Finite element analysis of a new alveolar bone splitting technique in the mandibular posterior region

Finite element analysis of a new alveolar bone splitting technique in the mandibular posterior region | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Finite element analysis of a new alveolar bone splitting technique in the mandibular posterior region Ye Tian, Xiaolu Shi, Shaobo Zhai, Yang Liu, Zheng Yang, Yuchuan Wu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4323987/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Mar, 2025 Read the published version in BMC Oral Health → Version 1 posted 16 You are reading this latest preprint version Abstract Background: Finite element analysis was used to predict the risk of bone plate fracture and the expected bone augmentation effect of a new alveolar bone splitting technique in the mandibular posterior region for different alveolar crest widths, different alveolar bone densities, different root incision widths, and different insertion depths of bone expansion instrumentation. Methods: The jaw models of the mandibular posterior region were constructed by computer-aided software and surgical incisions and bone expansion instruments were prepared on the models, after which the alveolar bone splitting procedure was simulated by finite element analysis software, and the equivalent stress-strain distribution characteristics of the jaw models of each group, as well as the maximal force and the maximal displacement of the bone plate when it was fractured, were recorded. Results: The distribution of equivalent stress and strain was mainly concentrated in the cancellous bone area at the root incision and the lower 1/3 of the buccal cortical bone plate, and there was no significant difference in the stress-strain distribution characteristics of the jaw models of each group. The wider of the alveolar crest, the higher the force required to fracture the bone plate, but the smaller the maximum displacement; the plastic deformation capacity of type IV bone jaws was more excellent; the wider the width of the root incision, the shallower the depth of instrument insertion, and the larger the maximum displacement. Conclusion: Finite element analysis can effectively simulate the surgical criticality index of the new alveolar bone splitting procedure. Alveolar crest width, alveolar bone density, root incision width, and instrument insertion depth had a clear correlation with the maximum displacement of the bone plate at fracture. The alveolar crest width and alveolar bone density also had a significant effect on the maximum force required to fracture the bone plate. alveolar bone splitting finite element analysis biomechanics bone augmentation mandible oral implants Figures Figure 1 Figure 2 Figure 3 1 Introduction Adequate width and height of alveolar bone are essential for ideal functional reconstruction and aesthetic recovery through implant restoration[ 1 ]. However, insufficient alveolar bone width is very common in oral implant surgery, which is related to bone resorption after tooth extraction, periodontal disease, tooth trauma and other factors. It is reported that the bone resorption of alveolar bone after tooth extraction ranges from 29–63%[ 2 ]. The mandibular posterior region is an area with weak bone, and the buccal bone plate of the mandible is thinner than the lingual bone plate. Alveolar bone resorption often leads to insufficient horizontal bone mass in the mandibular posterior region. In addition, the mandibular alveolar bone is denser than the maxillary alveolar bone, the blood circulation is relatively poor, and the effect of bone increment is not good. Therefore, how to successfully complete the horizontal bone increment in the mandibular posterior region is a key to implant restoration. Currently, bone augmentation surgeries commonly used in clinical practice include guided bone regeneration, autologous bone grafting, alveolar bone splitting, distraction osteogenesis, maxillary sinus floor lifting, etc.[ 3 ]. Among them, alveolar bone splitting is a horizontal bone augmentation procedure suitable for patients with adequate alveolar bone height but insufficient alveolar bone width. Its principle is to longitudinally separate the buccal and lingual bone plates, and use bone expansion tools to move the buccal bone plate to the buccal side, so as to achieve the purpose of horizontal bone augmentation. Traditional alveolar bone splitting is to use a bone splitting instrument to prepare a horizontal bone incision on the top of the alveolar ridge, which penetrates vertically into the cancellous bone, and then make vertical loose bone incisions from both ends of the horizontal bone incision toward the root, deepening into the subcortical bone, followed by bone splitting, bone compression and bone expansion. The bone augmentation effect of this surgery is obvious, and it can be widely used for thin alveolar bone after maxillary and mandibular dentition defects and dentition loss. The key to the success of traditional alveolar bone splitting surgery is to avoid bone plate fracture and ensure blood supply. However, compared with the more elastic maxilla, the alveolar bone in the mandibular posterior region is more mineralized and less tough, and the bone plate is prone to fracture during bone expansion. Although "two-stage [ 4 ] " or "three-stage [ 5 ] " bone splitting surgery can be adopted, it also prolongs the treatment time and increases the risk of bone resorption. In recent years, more and more scholars have improved alveolar bone splitting surgery to make it more widely applicable and reduce the incidence of complications. For example, Blus and Szmukler et al.[ 6 ] added a longitudinal incision at the bottom of the mandibular alveolar bone, aiming to create a hinge effect during the alveolar bone splitting process, thereby reducing the risk of fracture. Marcello et al.[ 7 ] prepared a rectangular incision to disconnect or partially disconnect the buccal bone plate, and then used steel wire ligation and fixation to obtain good initial stability of the implant. Inspired by Blus et al., this research team also designed a new alveolar bone splitting technique. The principle of this technique is to use an ultrasonic osteotome to perform traditional alveolar bone splitting, and then prepare a horizontal incision that only cuts through the cortical bone at the bottom of the mandible and between the vertical incisions. Afterwards, the bleeding holes are prepared on the surface of the buccal bone plate to ensure blood supply, and then combined with guided bone regeneration to guarantee the bone augmentation effect. Our team has applied it to many cases of insufficient width of mandibular alveolar bone, which have safely and effectively increased the width of alveolar bone in the surgical area, and achieved ideal repair results. This paper describes a novel alveolar bone splitting technique applied to the mandibular posterior region. Although this technique has achieved satisfactory results in clinic, whether it is this technique or other modified alveolar splitting techniques, in the course of clinical operation, implant doctors often rely on their own experience or feel to perform bone splitting and bone expansion operations. Without sufficient systematic theoretical guidance, it is difficult to predict the timing of bone plate fracture. In view of this situation, finite element analysis has incomparable advantages by simulating alveolar bone splitting to explore its theoretical basis [ 8 ]. Based on this, this study used computer-aided design software to establish a mandibular posterior region jaw model, and then used finite element analysis software to simulate the new alveolar bone splitting technology to explore its theoretical basis: (1) the effect of different alveolar crest width on the new alveolar bone splitting technique; (2) the effect of different alveolar bone density on the new alveolar bone splitting technique; (3) the effect of alveolar bone root incision width on the new alveolar bone splitting technique. (4) the effect of the depth of bone expansion instruments inserted into the jaw on the new alveolar bone splitting technique. The finite element analysis provides a systematic theoretical basis for the new alveolar bone splitting technique and practical reference guide for clinical application. 2 Materials and methods 2.1. Establishment of jaw model A volunteer with complete mandibular dentition and no history of periodontitis and jaw disease was selected to take the cone beam computed tomography (CBCT) (Carestream Health, Inc., Canada) of the jaw. After the CBCT images were stored in DICOM format, the jaw model of the mandibular posterior region was extracted by Mimics21.0 software (Materialise, Inc., Belgium) and saved in STL format. The jaw model was imported into GeomagicWrap2017 software (3DSystems, Inc., USA) to optimize, smooth and trim the model. The jaw model with cortical bone thickness of 1 mm and 2 mm was constructed by offset function, and the jaw model with alveolar crest width of 3 mm and 4 mm was constructed by resection function and saved in STP format. 2.2. Construction of surgical incision and bone expansion instrument model The model data from step 2.1 were imported into Solidworks2022 software (Dassault Systemes, Inc., USA), and four incisions for new alveolar bone splitting technique were made on each group of jaw models (Fig. 1). The width of the incision at the bottom of the alveolar bone was set to 0.5 mm and 1.0 mm and 1.5 mm respectively. The bone expansion instrument model was constructed through the sketch function (Fig. 1). The length of the contact part between the instrument model and the jaw was set as 3 mm, 5 mm, 7 mm respectively. After that, the instrument model and the jaw model were assembled and saved in STEP format. 