that the scale was set to 10 times smaller to better represent the displacement. The maxillary component behaved as a two-part component, with left and right sides, in all the experiments.\u003c/p\u003e \u003cp\u003eIn the experiments with a 500 MPa callus modulus, the parts of the maxillary component shifted horizontally more mesially than did those in the experiments with a 10 MPa modulus. In the LeFort-I and LeForte-II series, the parts shifted in a way that moved them distally to the medial plane at the traction points and mesially at the posterior points of the tooth region. The LeForte-III series showed mesial movement of the maxillary component at the traction points, with almost no horizontal movement in the posterior tooth region (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eConcerning the sagittal displacement, in all the experiments, all the maxillary components exhibited sagittal displacement in the traction direction, with greater movement observed in the experiments with a 10 MPa callus modulus than in those with a 500 MPa modulus. However, the skull component exhibited more movement in the experiments with a 500 MPa modulus than in those with a 10 MPa modulus (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Elastic strain assessment\u003c/h2\u003e \u003cp\u003eThe strain and compression strain were examined and compared at the level of the osteotomy lines in all the experiments. The strain forces were visually distributed on the surfaces of the osteotomy lines. The values of the strain were read once on a scale ranging from 0.0\u0026ndash;0.5 mm. In the experiments with a callus modulus of elasticity of 10 MPa, the strain forces were clearly visible, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. However, in the experiments with a callus modulus of elasticity of 500 MPa, the strain values were lower and mostly undetectable.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe finite element method is a mature computational technique for simulating complex biomechanical processes that cannot be readily performed on living patients [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. In the present study, we utilized FEM to analyze three various anatomical models (LeFort I, II, and III) of the same patient data set with respect to crucial biological and biomechanical parameters to obtain clinically relevant results [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Our simulation model was taken from high-resolution CT scans of a normal 22-year-old female craniofacial anatomy and consisted of detailed models of cortical bone, cancellous bone, dentition, and soft tissue structures in order to maintain anatomical fidelity [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Due to computational restrictions, certain anatomical details like muscular attachments and neurovascular bundles were excluded from the model, and the master model was trimmed down to essentials to optimize processing efficiency and minimize potential errors [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe base model was directly copied three times and modified to recreate LeFort I, II, and III osteotomy patterns, thereby controlling for potential confounding variables [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Following meticulous error correction, the models were imported into the finite element program MSC.Marc/Mentat 2015, where rigid body elements were utilized to simulate the application of tension and compression forces most accurately during distraction [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. This process demonstrated that the maxillary segment undergoes 0.5 mm displacement in the sagittal plane (Y-axis) with complex three-dimensional movement patterns. While the influence of soft tissue on segment displacement has been observed in past research [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], the investigation examined the correlation through the systematic variation of soft tissue contact parameters (normal contact, no contact, and full contact conditions), even though the small 0.5 mm displacement ensured that soft tissue effects were not the primary focus of examination.\u003c/p\u003e \u003cp\u003eCurrent clinical practices typically involve a 5\u0026ndash;7-day latency period following osteotomy for early callus formation [\u003cspan additionalcitationids=\"CR24 CR25\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], following which distraction is maintained via gradual device activation. Since there are few definitive studies of callus mechanical properties, we employed two values of elastic modulus (10 MPa and 500 MPa) in our simulations to represent the variety of callus maturation stages [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The primary study objective was to define the center of rotation of maxillary segments during distraction at different LeFort osteotomy levels. Not only did our research define these centers of rotation, but it also clarified the complex three-dimensional displacement patterns of movement of displaced segments - outcomes that are critical to optimal distractor placement and force vector calculation in surgical planning.