The aim of this study was to evaluate the stress distribution in implants of regular platforms and of wide diameter with different sizes of hexagon by the 3-dimensional finite element method. We used simulated 3-dimensional models with the aid of Solidworks 2006 and Rhinoceros 4.0 software for the design of the implant and abutment and the InVesalius software for the design of the bone. Each model represented a block of bone from the mandibular molar region with an implant 10 mm in length and different diameters. Model A was an implant 3.75 mm/regular hexagon, model B was an implant 5.00 mm/regular hexagon, and model C was an implant 5.00 mm/expanded hexagon. A load of 200 N was applied in the axial, lateral, and oblique directions. At implant, applying the load (axial, lateral, and oblique), the 3 models presented stress concentration at the threads in the cervical and middle regions, and the stress was higher for model A. At the abutment, models A and B showed a similar stress distribution, concentrated at the cervical and middle third; model C showed the highest stresses. On the cortical bone, the stress was concentrated at the cervical region for the 3 models and was higher for model A. In the trabecular bone, the stresses were less intense and concentrated around the implant body, and were more intense for model A. Among the models of wide diameter (models B and C), model B (implant 5.00 mm/regular hexagon) was more favorable with regard to distribution of stresses. Model A (implant 3.75 mm/regular hexagon) showed the largest areas and the most intense stress, and model B (implant 5.00 mm/regular hexagon) showed a more favorable stress distribution. The highest stresses were observed in the application of lateral load.
Introduction
Since the introduction of the Branemark system, the coronal aspect of the hexagon has gradually transformed to promote a better adaptation and an antirotational mechanism.1 The design of the original external hexagonal was designed as a gear mechanism and transfer of rotational torque to hold the implant during the surgical installation in the bone.2,3 The hexagon had a height of 0.7 mm to allow for adjustment during installation of the implant.2 Initially, the use of osseointegrated dental implants had been proposed only in fully edentulous patients. Gradually, that planning was expanded for partially edentulous patients and ultimately for the replacement of individual components. Prosthetic tooth implant solutions were the last to be developed by many implant systems.4,5 From that moment on, a significant number of clinical complications began to emerge.2,6
The increasing use of external hex implants resulted in significant complications, mostly related to loosening or fracture of the abutment screw, mainly in unitary prostheses.7–9 Thus, to minimize these difficulties, the external hexagon, transmucosal connections, and retaining screws underwent numerous modifications2 to provide a mechanism for indexing and antirotational restorations.10,11
A key factor for success or failure of dental implants is the way the tension is transferred to the surrounding bone. The overload of the implant may exceed the physiological limits and cause failures in rehabilitation or even the loss of osseointegration.7,12 Studies on the biology of the bone suggest that the overload in the implant can lead to their failure.13,14 When this load is greater than 2000 to 3000 microstrain, large deformations occur in the peri-implant bone,15,16 exceeding the physiological tolerance of the bone and possibly causing microfractures in the bone-implant interface.1,17 Therefore, it is essential to improve the chewing load distribution through the prostheses and from that to the implants and to the support bone.17,18
Some authors19,20 have suggested that the height of the hexagon could contribute to the stability of the union with the screw, and an optimal height could protect the screw from the effects of twist by the dispersion of forces to other components. Ohrnell et al21 recommended that the external connection of the hexagon should have at least 1.2 mm in height, to provide lateral and rotational stability, particularly in single restorations. For Weinberg20 and Ohrnell et al,21 an external geometry is particularly vulnerable because of the limited gear with its external components and the presence of a short fulcrum point (small platform) when tilted forces are applied.
On the world market, different companies offer options for different sizes of hex implants. Therefore, to obtain more data about the design of implants, this study proposes to evaluate the stress distribution in implants of regular platforms and of large diameter with different sizes of hexagon, using the 3-dimensional (3D) finite element method.
Materials and Methods
For this study, 3D models (Table 1) were fabricated, represented by a section of jawbone type III, composed of trabecular bone in the center surrounded by 1 mm of cortical bone in the region corresponding to the mandibular molar with an implant of associated prosthetic component.
The geometry of trabecular and cortical bone was obtained from the recomposition of a computerized tomography cross-molar region, made using the InVesalius software (CTI, São Paulo, Brazil), which allows the creation of virtual 3D models from cross-sectional tomography. Subsequently, the image was exported to the Rhinoceros 4.0 software (NURBS Modeling for Windows, Seattle, Wa) for geometry simplification and refinement of the design.