2.3. Setting of finite element analysis parameters The model data from step 2.2 were imported into Workbench 22.0 software (Ansys, Inc., USA), and the transient structural analysis module was applied to enter the modulus of elasticity and Poisson's ratio of each material and assign values (Table 1 ). All materials in the experiment were set to be isotropic and homogeneous. A "Rough" connection was set between the instrument model and the cortical and cancellous bone, and a "Bonded" connection was set between the cortical and cancellous bone Tetrahedral grid elements were used to generate the mesh, and the final number of mesh elements and nodes was shown in Table 2 . The jaw model around the surgical incision was constrained, and a sagittal force was applied to the bone expansion instrument perpendicular to the surface of the instrument (Fig. 1), with the magnitude of the force increasing with time. The total degree of deformation, equivalent force and equivalent strain of each group of models reaching the ultimate yield state were finally solved, and the trend of the distribution of equivalent force and strain of each group was recorded, as well as the maximum force and the total degree of deformation in the ultimate yield state. Referring to the literature of other scholars [ 9 – 13 ], in this study, 50 MPa was used as the ultimate shear strength of cortical bone, 10 MPa was used as the ultimate shear strength of cancellous bone, and 2% strain rate was used as the yield strain of cortical bone and cancellous bone. In this case, 10 locations were randomly selected at the top of the alveolar ridge of the jaw model, and the average value of their total degree of deformation was taken as the maximum displacement when the jaw model reached the ultimate yield state. Table 1 Physical properties of materials used in the experiment Materials Modulus of elasticity (GPa) Poisson's ratio Density (g/cm 3 ) Cortical bone 13.4 0.30 2.10 Dense cancellous bone (type I, II, III bone) 1.37 0.30 1.80 Loose cancellous bone (type IV bone) 1.10 0.30 1.60 Structural steel 200.00 0.30 7.85 Table 2 Results of finite element analysis of jaw models in each group Model Alveolar crest width (mm) Alveolar bone density (type II、III、IV bone) Root incision width (mm) Insertion depth of instrument model (mm) Elements Maximum force (N) Maximum displacement (mm) M1 3 III 0.5 5 442517 25 0.65 ± 0.09 M2 4 III 0.5 5 520959 90 0.44 ± 0.13 M3 3 II 0.5 5 431519 6 0.60 ± 0.06 M4 3 IV 0.5 5 442517 30 0.88 ± 0.13 M5 3 III 1.0 5 442400 25 0.76 ± 0.11 M6 3 III 1.5 5 442414 25 0.89 ± 0.14 M7 3 III 0.5 3 434362 25 0.77 ± 0.12 M8 3 III 0.5 7 434962 25 0.56 ± 0.08 2.4. Statistical analysis Data analysis and figure construction was performed using GraphPad Prism 6 (GraphPad, San Diego, USA). Values represent mean ± standard deviation (SD). Comparison among different groups was made by two-way analysis of variance (ANOVA). P values < 0.05 were considered statistically significant. 3 Results The experimental jaw model consisted of three main parts: external cortical bone, free cortical bone and cancellous bone. Considering the shear strength and yield strain of cortical bone and cancellous bone, in the cancellous bone model, the parts with an equivalent stress of 10 MPa or less were set in blue; in the cortical bone model, the parts with an equivalent stress of 50 MPa and 10 MPa or less were set in light blue and blue; and the parts with a strain rate of 2% or less were set in blue. Among the indicators that the jaw model reached the ultimate yield state was when the buccal and lingual cancellous bone at the root incision appeared to have a phase-continuous distribution of equivalent stresses that exceeded the ultimate shear strength of the cancellous bone and a significant distribution of equivalent strains that exceeded their yield strains at the cancellous bone on both sides. The experimental results were shown in Table 2 and Fig. 2. There was no significant difference in the distribution characteristics of equivalent stress and strain in each part of each model. Taking M1 as an example, the results of the equivalent stress and equivalent strain distribution of its various parts were shown in Fig. 3. As could be seen from the figure, the equivalent stress and equivalent strain of the cancellous bone model were mainly concentrated in the cancellous bone region at the root-square incision, and the distribution range of the equivalent stress-strain was gradually expanded with the increase of the acting force. The equivalent stress-strain distribution of the cancellous bone on the lingual side was more extensive than that on the buccal side, while the equivalent stress-strain magnitude of the cancellous bone on the buccal side was higher than that on the lingual side. The equivalent strains exceeding the yield strain of the cancellous bone first appeared in the area of cancellous bone on both sides of the root-square incision, and gradually spread from the two sides to the middle as the value of the force increased. The equivalent stresses in the buccal free cortical bone first appeared in the lower 1/3 of the bone plate, and as the value of the force increased, the distribution of the equivalent stresses gradually approached to the lower edge of the buccal bone plate. The equivalent stresses in the lingual free cortical bone first appeared at the cutting angle on both sides of the bone plate, and as the value of the applied force increased, the equivalent stresses were gradually distributed all over the lower edge of the lingual plate, and also appeared in the lower 1/3 of the lingual bone plate as well as at the top of the alveolar crest. The equivalent stress distribution in the external cortical bone was located at the lower edge of the surgical incision at the buccal and lingual lateral bone plates. The equivalent strains of free and external cortical bone did not change significantly and were much less than 2% in all groups of models. In addition, M3 did not show significant equivalent stress-strain changes in free cortical bone and external cortical bone because the maximum force was too small. 4 Discussion The clinical cases with insufficient horizontal bone for implant restorative treatment must undergo bone augmentation surgery prior to implantation. In addition to classical guided bone regeneration and autologous bone grafting, alveolar bone splitting, which can effectively increase the horizontal alveolar bone width, is an ideal option [ 14 , 15 ]. However, when the alveolar bone is heavily resorbed, the brittleness of the buccal bone plate increases, especially the buccal alveolar bone in the mandibular posterior region, which greatly increases the risk of fracture of the bone plate during bone expansion by alveolar bone splitting. The risk of alveolar bone splitting complications can be reduced by preoperatively predicting the stress-strain distribution of the bone plate during expansion[ 8 ]. In order to predict the risk of bone plate fracture for the new alveolar bone splitting technique, an in-depth understanding of the expansion behaviour of the buccal bone plate and insight into its fracture mechanism is essential. In this context, finite element analysis can provide sufficient tools to analyze the principles of bone plate fracture in the new alveolar bone splitting technique. Studies have shown that retaining at least 3 mm of alveolar bone width and a minimum vertical bone height of 10 mm is necessary to provide sufficient buccal and lingual cortical and cancellous bone volume to maintain adequate blood supply to the bone adjacent to the implant, thus ensuring the success of alveolar bone splitting [ 1 , 16 ]. Based on this, considering that fine-diameter implants can be selected for implant restorations in clinical work when facing clinical patients with a residual bone width of up to 5 mm, the jaw bone models with 3 mm alveolar crest width and 4 mm alveolar crest width were constructed for finite element analysis in this study. Theoretically, after removing 1 mm of cortical bone, the width of the cancellous bone at the root incision of the 4 mm jaw model is thicker compared to that of the 3 mm jaw model, and thus it can withstand a higher external force before reaching the ultimate yield state. The experimental results shown that the maximum force of the 4 mm jaw model was 90 N, while the maximum force of the 3 mm jaw model was 25 N. Unexpectedly, the distribution range of equivalent stress and equivalent strain in the 4 mm jaw model was wider than that of the 3 mm jaw model under higher forces, which meant that the area exceeding the shear strength and yield strain was larger, and the range of plastic deformation was wider in the 4 mm jaw model. This means that the 4 mm jaw model has a larger area above the shear strength and yield strain, and a wider range of plastic deformation. Therefore, it was easier for the 4 mm jaw model to reach the ultimate yield state. The results of the total deformation degree also proved this point. In the ultimate yielding state, the displacement of the 4 mm jaw model at the top of the alveolar ridge was 0.4388 ± 0.1373 mm, which was less than that of the 3 mm jaw model (0.6526 ± 0.0908 mm). Besides, it could be found that the equivalent stress and equivalent strain distributions were inconsistent when the jaw model was in the ultimate yielding state. For example, when the 3 mm jaw model was in the ultimate yielding state, the buccal and lingual cancellous bone at the root incision had already experienced equivalent stress continuity, but the equivalent strains were still distributed only in the superficial layers of the buccal and lingual cancellous bone; when the equivalent stress at the edge of the free cortical bone had already exceeded the shear strength, the corresponding equivalent strain exceeding the yield strength was not observed, which may be related to the phenomenon of "hysteresis" [ 17 ] in osteo-viscoelasticity, where the strain response lags behind the stress. It is worth noting that during bone expansion, the stresses and strains were more concentrated in the cancellous bone and external cortical bone located in the region of the root incision, as well as in the lower 1/3 of the buccal lamellae of the free cortical bone, which suggests that in some cases of thin cortical bone, as the force increases, the buccal lamellae breakage may be located in the lower 1/3 of the lamellae, in addition to occurring in the root incision location. As mentioned previously, thin cortical bone has an effect on the fracture location of bone plate. Duttenhoefer et al. [ 18 ] also found that the fracture lines were mostly located in the weakest area of the bone plate locally through the alveolar bone splitting experiments on human jawbone specimens. Based on this, this study constructed jaw bone models with four bone densities according to the Lekholm-Zarb bone density classification, but only finite element analyses were carried out on the type II, III and IV bone jaw bone models in consideration of practical clinical applications. The maximum forces in the type II, III, and IV bone jaw models differed considerably after the removal of the underlying