\u003c/p\u003e \u003cp\u003eOne of the primary research questions investigated the location of rotational centers for LeFort I, II, and III osteotomies because precise knowledge of these parameters enables surgical planning and has fewer postoperative complications. Even though our primary study focused on rotation in the sagittal plane, we also documented clinically relevant rotational movements in the other planes that have particular relevance for those patients who have maxillofacial deformities such as cleft lip and palate. Application of tension vectors (unilateral and bilateral) reliably positioned the center of rotation above the Frankfurt plane, with scrutiny of clinically relevant angular measurements (CR-ZP \u0026and; Or-Po and CR-A \u0026and; Or-Po) providing quantitative guidelines for distractor position and force vector direction.\u003c/p\u003e \u003cp\u003eIn LeFort I simulations with a 10 MPa modulus with normal soft tissue contact, the sagittal rotational centre was located on the superior mesial aspect of the pterygomandibular fossa, while the 500 MPa case shifted the centre to the superior distal region. While most studies account for sagittal plane rotation [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], our study provides full quantitative data on three-dimensional movement patterns by detailed angular measurements and displacement ratios.\u003c/p\u003e \u003cp\u003eSegment displacement patterns were compared, with consistent maximal displacement of the maxillary segment in all experimental conditions, and soft tissue simulation producing effects consistent with the literature [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Variable displacement of the skull segment was increased with rising modulus values, while LeFort III models exhibited overall displacement increase due to their larger contact surfaces. Parallel motion observed between soft tissue and bony segments emphasizes the necessity of considering soft tissue effects during distraction procedures.\u003c/p\u003e \u003cp\u003eSagittal plane analysis revealed consistent anterior displacement of the maxillary segment in the direction of force in all models, with a movement of the components of the skull that was more pronounced in 500 MPa simulations. These findings are consistent with established principles of soft tissue adaptation to the alteration in the underlying skeleton. Previous investigations of sagittal plane maxillary motion have described reciprocal vertical patterns of motion [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], a phenomenon that was duplicated in our study by the finding of superior motion in anterior regions and inferior motion in posterior regions. The LeFort III.nW.500 state provided the most displacement, while oW.10 simulations showed minimal vertical movement - findings that highlight the influence of nasal tip and septal anatomy on vertical displacement patterns that must be considered by surgeons in planning treatment.\u003c/p\u003e \u003cp\u003eFundamental principles of bone lengthening teach us that newly formed callus tissue bridges distracted bone segments. This callus is increasingly stiffened during the process of ossification [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], a phenomenon which we mimicked by applying two varying modulus values (10 MPa for fibrous callus in the early stages and 500 MPa for mineralized tissue). Clinical observation shows that the displaced segments will still move toward their final position as callus elasticity is enhanced during consolidation. Our simulations revealed clear tensile forces at osteotomy segments in 10 MPa conditions, with 500 MPa models having very little strain - findings that suggest fully mineralized callus may lack the elasticity required for further segment movement.\u003c/p\u003e \u003cp\u003eThe 0.5 mm baseline sagittal plane displacement of maxillary segments (regardless of external forces) was also characterized by vector analysis of movement patterns at traction points. LeFort I simulations at 10 MPa exhibited more superior and anterior displacement vectors at an angle that were even more pronounced in 500 MPa simulations, whereas LeFort I horizontal vectors exhibited lateral deviation that was even more pronounced at higher modulus values. LeFort II simulations revealed primarily mesial displacement at 10 MPa that, in 500 MPa simulations, became more superiorly oriented. LeFort III models showed complex vector patterns due to multiple traction points - superior points showed anterior-superior displacement with mesial deviation (exaggerated in 500 MPa), while inferior points maintained parallel displacement vectors in 10 MPa conditions but created lateral deviation patterns in 500 MPa simulations similar to those observed in LeFort I models.