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.