cortical bone. In the type II bone model, only a few cancellous bones remained to maintain the jaw morphology after the removal of the 2 mm thickness of cortical bone, and the type II bone model reached the ultimate yield state at a very low force, taking into account the lower shear strength of cancellous bone. At the root incision, the difference between the type II bone model and the type III bone model only lay in the thickness of the cancellous bone, so the equivalent stress-strain distribution characteristics of the two were not significantly different. Because of the low maximum force, the type II bone model did not show significant equivalent stress-strain distribution in the free cortical bone and external cortical bone. In addition, the difference between the type III and IV bone models is only reflected in the physical property parameters of the internal cancellous bone, so there is no significant difference in the equivalent stress-strain distribution characteristics between the two models. The results of the total deformation of the jaw models with different alveolar bone densities showed that the maximum displacement was the lowest in the type II bone model, which may be related to the width of the remaining cancellous bone at its root incision. There was a significant difference in the maximum displacement between the type III and IV bone models, indicating that there is an effect of different physical parameters of cancellous bone on the degree of deformation, which may be related to the fact that cancellous bone is a highly functionally compliant tissue. Numerous studies have shown that the mechanical properties of cancellous bone in different parts of the human body vary greatly, and this variation is mainly due to the fact that cancellous bone has different types of microstructures, and therefore its biomechanical properties are very complex. The results of this study suggest that lax cancellous bone may possess more excellent plastic deformation ability than dense cancellous bone. The improvement of the new alveolar bone splitting technique lies in the new root incision between the vertical incisions on both sides. At this position, when the cortical bone on the surface of the buccal bone plate is removed, only the cancellous bone is retained to maintain the continuity of the bone plate. The area of cancellous bone uncovered by cortical bone varies according to the width of the root incision, which is certainly a critical factor in alveolar bone splitting, which relies primarily on the ability of cancellous bone to deform plastically for bone expansion. Based on this, this study constructed 0.5 mm incision, 1.0 mm incision, and 1.5 mm incision jaw models to investigate whether there is any effect on the bone augmentation effect of the new alveolar bone splitting technique. The maximum force of the three jaw models was 25 N. It was found that there may not be a clear relationship between the width of the root incision and the maximum force. The results of equivalent stress-strain distribution characteristics showed that the area of cancellous bone without cortical bone coverage increased with increasing incision width, and the wider incision model had a wider range of equivalent stress-strain distribution and higher equivalent stress and equivalent strain magnitudes under the same value of acting force. It is noteworthy that the maximum displacement of each jaw model gradually increased with the increase of the root incision width after reaching the ultimate yield state, which implies that the larger the area of the cancellous bone region without cortical bone coverage, the greater the plastic deformation capacity under the same cancellous bone physical property parameters. The increase of the width of the surgical incision also resulted in a decrease in the area of cortical bone in the buccal bone plate. However, there was no significant difference in the equivalent stress distribution and size of the cortical bone in the 0.5 mm incision, 1.0 mm incision, and 1.5 mm incision jaw models, indicating that the stress concentration area of the buccal bone plate was relatively fixed during bone expansion, which may not be related to the remaining area of cortical bone. The bone expansion principle of the new alveolar bone splitting is to prepare the root cortical bone incision and make use of the adaptability and plasticity of cancellous bone to reduce the risk of cortical bone fracture. During bone expansion, the buccal bone plate is rotated by the acting force of the bone expansion instrument, using the inner edge of the root incision as the fulcrum. If the distance between the bone expansion instrument and the root incision is farther, which corresponds to the longer power arm, the greater the stress at the root incision under the same force conditions. Based on this, the jaw models of 3 mm depth, 5 mm depth and 7 mm depth were constructed to explore the effect of new alveolar bone splitting technique with different depth of bone expansion instruments. The experimental results demonstrated that there was no significant difference in the equivalent stress-strain distribution characteristics of the 3 mm depth, 5 mm depth, and 7 mm depth jaw models, but the magnitude of the equivalent stresses in each jaw model under the same force gradually decreased with the increase of the insertion depth of the instrumented model, which was consistent with the previous hypothesis. There was no difference in the maximum force in the jaw models with different instrument insertion depths, indicating that the distance between the instrumented model and the root incision was not sufficient in the jaw models to affect a change in the value of the force that would bring the cancellous bone to its ultimate yield state. However, the maximum displacement of the jaw models with different instrument insertion depths decreased with increasing insertion depth, indicating that the deeper the insertion depth, the larger the contact area between the instrumented model and the cancellous bone, and the smaller the pressure borne by the cancellous bone per unit area under the same acting force, i.e., the lower the stress. In a low stress state, the ability of cancellous bone to deform plastically may be limited. It is very difficult to map the bone expansion mechanism and stress distribution of the new alveolar bone splitting technique in clinical practice. Hence, for exploring the theoretical basis of the technique, biomechanical analysis tools are needed. To date, finite element analysis is a commonly used tool in mechanics and biomechanics virtual analysis of mechanical strength and stress shielding [ 19 ], among others, and its emergence has provided new ideas and solutions to study the bone plate fracture mechanism of alveolar bone splitting. In this experiment, the influence of four factors, namely, alveolar crest width, alveolar bone density, surgical incision width, and instrument insertion depth, on the bone augmentation effect of the new alveolar bone splitting technique was investigated by means of finite element analysis, and the corresponding results were obtained. Nevertheless, there are still some limitations and need to be improved in the course of this study, and the shortcomings are as follows. The parameter settings of the research model are not reasonable enough. It is well known that cortical bone and cancellous bone have biomechanical properties such as anisotropy and non-homogeneity. However, in this study, the cortical bone and cancellous bone were set to be isotropic and homogeneous in order to facilitate the calculation. The change in material properties will undoubtedly affect the accuracy of the experimental results. Differential material assignment can be considered through the grey value of the CBCT image of each grid element in the model to obtain an anisotropic, non-homogeneous jaw model. The research on the basis of system theory was not thorough enough. Although this study investigated the effects of four different factors on the new alveolar bone splitting technique to explore the theoretical basis of the technique, it was not thorough enough. Mainly reflected in: (1) Alveolar bone splitting, as a bone augmentation method, is also affected by its subsequent treatment process, such as implant placement, which also extrudes the buccal bone plate and further expands the width of alveolar bone. Therefore, it can be considered to add the implant implantation process to the subsequent research process, so as to analyze the influence of the new alveolar bone splitting on the bone augmentation effect of implant restorations in a more complete way. (2) In this experiment, the study subjects were various jaw models that underwent only the new alveolar bone splitting procedure, and the control group was missing. In order to reflect the changes in the improved alveolar bone splitting technique, finite element analysis of the traditional alveolar bone splitting technique could be added to explore the shortcomings of the new alveolar bone splitting technique through a comparative study so that the technique can be further improved. (3) There are more variables in alveolar bone splitting than the four factors studied in this experiment, such as the depth of the surgical incision, the thickness of the bone plate at the base of the jaw, etc., and the corresponding jaw models can be constructed for the finite element analysis in order to improve the theoretical basis of this technique. There is a discrepancy between finite element theoretical analysis and real practice. Simple jaw models can accurately predict the timing and location of bone plate fracture through finite element analysis, but the human jaw is not only a biomaterial with complex mechanical properties, but also a biological organ that carries mechanical loads, and the growth and development of cells and metabolism will lead to changes in the quantity and quality of the jawbone, which will affect its complex mechanical properties. Furthermore, the thicknesses of cortical bone and cancellous bone in the various jaw models in this study were relatively fixed, while the thicknesses of cortical bone and cancellous bone in human jaws in real life are varied and not uniform. Although the material parameters and deformation conditions are set reasonably, further basic research is still needed to prove the accuracy of the finite element modelling theory, and only by combining the theory with practice can the theoretical basis of the technique be truly formed. 