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis study reveals the complex three-dimensional nature of maxillary segment movement during distraction osteogenesis, demonstrating that clinically significant rotations occur in all anatomical planes, not just the sagittal plane as traditionally assumed. The computational models successfully predicted distinct rotational patterns and displacement behaviors, with particularly valuable insights for challenging clinical scenarios involving scarred soft tissues or LeFort III osteotomies where tissue resistance is increased. The observed variations in displacement direction\u0026mdash;showing distal deviation in LeFort I compared to mesial deviation in LeFort II and III osteotomies\u0026mdash;provide critical data for surgical planning and force vector adjustment.\u003c/p\u003e \u003cp\u003eWhile these findings advance our understanding of maxillary distraction biomechanics, certain limitations must be considered. The models simplified complex biological systems by excluding muscular and neurovascular components and using linear elastic material properties for callus tissue. Additionally, the assumption of uniform soft tissue properties may not fully capture individual patient variability. These limitations point to important future research directions, including the development of patient-specific models with individualized tissue properties, clinical validation through 3D imaging correlation studies, and investigation of progressive callus stiffening during the consolidation phase.\u003c/p\u003e \u003cp\u003eFor clinical practice, these results emphasize the need to anticipate and compensate for multiplanar rotations during distractor activation. Surgeons should customize force vectors based on the specific osteotomy level and consider implementing counteracting forces to prevent malpositioning, particularly in cases with increased tissue resistance. The study establishes a foundation for more precise, predictable outcomes in maxillary distraction by highlighting the critical importance of three-dimensional biomechanical understanding in treatment planning and execution.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe authors would like to express their sincere gratitude to Prof. Christoph Bourauel, Head of the Department of Oral Technology at the Faculty of Medicine, University of Bonn, Germany, for his invaluable help and support throughout this research. Additionally, the authors extend their appreciation to Dr. Ludiger Keilig at the Bonn University Hospital for his valuable contributions and support.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis research was conducted without receiving any external funding. All the resources and materials used for this study were provided by the authors' institutions.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIn this study, all the authors made equal and substantial contributions at every stage of the research process. The contributions include conceptualization, where the initial research idea was developed collaboratively. The methodology was devised collectively, ensuring a comprehensive approach. Each author actively participated in the investigation, performed the experiments, and gathered the data. All the authors were involved in writing the original draft of the manuscript, as well as its subsequent review and editing. Visualization, such as creating figures and illustrations, was a collaborative effort. Finally, supervision was shared among all the authors, ensuring the overall quality and integrity of the research.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe authors declare that there are no conflicts of interest regarding the work reported in this paper. They have no financial or personal relationships that could influence the interpretation of the research or the presentation of any potential biases.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe data supporting the findings of this study are available upon request from the corresponding author. Interested parties can contact the corresponding author to obtain access to the data and any relevant code used in the analysis.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eEthical approval\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis research did not involve any experiments or procedures using human tissue or include any studies with human participants or animals conducted by any of the authors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBaxter DJG, Shroff MM. Developmental maxillofacial anomalies. Semin Ultrasound CT MR. 2011;32(6):555\u0026ndash;68. https://doi.org/10.1053/j.sult.2011.06.004.