The geometry of the implants was obtained from the Connection system (Master Screw, Conexão Sistemas de Prótese Ltda, São Paulo, Brazil) of 10 mm in length and its corresponding component prosthetic UCLA (abutment). All implants and components had their geometries simplified through the SolidWorks 2006 (SolidWorks Corp, Concord, Mass) and Rhinoceros 4.0 software (Table 2).
The set of abutment-implant was inserted into the bony portion of the bone block in a centralized location. After the fabrication of the models, the geometries were exported to the FEMAP 10.0 finite element software (Siemens PLM Software Inc, Santa Ana, Calif) in STEP format. Then, finite element meshes with parabolic solid elements were generated.
The corresponding mechanical properties of each material, Young's modulus and Poisson's ratio, were assigned to the mesh using the values found in the literature22 (Table 3). All materials were considered isotropic, linearly elastic, and homogeneous. The contacts between the prosthetic component/screw, implant/cortical bone, implant/trabecular bone, cortical/trabecular bone, and implant/screw were assumed to be bonded. Boundary conditions were established as prescribed in the 3 axes (x, y, and z) on the side surfaces of cortical and trabecular bone, with the rest of the set free from restrictions. The axial load applied in the model was 200 N, based on the literature,23 and was applied to the surface of the abutment. The load was always divided into 4 points, in the form of force per area, in an area of approximately 0.17 mm2.
The analysis was then generated in the finite element software (FEMAP 10.0) and exported to the NeiNastran version 9.2 calculation software (Noran Engineering, Inc, Westminster, Calif) running on a workstation (Sun Microsystems Inc, São Paulo, Brazil). The results were then imported back into the FEMAP 10.0 software for viewing and postprocessing of the maps of von Mises stress and maximum principal stress maps.
Results
Von Mises stress maps
In the general map, we observed a low stress concentration for the axial load for the 3 models. In the application, loads and lateral oblique stress concentrated on the prosthetic component and the threads of the implant by dissipating a larger area and greater stress intensity on all models. In comparative analysis, model C had the highest stress (under the 3 loads), and this was located mainly in the narrowing of UCLA.
In the von Mises stress maps of the implant, the application of the axial load showed that tensions were low for all 3 models. In applying the oblique and lateral loads, the 3 models presented stress concentration at the level of the platform and the threads in the cervical and middle third, at 68.7–34.38 MPa. The stress on model A was concentrated on the first 3 threads of the implant, and in models B and C, strains were more evenly distributed. Comparing the models, it was observed that the strain was distributed by a larger area, respectively, in models C, A, and B and that the application side showed lower stress intensity than the opposite side. The models under side load showed higher concentrated areas of stress.
The stress maps of the abutment in the application of axial load in the 3 models showed low concentrations of stress, being slightly higher at the middle third and upper abutment level, reaching 48.75 MPa. In model C, this region presented the highest stress in the region of narrowing of UCLA, in the range of 52.81–24.38 MPa. In the application of oblique and lateral loads, the models showed similar distribution patterns, with stress concentrations in the middle third and upper abutment. In model C, besides these regions, stress also was concentrated on the area of narrowing UCLA.
Comparing the 3 models showed that the largest areas of stress concentration were under the load side and that the stress was higher for model C under axial, lateral, and oblique load.
Maximum principal stress
In a sagittal section cut of cortical and trabecular bone (Figures 1–3), stress concentration was observed in the application of axial load at the cervical and the first implant thread, where the 3 models presented similarity (Figure 1). In the application of oblique and lateral loading, the 3 models had areas of stress concentration in the cervical region, showing areas of tensile stress of 15 MPa. Model A had the largest areas of tension in both the surface and in the thickness of cortical bone. In comparative analysis, the largest areas were observed in the application of lateral load for the 3 models. The range of areas of compression were observed on the opposite side of the application of load and tensile areas on the opposite side (Figures 1–3).
Figure 1. Maximum principal stress of cortical and trabecular bone, axial load. Figure 2. Maximum principal stress of cortical and trabecular bone, oblique load. Figure 3. Maximum principal stress of cortical and trabecular bone, lateral load.
Figure 1. Maximum principal stress of cortical and trabecular bone, axial load. Figure 2. Maximum principal stress of cortical and trabecular bone, oblique load. Figure 3. Maximum principal stress of cortical and trabecular bone, lateral load.