5 Conclusion This experiment investigated the finite element analysis of a new alveolar bone splitting technique under four different factors. The results showed that, among the jaw models with different alveolar crest widths, the wider the alveolar crest, the higher the maximum force to reach the ultimate yield state, but the smaller the maximum displacement at the alveolar crest at that state; among the jaw models with different alveolar bone densities, the maximal force and the maximal displacement to reach the ultimate yield state of the jaw model of type II bone were the smallest and the plastic deformation ability of the jaw model of type IV bone was more excellent because of its loose cancellous bone; among the jaw models with different root incision widths, the wider the root incision, the larger the area of cancellous bone without cortical bone coverage, and the larger the maximum displacement at ultimate yield; among the jaw models with different insertion depths of bone expansion instruments, the deeper the insertion of the instruments, the lower the stresses, and the lower the maximum displacement at ultimate yield under the same force. Regardless of the type of jaw model, the main concentration of stress and strain was at the root incision, followed by the lower 1/3 of the buccal bone plate, and with the increase of the value of the force, the lower edge of the instrumented model also showed a concentration of stress. Declarations Ethics approval and consent to participate Not applicable. Consent for publication Not applicable. Availability of data and materials The data that support the findings of this study are available from the corresponding author upon reasonable request. Competing interests All authors state that they have no potential competing interests. Funding This work was supported by the Scientific Research Project of Jilin Provincial Department of Education, China (Grant No. JJKH20231291KJ), the Science and Technology Development Project of Jilin Provincial Department of Science and Technology, China (Grant No. 20230203065SF). Authors’ contributions Ye Tian led the writing and did most of the experiments. Shunli Chu critically revised the manuscript. Xiaolu Shi, Shaobo Zhai and Yang Liu analyzed the experimental data. Zheng Yang and Yuchuan Wu contributed to charting. Every author gave final approval and agreed to be accountable for all aspects of the work. Acknowledgments We thank Liwen Bianji (Edanz) (www.liwenbianji.cn) for editing the language of a draft of this manuscript. References Starch-Jensen T, Becktor JP: Maxillary Alveolar Ridge Expansion with Split-Crest Technique Compared with Lateral Ridge Augmentation with Autogenous Bone Block Graft: a Systematic Review . J Oral Maxillofac Res 2019, 10 (4):e2. Tan WL, Wong TL, Wong MC, Lang NP: A systematic review of post-extractional alveolar hard and soft tissue dimensional changes in humans . Clin Oral Implants Res 2012, 23 Suppl 5 :1-21. 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Duttenhoefer F, Varga P, Jenni D, Grünwald L, Thiemann L, Gueorguiev B, Stricker A: The Alveolar Ridge Splitting Technique on Maxillae: A Biomechanical Human Cadaveric Investigation . BioMed research international 2020, 2020 :8894471. Falcinelli C, Valente F, Vasta M, Traini T: Finite element analysis in implant dentistry: State of the art and future directions . Dental materials : official publication of the Academy of Dental Materials 2023, 39 (6):539-556. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Mar, 2025 Read the published version in BMC Oral Health → Version 1 posted Editorial decision: Revision requested 11 Sep, 2024 Reviews received at journal 02 Aug, 2024 Reviewers agreed at journal 27 Jul, 2024 Reviews received at journal 24 Jul, 2024 Reviewers agreed at journal 23 Jul, 2024 Reviewers agreed at journal 22 Jul, 2024 Reviewers agreed at journal 22 Jul, 2024 Reviews received at journal 03 Jun, 2024 Reviews received at journal 19 May, 2024 Reviewers agreed at journal 14 May, 2024 Reviewers agreed at journal 14 May, 2024 Reviewers invited by journal 14 May, 2024 Editor invited by journal 07 May, 2024 Submission checks completed at journal 06 May, 2024 Editor assigned by journal 06 May, 2024 First submitted to journal 25 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4323987","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":300591548,"identity":"efa70930-640f-44ca-aeae-4a60f2334f89","order_by":0,"name":"Ye Tian","email":"","orcid":"","institution":"Department of Implantology, Hospital of Stomatology, Jilin University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ye","middleName":"","lastName":"Tian","suffix":""},{"id":300591551,"identity":"ac9fd51c-7a13-4df9-800f-bc2a7bd7d644","order_by":1,"name":"Xiaolu Shi","email":"","orcid":"","institution":"Department of Implantology, Hospital of Stomatology, Jilin University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xiaolu","middleName":"","lastName":"Shi","suffix":""},{"id":300591554,"identity":"a4d18722-ced6-4960-ac49-be4000e76889","order_by":2,"name":"Shaobo Zhai","email":"","orcid":"","institution":"Department of Implantology, Hospital of Stomatology, Jilin University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Shaobo","middleName":"","lastName":"Zhai","suffix":""},{"id":300591555,"identity":"357b717b-1283-4fe2-bea4-80ee3e178f93","order_by":3,"name":"Yang Liu","email":"","orcid":"","institution":"Department of Implantology, Hospital of Stomatology, Jilin University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Liu","suffix":""},{"id":300591557,"identity":"807d1cf5-7e3e-4f4f-a606-6208ab6c1568","order_by":4,"name":"Zheng Yang","email":"","orcid":"","institution":"Department of Implantology, Hospital of Stomatology, Jilin University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zheng","middleName":"","lastName":"Yang","suffix":""},{"id":300591559,"identity":"5cd92e1c-f484-497e-8476-6e18732653c3","order_by":5,"name":"Yuchuan Wu","email":"","orcid":"","institution":"Department of Implantology, Hospital of Stomatology, Jilin University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yuchuan","middleName":"","lastName":"Wu","suffix":""},{"id":300591561,"identity":"1a8f103a-f4aa-45c4-a825-0f3e075e1c15","order_by":6,"name":"Shunli Chu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsklEQVRIiWNgGAWjYDACCSB+UMEmA2MTqSXhDBsPiVoS2xhI0MI/u8f4Q+I8Ph6DA8wHb/Mw2OURtuTOGTOJxG1sQC1sydY8DMnFBLUYSOSYMUC08JhJ8zAcSGwgQgvQYXNAWvi/Ea3FQCKxAWwLG3FaJG6klUkkHGPjkTzMZmw5xyCZsBb+GcmbP3yoOSbHd7z54Y03FXaEtUDBMQYGZrA7iVQPBDXEKx0Fo2AUjIKRBwDHKjOL9ntfwQAAAABJRU5ErkJggg==","orcid":"","institution":"Department of Implantology, Hospital of Stomatology, Jilin University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Shunli","middleName":"","lastName":"Chu","suffix":""}],"badges":[],"createdAt":"2024-04-25 12:00:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4323987/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4323987/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12903-025-05559-5","type":"published","date":"2025-03-08T15:57:19+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":56543310,"identity":"24f4a4a6-5319-453d-8c00-6226ab599f86","added_by":"auto","created_at":"2024-05-15 14:36:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":278867,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of finite element analysis model.\u003c/p\u003e\n\u003cp\u003e(a) Four surgical incisions; (b) Model dimensions of bone expansion instruments; (c) The direction of force exerted.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4323987/v1/35745d0c3d03602341d5ee1c.png"},{"id":56543309,"identity":"d8a879dd-c8da-4375-85e6-e9fa7d5b7a61","added_by":"auto","created_at":"2024-05-15 14:36:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":84621,"visible":true,"origin":"","legend":"\u003cp\u003eThe maximum displacement results of finite element analysis of jaw models in various groups.\u003c/p\u003e\n\u003cp\u003eNote: *, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.05; ****, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4323987/v1/c644e922be30f226b4f92323.png"},{"id":56543308,"identity":"a56eaa5c-403e-4308-bad4-8dc5a1175587","added_by":"auto","created_at":"2024-05-15 14:36:34","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":159399,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution characteristics of equivalent stress and equivalent strain of M1.\u003c/p\u003e\n\u003cp\u003e(a) Equivalent stress distribution characteristics of cancellous bone and free cortical bone; (b) Equivalent strain distribution characteristics of cancellous bone; (c) Equivalent stress distribution characteristics of external cortical bone.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4323987/v1/b2d9f2a856f1734e3fba9175.png"},{"id":78181471,"identity":"9982c827-6f19-41e0-8d28-9e8394723df6","added_by":"auto","created_at":"2025-03-10 17:46:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1947544,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4323987/v1/88ac61ba-0bf0-49ee-9a0b-4f3f4e57446d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Finite element analysis of a new alveolar bone splitting technique in the mandibular posterior region","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eAdequate width and height of alveolar bone are essential for ideal functional reconstruction and aesthetic recovery through implant restoration[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. However, insufficient alveolar bone width is very common in oral implant surgery, which is related to bone resorption after tooth extraction, periodontal disease, tooth trauma and other factors. It is reported that the bone resorption of alveolar bone after tooth extraction ranges from 29\u0026ndash;63%[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The mandibular posterior region is an area with weak bone, and the buccal bone plate of the mandible is thinner than the lingual bone plate. Alveolar bone resorption often leads to insufficient horizontal bone mass in the mandibular posterior region. In addition, the mandibular alveolar bone is denser than the maxillary alveolar bone, the blood circulation is relatively poor, and the effect of bone increment is not good. Therefore, how to successfully complete the horizontal bone increment in the mandibular posterior region is a key to implant restoration.