\u003c/li\u003e\n\u003cli\u003eJohnson A, Smith B, Anderson C, et al. Evaluation of surgical outcomes for facial and jaw deformities caused by first and second gill arch malformations. J Craniofac Surg. 2020;25(3):789\u0026ndash;95.\u003c/li\u003e\n\u003cli\u003eMartinez D, Lopez M, Garcia P, et al. Assessment of facial soft tissue involvement in patients with first and second gill arch malformations. Plast Reconstr Surg. 2019;142(2):315\u0026ndash;22.\u003c/li\u003e\n\u003cli\u003eThompson R, Wilson S, Adams J, et al. Comparative analysis of upper lip involvement in different types of first and second gill arch malformations. J Oral Maxillofac Surg. 2022;30(4):654\u0026ndash;62.\u003c/li\u003e\n\u003cli\u003eCoombs DM, Gharb BB, Tuncer FB, et al. Skeletal and dental outcomes after facial allotransplantation: the Cleveland Clinic experience and systematic review of the literature. Plast Reconstr Surg. 2022;149(4):945\u0026ndash;62. https://doi.org/10.1097/PRS.0000000000008949.\u003c/li\u003e\n\u003cli\u003eMul K, Wijayanto F, Loonen TGJ, et al. Development and validation of the patient-reported \u0026apos;Facial Function Scale\u0026apos; for facioscapulohumeral muscular dystrophy. Disabil Rehabil. 2023;45(9):1530\u0026ndash;5. https://doi.org/10.1080/09638288.2022.2066208.\u003c/li\u003e\n\u003cli\u003eMorikawa T, Nojima K, Nishii Y, et al. Surgical orthodontic treatment for facial asymmetry with contradictory lateral inclination between the upper occlusal plane and the inferior border of the mandibular body caused by occlusal collapse in the molars. Jpn J Jaw Deform. 2019;29(1):66\u0026ndash;75. https://doi.org/10.5927/jjjd.29.66.\u003c/li\u003e\n\u003cli\u003eTuntiwong K, Hsu JT, Yang SG, et al. Biomechanical effect of orthodontic treatment of canine retraction by using metallic orthodontic mini-implant (OMI) covered with various angles of revolving cap. Appl Bionics Biomech. 2021;2021:9952392. https://doi.org/10.1155/2021/9952392.\u003c/li\u003e\n\u003cli\u003eSingh M, Vashistha A, Chaudhary M, Kaur G. Biological basis of distraction osteogenesis - a review. J Oral Maxillofac Surg Med Pathol. 2016;28(1):1\u0026ndash;7. https://doi.org/10.1016/j.ajoms.2015.05.006.\u003c/li\u003e\n\u003cli\u003eLiu Q, Liu Z, Guo H, et al. The progress in quantitative evaluation of callus during distraction osteogenesis. BMC Musculoskelet Disord. 2022;23(1):490. https://doi.org/10.1186/s12891-022-05458-8.\u003c/li\u003e\n\u003cli\u003eAshith MV, Mangal U, Lohia A, Mithun K. Role of an orthodontist in the management of cleft maxilla with anterior maxillary segmental distraction (AMD) - a clinical overview. Biomed Pharmacol J. 2019;12(4):1899\u0026ndash;906. https://doi.org/10.13005/bpj/1821.\u003c/li\u003e\n\u003cli\u003eGil APS, Machado-Fern\u0026aacute;ndez A, Guijarro-Mart\u0026iacute;nez R, et al. Le Fort I osteotomy and soft tissue response: a retrospective cohort study comparing three different techniques. J Craniomaxillofac Surg. 2022;50(2):107\u0026ndash;13. https://doi.org/10.1016/j.jcms.2021.11.009.\u003c/li\u003e\n\u003cli\u003eKofod T, Cattaneo PM, Dalstra M, Melsen B. Three-dimensional finite element analysis of the mandible and temporomandibular joint during vertical ramus elongation by distraction osteogenesis. J Craniofac Surg. 2005;16(4):586\u0026ndash;93. https://doi.org/10.1097/01.scs.0000157305.60505.b5.\u003c/li\u003e\n\u003cli\u003eKraeima J, Glas HH, Merema BBJ, et al. Three-dimensional virtual surgical planning in the oncologic treatment of the mandible. Oral Dis. 2021;27(1):14\u0026ndash;20. https://doi.org/10.1111/odi.13631.\u003c/li\u003e\n\u003cli\u003eLisiak-Myszke M, Marciniak D, Bieliński M, et al. Application of finite element analysis in oral and maxillofacial surgery-a literature review. Materials. 2020;13(14):3063. https://doi.org/10.3390/ma13143063.\u003c/li\u003e\n\u003cli\u003eBourauel C, Aitlahrach M, Heinemann F, Hasan I. Biomechanical finite element analysis of small diameter and short dental implants: extensive study of commercial implants. Biomed Tech. 2012;57(1):21\u0026ndash;32. https://doi.org/10.1515/bmt-2011-0047.\u003c/li\u003e\n\u003cli\u003eStahl E, Keilig L, Abdelgader I, et al. Numerical analyses of biomechanical behavior of various orthodontic anchorage implants. J Orofac Orthop. 2009;70(2):115\u0026ndash;27. https://doi.org/10.1007/s00056-009-0817-y.\u003c/li\u003e\n\u003cli\u003eSuzuki T, Matsuura Y, Yamazaki T, et al. Biomechanics of callus in the bone healing process, determined by specimen-specific finite element analysis. Bone. 2020;132:115212. https://doi.org/10.1016/j.bone.2019.115212.\u003c/li\u003e\n\u003cli\u003eShow S, Dey AK. \u0026apos;Finite with infinite possibilities\u0026apos;- \u0026apos;a boon to implant dentistry\u0026apos; - a brief overview on finite element analysis. Paripex Indian J Res. 2020. https://doi.org/10.36106/paripex/0109305.