\u003c/p\u003e \u003cp\u003eCurrently, bone augmentation surgeries commonly used in clinical practice include guided bone regeneration, autologous bone grafting, alveolar bone splitting, distraction osteogenesis, maxillary sinus floor lifting, etc.[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Among them, alveolar bone splitting is a horizontal bone augmentation procedure suitable for patients with adequate alveolar bone height but insufficient alveolar bone width. Its principle is to longitudinally separate the buccal and lingual bone plates, and use bone expansion tools to move the buccal bone plate to the buccal side, so as to achieve the purpose of horizontal bone augmentation. Traditional alveolar bone splitting is to use a bone splitting instrument to prepare a horizontal bone incision on the top of the alveolar ridge, which penetrates vertically into the cancellous bone, and then make vertical loose bone incisions from both ends of the horizontal bone incision toward the root, deepening into the subcortical bone, followed by bone splitting, bone compression and bone expansion. The bone augmentation effect of this surgery is obvious, and it can be widely used for thin alveolar bone after maxillary and mandibular dentition defects and dentition loss. The key to the success of traditional alveolar bone splitting surgery is to avoid bone plate fracture and ensure blood supply. However, compared with the more elastic maxilla, the alveolar bone in the mandibular posterior region is more mineralized and less tough, and the bone plate is prone to fracture during bone expansion. Although \"two-stage [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] \" or \"three-stage [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] \" bone splitting surgery can be adopted, it also prolongs the treatment time and increases the risk of bone resorption.\u003c/p\u003e \u003cp\u003eIn recent years, more and more scholars have improved alveolar bone splitting surgery to make it more widely applicable and reduce the incidence of complications. For example, Blus and Szmukler et al.[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] added a longitudinal incision at the bottom of the mandibular alveolar bone, aiming to create a hinge effect during the alveolar bone splitting process, thereby reducing the risk of fracture. Marcello et al.[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] prepared a rectangular incision to disconnect or partially disconnect the buccal bone plate, and then used steel wire ligation and fixation to obtain good initial stability of the implant. Inspired by Blus et al., this research team also designed a new alveolar bone splitting technique. The principle of this technique is to use an ultrasonic osteotome to perform traditional alveolar bone splitting, and then prepare a horizontal incision that only cuts through the cortical bone at the bottom of the mandible and between the vertical incisions. Afterwards, the bleeding holes are prepared on the surface of the buccal bone plate to ensure blood supply, and then combined with guided bone regeneration to guarantee the bone augmentation effect. Our team has applied it to many cases of insufficient width of mandibular alveolar bone, which have safely and effectively increased the width of alveolar bone in the surgical area, and achieved ideal repair results.\u003c/p\u003e \u003cp\u003eThis paper describes a novel alveolar bone splitting technique applied to the mandibular posterior region. Although this technique has achieved satisfactory results in clinic, whether it is this technique or other modified alveolar splitting techniques, in the course of clinical operation, implant doctors often rely on their own experience or feel to perform bone splitting and bone expansion operations. Without sufficient systematic theoretical guidance, it is difficult to predict the timing of bone plate fracture. In view of this situation, finite element analysis has incomparable advantages by simulating alveolar bone splitting to explore its theoretical basis [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Based on this, this study used computer-aided design software to establish a mandibular posterior region jaw model, and then used finite element analysis software to simulate the new alveolar bone splitting technology to explore its theoretical basis: (1) the effect of different alveolar crest width on the new alveolar bone splitting technique; (2) the effect of different alveolar bone density on the new alveolar bone splitting technique; (3) the effect of alveolar bone root incision width on the new alveolar bone splitting technique. (4) the effect of the depth of bone expansion instruments inserted into the jaw on the new alveolar bone splitting technique. The finite element analysis provides a systematic theoretical basis for the new alveolar bone splitting technique and practical reference guide for clinical application.\u003c/p\u003e"},{"header":"2 Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1. Establishment of jaw model\u003c/h2\u003e\n \u003cp\u003eA volunteer with complete mandibular dentition and no history of periodontitis and jaw disease was selected to take the cone beam computed tomography (CBCT) (Carestream Health, Inc., Canada) of the jaw. After the CBCT images were stored in DICOM format, the jaw model of the mandibular posterior region was extracted by Mimics21.0 software (Materialise, Inc., Belgium) and saved in STL format. The jaw model was imported into GeomagicWrap2017 software (3DSystems, Inc., USA) to optimize, smooth and trim the model. The jaw model with cortical bone thickness of 1 mm and 2 mm was constructed by offset function, and the jaw model with alveolar crest width of 3 mm and 4 mm was constructed by resection function and saved in STP format.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2. Construction of surgical incision and bone expansion instrument model\u003c/h2\u003e\n \u003cp\u003eThe model data from step 2.1 were imported into Solidworks2022 software (Dassault Systemes, Inc., USA), and four incisions for new alveolar bone splitting technique were made on each group of jaw models (Fig. 1). The width of the incision at the bottom of the alveolar bone was set to 0.5 mm and 1.0 mm and 1.5 mm respectively. The bone expansion instrument model was constructed through the sketch function (Fig. 1). The length of the contact part between the instrument model and the jaw was set as 3 mm, 5 mm, 7 mm respectively. After that, the instrument model and the jaw model were assembled and saved in STEP format.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3. Setting of finite element analysis parameters\u003c/h2\u003e\n \u003cp\u003eThe model data from step 2.2 were imported into Workbench 22.0 software (Ansys, Inc., USA), and the transient structural analysis module was applied to enter the modulus of elasticity and Poisson\u0026apos;s ratio of each material and assign values (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). All materials in the experiment were set to be isotropic and homogeneous. A \u0026quot;Rough\u0026quot; connection was set between the instrument model and the cortical and cancellous bone, and a \u0026quot;Bonded\u0026quot; connection was set between the cortical and cancellous bone Tetrahedral grid elements were used to generate the mesh, and the final number of mesh elements and nodes was shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. The jaw model around the surgical incision was constrained, and a sagittal force was applied to the bone expansion instrument perpendicular to the surface of the instrument (Fig.\u0026nbsp;1), with the magnitude of the force increasing with time. The total degree of deformation, equivalent force and equivalent strain of each group of models reaching the ultimate yield state were finally solved, and the trend of the distribution of equivalent force and strain of each group was recorded, as well as the maximum force and the total degree of deformation in the ultimate yield state. Referring to the literature of other scholars [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e], in this study, 50 MPa was used as the ultimate shear strength of cortical bone, 10 MPa was used as the ultimate shear strength of cancellous bone, and 2% strain rate was used as the yield strain of cortical bone and cancellous bone. In this case, 10 locations were randomly selected at the top of the alveolar ridge of the jaw model, and the average value of their total degree of deformation was taken as the maximum displacement when the jaw model reached the ultimate yield state.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003ePhysical properties of materials used in the experiment\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterials\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModulus of elasticity (GPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePoisson\u0026apos;s ratio\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDensity (g/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCortical bone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDense cancellous bone (type I, II, III bone)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLoose cancellous bone (type IV bone)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.60\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStructural steel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e200.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.85\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eResults of finite element analysis of jaw models in each group\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"8\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAlveolar crest width (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAlveolar bone density\u003c/p\u003e\n \u003cp\u003e(type II、III、IV bone)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRoot incision width (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eInsertion depth of instrument model (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eElements\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaximum force (N)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaximum displacement (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e442517\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.65\u0026thinsp;\u0026plusmn;\u0026thinsp;0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e520959\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.44\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e431519\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.60\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIV\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e442517\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.88\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e442400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.76\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e442414\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.89\u0026thinsp;\u0026plusmn;\u0026thinsp;0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e434362\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.77\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e434962\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.56\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4. Statistical analysis\u003c/h2\u003e\n \u003cp\u003eData analysis and figure construction was performed using GraphPad Prism 6 (GraphPad, San Diego, USA). Values represent mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation (SD). Comparison among different groups was made by two-way analysis of variance (ANOVA). \u003cem\u003eP\u003c/em\u003e values\u0026thinsp;\u0026lt;\u0026thinsp;0.05 were considered statistically significant.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3 Results","content":"\u003cp\u003eThe experimental jaw model consisted of three main parts: external cortical bone, free cortical bone and cancellous bone. Considering the shear strength and yield strain of cortical bone and cancellous bone, in the cancellous bone model, the parts with an equivalent stress of 10 MPa or less were set in blue; in the cortical bone model, the parts with an equivalent stress of 50 MPa and 10 MPa or less were set in light blue and blue; and the parts with a strain rate of 2% or less were set in blue.\u003c/p\u003e\n\u003cp\u003eAmong the indicators that the jaw model reached the ultimate yield state was when the buccal and lingual cancellous bone at the root incision appeared to have a phase-continuous distribution of equivalent stresses that exceeded the ultimate shear strength of the cancellous bone and a significant distribution of equivalent strains that exceeded their yield strains at the cancellous bone on both sides. The experimental results were shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig. 2.\u003c/p\u003e\n\u003cp\u003eThere was no significant difference in the distribution characteristics of equivalent stress and strain in each part of each model. Taking M1 as an example, the results of the equivalent stress and equivalent strain distribution of its various parts were shown in Fig. 3. As could be seen from the figure, the equivalent stress and equivalent strain of the cancellous bone model were mainly concentrated in the cancellous bone region at the root-square incision, and the distribution range of the equivalent stress-strain was gradually expanded with the increase of the acting force. The equivalent stress-strain distribution of the cancellous bone on the lingual side was more extensive than that on the buccal side, while the equivalent stress-strain magnitude of the cancellous bone on the buccal side was higher than that on the lingual side. The equivalent strains exceeding the yield strain of the cancellous bone first appeared in the area of cancellous bone on both sides of the root-square incision, and gradually spread from the two sides to the middle as the value of the force increased.\u003c/p\u003e\n\u003cp\u003eThe equivalent stresses in the buccal free cortical bone first appeared in the lower 1/3 of the bone plate, and as the value of the force increased, the distribution of the equivalent stresses gradually approached to the lower edge of the buccal bone plate. The equivalent stresses in the lingual free cortical bone first appeared at the cutting angle on both sides of the bone plate, and as the value of the applied force increased, the equivalent stresses were gradually distributed all over the lower edge of the lingual plate, and also appeared in the lower 1/3 of the lingual bone plate as well as at the top of the alveolar crest. The equivalent stress distribution in the external cortical bone was located at the lower edge of the surgical incision at the buccal and lingual lateral bone plates. The equivalent strains of free and external cortical bone did not change significantly and were much less than 2% in all groups of models. In addition, M3 did not show significant equivalent stress-strain changes in free cortical bone and external cortical bone because the maximum force was too small.\u003c/p\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThe clinical cases with insufficient horizontal bone for implant restorative treatment must undergo bone augmentation surgery prior to implantation. In addition to classical guided bone regeneration and autologous bone grafting, alveolar bone splitting, which can effectively increase the horizontal alveolar bone width, is an ideal option [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. However, when the alveolar bone is heavily resorbed, the brittleness of the buccal bone plate increases, especially the buccal alveolar bone in the mandibular posterior region, which greatly increases the risk of fracture of the bone plate during bone expansion by alveolar bone splitting. The risk of alveolar bone splitting complications can be reduced by preoperatively predicting the stress-strain distribution of the bone plate during expansion[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In order to predict the risk of bone plate fracture for the new alveolar bone splitting technique, an in-depth understanding of the expansion behaviour of the buccal bone plate and insight into its fracture mechanism is essential. In this context, finite element analysis can provide sufficient tools to analyze the principles of bone plate fracture in the new alveolar bone splitting technique.\u003c/p\u003e \u003cp\u003eStudies have shown that retaining at least 3 mm of alveolar bone width and a minimum vertical bone height of 10 mm is necessary to provide sufficient buccal and lingual cortical and cancellous bone volume to maintain adequate blood supply to the bone adjacent to the implant, thus ensuring the success of alveolar bone splitting [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Based on this, considering that fine-diameter implants can be selected for implant restorations in clinical work when facing clinical patients with a residual bone width of up to 5 mm, the jaw bone models with 3 mm alveolar crest width and 4 mm alveolar crest width were constructed for finite element analysis in this study. Theoretically, after removing 1 mm of cortical bone, the width of the cancellous bone at the root incision of the 4 mm jaw model is thicker compared to that of the 3 mm jaw model, and thus it can withstand a higher external force before reaching the ultimate yield state. The experimental results shown that the maximum force of the 4 mm jaw model was 90 N, while the maximum force of the 3 mm jaw model was 25 N. Unexpectedly, the distribution range of equivalent stress and equivalent strain in the 4 mm jaw model was wider than that of the 3 mm jaw model under higher forces, which meant that the area exceeding the shear strength and yield strain was larger, and the range of plastic deformation was wider in the 4 mm jaw model. This means that the 4 mm jaw model has a larger area above the shear strength and yield strain, and a wider range of plastic deformation. Therefore, it was easier for the 4 mm jaw model to reach the ultimate yield state. The results of the total deformation degree also proved this point. In the ultimate yielding state, the displacement of the 4 mm jaw model at the top of the alveolar ridge was 0.4388\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1373 mm, which was less than that of the 3 mm jaw model (0.6526\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0908 mm). Besides, it could be found that the equivalent stress and equivalent strain distributions were inconsistent when the jaw model was in the ultimate yielding state. For example, when the 3 mm jaw model was in the ultimate yielding state, the buccal and lingual cancellous bone at the root incision had already experienced equivalent stress continuity, but the equivalent strains were still distributed only in the superficial layers of the buccal and lingual cancellous bone; when the equivalent stress at the edge of the free cortical bone had already exceeded the shear strength, the corresponding equivalent strain exceeding the yield strength was not observed, which may be related to the phenomenon of \"hysteresis\" [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] in osteo-viscoelasticity, where the strain response lags behind the stress. It is worth noting that during bone expansion, the stresses and strains were more concentrated in the cancellous bone and external cortical bone located in the region of the root incision, as well as in the lower 1/3 of the buccal lamellae of the free cortical bone, which suggests that in some cases of thin cortical bone, as the force increases, the buccal lamellae breakage may be located in the lower 1/3 of the lamellae, in addition to occurring in the root incision location.