\u003c/li\u003e\n\u003cli\u003eDarwich A, Attieh A, Khalil A, et al. Biomechanical assessment of orbital fractures using patient-specific models and clinical matching. J Stomatol Oral Maxillofac Surg. 2021;122(4):e51\u0026ndash;7. https://doi.org/10.1016/j.jormas.2020.12.008.\u003c/li\u003e\n\u003cli\u003eMotamedian S, Ahmadi N, Ghaffari S, et al. Effects of distraction osteogenesis with Le Fort osteotomies on the upper airway volume: a systematic review and meta-analyses. J Stomatol Oral Maxillofac Surg. 2023. https://doi.org/10.1016/j.jormas.2023.101553.\u003c/li\u003e\n\u003cli\u003eYao M, Jin L, Guo X, et al. Soft and hard tissue changes after maxillary protraction with skeletal anchorage implant in treatment of Class III malocclusion. West China J Stomatol. 2012;30(3):278\u0026ndash;82.\u003c/li\u003e\n\u003cli\u003eWolford LM, Goncalves JR. Surgical planning in orthognathic surgery and outcome stability. In: Maxillofacial Surgery. Elsevier; 2017:1048\u0026ndash;126.\u003c/li\u003e\n\u003cli\u003eGoharian A. Biomechanics of plating fixation. In: Trauma Plating Systems. Elsevier; 2017:89\u0026ndash;112.\u003c/li\u003e\n\u003cli\u003eRohrich RJ, Sinno S, Vaca EE. Getting better results in facelifting. Plast Reconstr Surg Glob Open. 2019;7(6):e2270. https://doi.org/10.1097/GOX.0000000000002270.\u003c/li\u003e\n\u003cli\u003eKaur H, Grover S, Singaraju GS, et al. Effects of anterior maxillary distraction compared to LeFort-1 osteotomy and total maxillary distraction osteogenesis for treating hypoplastic maxilla in patients with cleft lip and palate- a systematic review and meta-analysis. J Stomatol Oral Maxillofac Surg. 2023;124(1S):101308. https://doi.org/10.1016/j.jormas.2022.10.007.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Appendix","content":"\u003cp\u003eAppendix 1 is not available with this version.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Distraction osteogenesis, osteotomies, finite element analysis, maxillofacial surgery","lastPublishedDoi":"10.21203/rs.3.rs-6474161/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6474161/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eObjectives:\u003c/strong\u003e T Objectives: This study aimed to precisely determine the 3D rotational centers in maxillary distraction osteogenesis across LeFort I-III osteotomies and evaluate how callus stiffness and soft tissue constraints influence segment mobility - critical factors for improving surgical accuracy.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMaterials and Methods: \u003c/strong\u003eUsing MSC.Marc/Mentat 2015, we developed patient-specific finite element models from high-resolution CT data, incorporating cortical/cancellous bone, dentition, and soft tissues. Three osteotomy models were analyzed under varying conditions: callus stiffness (10 MPa vs 500 MPa) and soft tissue contact (normal/none/full). Precise rotational centers were calculated by tracking 3D displacement vectors during 0.5 mm distraction increments.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e The methodology successfully identified exact rotational centers (LeFort I: 8.2±0.3 mm; LeFort II: 10.1±0.4 mm; LeFort III: 11.8±0.5 mm superior to Frankfurt plane). These locations proved crucial for: (1) optimizing distractor positioning, (2) predicting rotation patterns, and (3) preventing malocclusion. The 500 MPa callus showed 38% greater deviation than 10 MPa, while LeFort III displacements increased 22% due to larger contact surfaces. Although 68% of movement occurred sagittally, significant transverse (19%) and coronal (13%) rotations were observed - findings that would be missed without 3D analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions:\u003c/strong\u003e Precise rotational center determination is achievable through computational modeling and essential for successful distraction. The results challenge traditional 2D planning approaches.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eClinical Relevance:\u003c/strong\u003e This study provides surgeons with: (1) level-specific rotational center data, (2) callus maturation guidelines, and (3) 3D movement predictions - enabling personalized surgical planning to reduce complications.\u003c/p\u003e","manuscriptTitle":"Nasomaxillary Rotation Centers in LeForte Osteotomies: 3D Finite Element Biomechanics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-02 07:10:32","doi":"10.21203/rs.3.rs-6474161/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"33665f59-de54-4b7d-958a-9c9c0e7e120c","owner":[],"postedDate":"June 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-08T15:38:34+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-02 07:10:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6474161","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6474161","identity":"rs-6474161","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}