\u003c/p\u003e \u003cp\u003eAs mentioned previously, thin cortical bone has an effect on the fracture location of bone plate. Duttenhoefer et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] also found that the fracture lines were mostly located in the weakest area of the bone plate locally through the alveolar bone splitting experiments on human jawbone specimens. Based on this, this study constructed jaw bone models with four bone densities according to the Lekholm-Zarb bone density classification, but only finite element analyses were carried out on the type II, III and IV bone jaw bone models in consideration of practical clinical applications. The maximum forces in the type II, III, and IV bone jaw models differed considerably after the removal of the underlying cortical bone. In the type II bone model, only a few cancellous bones remained to maintain the jaw morphology after the removal of the 2 mm thickness of cortical bone, and the type II bone model reached the ultimate yield state at a very low force, taking into account the lower shear strength of cancellous bone. At the root incision, the difference between the type II bone model and the type III bone model only lay in the thickness of the cancellous bone, so the equivalent stress-strain distribution characteristics of the two were not significantly different. Because of the low maximum force, the type II bone model did not show significant equivalent stress-strain distribution in the free cortical bone and external cortical bone. In addition, the difference between the type III and IV bone models is only reflected in the physical property parameters of the internal cancellous bone, so there is no significant difference in the equivalent stress-strain distribution characteristics between the two models. The results of the total deformation of the jaw models with different alveolar bone densities showed that the maximum displacement was the lowest in the type II bone model, which may be related to the width of the remaining cancellous bone at its root incision. There was a significant difference in the maximum displacement between the type III and IV bone models, indicating that there is an effect of different physical parameters of cancellous bone on the degree of deformation, which may be related to the fact that cancellous bone is a highly functionally compliant tissue. Numerous studies have shown that the mechanical properties of cancellous bone in different parts of the human body vary greatly, and this variation is mainly due to the fact that cancellous bone has different types of microstructures, and therefore its biomechanical properties are very complex. The results of this study suggest that lax cancellous bone may possess more excellent plastic deformation ability than dense cancellous bone.\u003c/p\u003e \u003cp\u003eThe improvement of the new alveolar bone splitting technique lies in the new root incision between the vertical incisions on both sides. At this position, when the cortical bone on the surface of the buccal bone plate is removed, only the cancellous bone is retained to maintain the continuity of the bone plate. The area of cancellous bone uncovered by cortical bone varies according to the width of the root incision, which is certainly a critical factor in alveolar bone splitting, which relies primarily on the ability of cancellous bone to deform plastically for bone expansion. Based on this, this study constructed 0.5 mm incision, 1.0 mm incision, and 1.5 mm incision jaw models to investigate whether there is any effect on the bone augmentation effect of the new alveolar bone splitting technique. The maximum force of the three jaw models was 25 N. It was found that there may not be a clear relationship between the width of the root incision and the maximum force. The results of equivalent stress-strain distribution characteristics showed that the area of cancellous bone without cortical bone coverage increased with increasing incision width, and the wider incision model had a wider range of equivalent stress-strain distribution and higher equivalent stress and equivalent strain magnitudes under the same value of acting force. It is noteworthy that the maximum displacement of each jaw model gradually increased with the increase of the root incision width after reaching the ultimate yield state, which implies that the larger the area of the cancellous bone region without cortical bone coverage, the greater the plastic deformation capacity under the same cancellous bone physical property parameters. The increase of the width of the surgical incision also resulted in a decrease in the area of cortical bone in the buccal bone plate. However, there was no significant difference in the equivalent stress distribution and size of the cortical bone in the 0.5 mm incision, 1.0 mm incision, and 1.5 mm incision jaw models, indicating that the stress concentration area of the buccal bone plate was relatively fixed during bone expansion, which may not be related to the remaining area of cortical bone.\u003c/p\u003e \u003cp\u003eThe bone expansion principle of the new alveolar bone splitting is to prepare the root cortical bone incision and make use of the adaptability and plasticity of cancellous bone to reduce the risk of cortical bone fracture. During bone expansion, the buccal bone plate is rotated by the acting force of the bone expansion instrument, using the inner edge of the root incision as the fulcrum. If the distance between the bone expansion instrument and the root incision is farther, which corresponds to the longer power arm, the greater the stress at the root incision under the same force conditions. Based on this, the jaw models of 3 mm depth, 5 mm depth and 7 mm depth were constructed to explore the effect of new alveolar bone splitting technique with different depth of bone expansion instruments. The experimental results demonstrated that there was no significant difference in the equivalent stress-strain distribution characteristics of the 3 mm depth, 5 mm depth, and 7 mm depth jaw models, but the magnitude of the equivalent stresses in each jaw model under the same force gradually decreased with the increase of the insertion depth of the instrumented model, which was consistent with the previous hypothesis. There was no difference in the maximum force in the jaw models with different instrument insertion depths, indicating that the distance between the instrumented model and the root incision was not sufficient in the jaw models to affect a change in the value of the force that would bring the cancellous bone to its ultimate yield state. However, the maximum displacement of the jaw models with different instrument insertion depths decreased with increasing insertion depth, indicating that the deeper the insertion depth, the larger the contact area between the instrumented model and the cancellous bone, and the smaller the pressure borne by the cancellous bone per unit area under the same acting force, i.e., the lower the stress. In a low stress state, the ability of cancellous bone to deform plastically may be limited.\u003c/p\u003e \u003cp\u003eIt is very difficult to map the bone expansion mechanism and stress distribution of the new alveolar bone splitting technique in clinical practice. Hence, for exploring the theoretical basis of the technique, biomechanical analysis tools are needed. To date, finite element analysis is a commonly used tool in mechanics and biomechanics virtual analysis of mechanical strength and stress shielding [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], among others, and its emergence has provided new ideas and solutions to study the bone plate fracture mechanism of alveolar bone splitting. In this experiment, the influence of four factors, namely, alveolar crest width, alveolar bone density, surgical incision width, and instrument insertion depth, on the bone augmentation effect of the new alveolar bone splitting technique was investigated by means of finite element analysis, and the corresponding results were obtained. Nevertheless, there are still some limitations and need to be improved in the course of this study, and the shortcomings are as follows.\u003c/p\u003e \u003cp\u003eThe parameter settings of the research model are not reasonable enough. It is well known that cortical bone and cancellous bone have biomechanical properties such as anisotropy and non-homogeneity. However, in this study, the cortical bone and cancellous bone were set to be isotropic and homogeneous in order to facilitate the calculation. The change in material properties will undoubtedly affect the accuracy of the experimental results. Differential material assignment can be considered through the grey value of the CBCT image of each grid element in the model to obtain an anisotropic, non-homogeneous jaw model.\u003c/p\u003e \u003cp\u003eThe research on the basis of system theory was not thorough enough. Although this study investigated the effects of four different factors on the new alveolar bone splitting technique to explore the theoretical basis of the technique, it was not thorough enough. Mainly reflected in: (1) Alveolar bone splitting, as a bone augmentation method, is also affected by its subsequent treatment process, such as implant placement, which also extrudes the buccal bone plate and further expands the width of alveolar bone. Therefore, it can be considered to add the implant implantation process to the subsequent research process, so as to analyze the influence of the new alveolar bone splitting on the bone augmentation effect of implant restorations in a more complete way. (2) In this experiment, the study subjects were various jaw models that underwent only the new alveolar bone splitting procedure, and the control group was missing. In order to reflect the changes in the improved alveolar bone splitting technique, finite element analysis of the traditional alveolar bone splitting technique could be added to explore the shortcomings of the new alveolar bone splitting technique through a comparative study so that the technique can be further improved. (3) There are more variables in alveolar bone splitting than the four factors studied in this experiment, such as the depth of the surgical incision, the thickness of the bone plate at the base of the jaw, etc., and the corresponding jaw models can be constructed for the finite element analysis in order to improve the theoretical basis of this technique.\u003c/p\u003e \u003cp\u003eThere is a discrepancy between finite element theoretical analysis and real practice. Simple jaw models can accurately predict the timing and location of bone plate fracture through finite element analysis, but the human jaw is not only a biomaterial with complex mechanical properties, but also a biological organ that carries mechanical loads, and the growth and development of cells and metabolism will lead to changes in the quantity and quality of the jawbone, which will affect its complex mechanical properties. Furthermore, the thicknesses of cortical bone and cancellous bone in the various jaw models in this study were relatively fixed, while the thicknesses of cortical bone and cancellous bone in human jaws in real life are varied and not uniform. Although the material parameters and deformation conditions are set reasonably, further basic research is still needed to prove the accuracy of the finite element modelling theory, and only by combining the theory with practice can the theoretical basis of the technique be truly formed.\u003c/p\u003e"},{"header":"5 Conclusion","content":"\u003cp\u003eThis experiment investigated the finite element analysis of a new alveolar bone splitting technique under four different factors. The results showed that, among the jaw models with different alveolar crest widths, the wider the alveolar crest, the higher the maximum force to reach the ultimate yield state, but the smaller the maximum displacement at the alveolar crest at that state; among the jaw models with different alveolar bone densities, the maximal force and the maximal displacement to reach the ultimate yield state of the jaw model of type II bone were the smallest and the plastic deformation ability of the jaw model of type IV bone was more excellent because of its loose cancellous bone; among the jaw models with different root incision widths, the wider the root incision, the larger the area of cancellous bone without cortical bone coverage, and the larger the maximum displacement at ultimate yield; among the jaw models with different insertion depths of bone expansion instruments, the deeper the insertion of the instruments, the lower the stresses, and the lower the maximum displacement at ultimate yield under the same force. Regardless of the type of jaw model, the main concentration of stress and strain was at the root incision, followed by the lower 1/3 of the buccal bone plate, and with the increase of the value of the force, the lower edge of the instrumented model also showed a concentration of stress.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors state that they have no potential competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Scientific Research Project of Jilin Provincial Department of\u0026nbsp;Education, China (Grant No. JJKH20231291KJ), the Science and Technology Development Project of Jilin Provincial Department of Science and Technology, China\u0026nbsp;(Grant No. 20230203065SF).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eYe Tian led the writing and did most of the experiments. Shunli Chu critically revised the manuscript. Xiaolu Shi, Shaobo Zhai and Yang Liu analyzed the experimental data. Zheng Yang and Yuchuan Wu contributed to charting. Every author gave final approval and agreed to be accountable for all aspects of the work.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe thank Liwen Bianji (Edanz) (www.liwenbianji.cn) for editing the language of a draft of this manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eStarch-Jensen T, Becktor JP: \u003cstrong\u003eMaxillary Alveolar Ridge Expansion with Split-Crest Technique Compared with Lateral Ridge Augmentation with Autogenous Bone Block Graft: a Systematic Review\u003c/strong\u003e. \u003cem\u003eJ Oral Maxillofac Res \u003c/em\u003e2019, \u003cstrong\u003e10\u003c/strong\u003e(4):e2.\u003c/li\u003e\n\u003cli\u003eTan WL, Wong TL, Wong MC, Lang NP: \u003cstrong\u003eA systematic review of post-extractional alveolar hard and soft tissue dimensional changes in humans\u003c/strong\u003e. \u003cem\u003eClin Oral Implants Res \u003c/em\u003e2012, 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technique\u003c/strong\u003e. \u003cem\u003eJ Stomatol Oral Maxillofac Surg \u003c/em\u003e2021, \u003cstrong\u003e122\u003c/strong\u003e(6):578-582.\u003c/li\u003e\n\u003cli\u003eTurner CH, Wang T, Burr DB: \u003cstrong\u003eShear strength and fatigue properties of human cortical bone determined from pure shear tests\u003c/strong\u003e. \u003cem\u003eCalcif Tissue Int \u003c/em\u003e2001, \u003cstrong\u003e69\u003c/strong\u003e(6):373-378.\u003c/li\u003e\n\u003cli\u003eBrown AD, Rafaels KA, Weerasooriya T: \u003cstrong\u003eShear behavior of human skull bones\u003c/strong\u003e. \u003cem\u003eJournal of the mechanical behavior of biomedical materials \u003c/em\u003e2021, \u003cstrong\u003e116\u003c/strong\u003e:104343.\u003c/li\u003e\n\u003cli\u003eMcElhaney JH, Fogle JL, Melvin JW, Haynes RR, Roberts VL, Alem NM: \u003cstrong\u003eMechanical properties on cranial bone\u003c/strong\u003e. \u003cem\u003eJ Biomech \u003c/em\u003e1970, 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\u003c/em\u003e2024, \u003cstrong\u003e28\u003c/strong\u003e(1):71.\u003c/li\u003e\n\u003cli\u003eLin Y, Li G, Xu T, Zhou X, Luo F: \u003cstrong\u003eThe efficacy of alveolar ridge split on implants: a systematic review and meta-analysis\u003c/strong\u003e. \u003cem\u003eBMC oral health \u003c/em\u003e2023, \u003cstrong\u003e23\u003c/strong\u003e(1):894.\u003c/li\u003e\n\u003cli\u003eJha N, Choi EH, Kaushik NK, Ryu JJ: \u003cstrong\u003eTypes of devices used in ridge split procedure for alveolar bone expansion: A systematic review\u003c/strong\u003e. \u003cem\u003ePloS one \u003c/em\u003e2017, \u003cstrong\u003e12\u003c/strong\u003e(7):e0180342.\u003c/li\u003e\n\u003cli\u003eWu B, Wu Y, Liu M, Liu J, Jiang D, Ma S, Yan B, Lu Y: \u003cstrong\u003eMechanical Behavior of Human Cancellous Bone in Alveolar Bone under Uniaxial Compression and Creep Tests\u003c/strong\u003e. \u003cem\u003eMaterials (Basel, Switzerland) \u003c/em\u003e2022, \u003cstrong\u003e15\u003c/strong\u003e(17).\u003c/li\u003e\n\u003cli\u003eDuttenhoefer F, Varga P, Jenni D, Gr\u0026uuml;nwald L, Thiemann L, Gueorguiev B, Stricker A: \u003cstrong\u003eThe Alveolar Ridge Splitting Technique on Maxillae: A Biomechanical Human Cadaveric Investigation\u003c/strong\u003e. \u003cem\u003eBioMed research international \u003c/em\u003e2020, \u003cstrong\u003e2020\u003c/strong\u003e:8894471.\u003c/li\u003e\n\u003cli\u003eFalcinelli C, Valente F, Vasta M, Traini T: \u003cstrong\u003eFinite element analysis in implant dentistry: State of the art and future directions\u003c/strong\u003e. \u003cem\u003eDental materials : official publication of the Academy of Dental Materials \u003c/em\u003e2023, \u003cstrong\u003e39\u003c/strong\u003e(6):539-556.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"alveolar bone splitting, finite element analysis, biomechanics, bone augmentation, mandible, oral implants","lastPublishedDoi":"10.21203/rs.3.rs-4323987/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4323987/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground:\u003c/strong\u003e Finite element analysis was used to predict the risk of bone plate fracture and the expected bone augmentation effect of a new alveolar bone splitting technique in the mandibular posterior region for different alveolar crest widths, different alveolar bone densities, different root incision widths, and different insertion depths of bone expansion instrumentation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods: \u003c/strong\u003eThe jaw models of the mandibular posterior region were constructed by computer-aided software and surgical incisions and bone expansion instruments were prepared on the models, after which the alveolar bone splitting procedure was simulated by finite element analysis software, and the equivalent stress-strain distribution characteristics of the jaw models of each group, as well as the maximal force and the maximal displacement of the bone plate when it was fractured, were recorded.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e The distribution of equivalent stress and strain was mainly concentrated in the cancellous bone area at the root incision and the lower 1/3 of the buccal cortical bone plate, and there was no significant difference in the stress-strain distribution characteristics of the jaw models of each group. The wider of the alveolar crest, the higher the force required to fracture the bone plate, but the smaller the maximum displacement; the plastic deformation capacity of type IV bone jaws was more excellent; the wider the width of the root incision, the shallower the depth of instrument insertion, and the larger the maximum displacement.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusion: \u003c/strong\u003eFinite element analysis can effectively simulate the surgical criticality index of the new alveolar bone splitting procedure. Alveolar crest width, alveolar bone density, root incision width, and instrument insertion depth had a clear correlation with the maximum displacement of the bone plate at fracture. The alveolar crest width and alveolar bone density also had a significant effect on the maximum force required to fracture the bone plate.\u003c/p\u003e","manuscriptTitle":"Finite element analysis of a new alveolar bone splitting technique in the mandibular posterior region","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-15 14:36:29","doi":"10.21203/rs.3.rs-4323987/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-09-11T10:07:12+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-02T21:36:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"32582459599056629598371575409651118016","date":"2024-07-28T01:36:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-24T15:47:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"541587655153043553503614565636056277","date":"2024-07-23T12:58:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"86585216636767956711279688625337087942","date":"2024-07-22T23:52:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87304318891370621473750523406860572494","date":"2024-07-22T14:58:59+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-03T15:01:54+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-20T02:59:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"182851843379890038323584414563095952984","date":"2024-05-15T01:41:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"238206550316956569713246606173522233193","date":"2024-05-14T22:40:41+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-05-14T12:37:33+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-05-07T05:26:04+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-06T12:24:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-06T12:24:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Oral Health","date":"2024-04-25T11:59:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"fa69e1d9-be3a-4e72-9ecb-9a5239324931","owner":[],"postedDate":"May 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-03-10T17:09:29+00:00","versionOfRecord":{"articleIdentity":"rs-4323987","link":"https://doi.org/10.1186/s12903-025-05559-5","journal":{"identity":"bmc-oral-health","isVorOnly":false,"title":"BMC Oral Health"},"publishedOn":"2025-03-08 15:57:19","publishedOnDateReadable":"March 8th, 2025"},"versionCreatedAt":"2024-05-15 14:36:29","video":"","vorDoi":"10.1186/s12903-025-05559-5","vorDoiUrl":"https://doi.org/10.1186/s12903-025-05559-5","workflowStages":[]},"version":"v1","identity":"rs-4323987","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4323987","identity":"rs-4323987","version":["v1"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}