In an occlusal view (Figures 4–6), with the application of axial load, the models showed low tension, and this was concentrated in the area corresponding to the coronal region of the implant. In the application of oblique and lateral load, the models showed similar patterns of stress distribution, and the tensile stresses were located on the side of the load application and the areas of compression on the opposite side. A comparative analysis showed that model A presented the largest areas of tension for all load applications and that the 3 models showed the highest levels of compressive and tensile stress with side loading.
Figure 4. Maximum principal stress of cortical bone (occlusal view), axial load. Figure 5. Maximum principal stress of cortical bone (occlusal view), oblique load. Figure 6. Maximum principal stress of cortical bone (occlusal view), lateral load.
Figure 4. Maximum principal stress of cortical bone (occlusal view), axial load. Figure 5. Maximum principal stress of cortical bone (occlusal view), oblique load. Figure 6. Maximum principal stress of cortical bone (occlusal view), lateral load.
On the maps of maximum principal stress of the trabecular bone (Figures 7–9) for all load applications, tensions were located around the threads of the implant, and we observed a larger area with the highest voltages for model A, model B, and model C, respectively, and values were in the range of 1.5–0.5 MPa. For all 3 models, the highest stress intensity was located at the platform level of the implant. The largest areas of tensile stress were observed in the 3 models in the application of lateral load.
Figure 7. Maximum principal stress of trabecular bone, axial load. Figure 8. Maximum principal stress of trabecular bone, oblique load. Figure 9. Maximum principal stress of trabecular bone, lateral load.
Figure 7. Maximum principal stress of trabecular bone, axial load. Figure 8. Maximum principal stress of trabecular bone, oblique load. Figure 9. Maximum principal stress of trabecular bone, lateral load.
In general, taking into account the 3 applied forces, a lower compressive stress and tension were observed in a smaller area in the models of large diameter in both the cortical bone and trabecular bone.
Discussion
Analyzing the stress maps of the abutment in all applications of load, there was a greater area of high stress intensity for model C, unlike other models. The stress was concentrated in the area of narrowing of UCLA, and this is probably due to the width of the hexagon being greater than the other models, which reduced the settlement area on the platform, decreasing the thickness of the UCLA and thus producing a higher stress concentration. This was explained by Bidez and Misch,24 who reported that the magnitude of stress is dependent on 2 variables: the magnitude of force and the area over which the force is dissipated. Therefore, a smaller area would lead to greater stress concentration.
The stress in model A was located in the first thread of the implant in the oblique load on the side with the largest areas of stress intensity, which is reflected in cortical areas showing higher tensile (red areas) and shear, as observed in other studies and theoretical analysis.17,19,24 As for models B and C, both had a better layout with smaller areas of compression and tension. According to Bidez and Misch,24 compression force tends to maintain the integrity of the bone-implant interface, while the tensile forces tend to separate the interface, being the most destructive.
According to Martin et al,25 on the cortical bone, the maximum stress is higher in compression (170 MPa) than tensile stress (100 MPa). Furthermore, the resistance of trabecular bone is the same in compression and tensile stress, being approximately 2–5 MPa. Thus, considering the citations of these authors, the values obtained in this study (0–1.5 MPa) are compatible with the values of these studies and appear to be within physiological limits.
Comparing models B and C, model C generated a greater area of tension because the settlement area of the abutment was lower, allowing a greater displacement of the last, transferring tension to the surrounding bone (cortical and trabecular). On trabecular bone, the stresses were low compared with that of cortical bone. It is known that cortical bone has a higher elastic modulus and therefore a lower deformation, concentrating higher stress. On the other hand, the trabecular bone, because it has a smaller Young's modulus, concentrated less stress around the implant body,24 which was verified in the results of this study. However, the stress areas were higher in model A because of a smaller area (diameter) for the stress distribution. Between models B and C, model C showed larger stress areas probably due to the difference in the diameter of the hexagon.
In the models analyzed, it was observed that the axial load presented a lower stress concentration; with the application of oblique and lateral loads, the models showed higher stress concentrations, which is in agreement with studies that reported that external hexagon implants are vulnerable to oblique and lateral loads.19,20
The results of the present study are significant since it was demonstrated that the higher the hexagon width in relation to the implant platform, the higher the stress transferred to the bone tissue. Clinically, the insertion of implants with large diameter and smaller hexagon may be more favorable since they allow fitting of the prosthetic component to a larger area of the implant platform. It also allows for the platform-switching technique when abutments with smaller diameter are used (the hexagon dimension is similar for regular- and large-diameter implants).
Conclusion
Based on the methodology, the following conclusions were made:
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Among the models of wide diameter (models B and C), model B was more favorable in the distribution of stresses.
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Model A (implant 3.75 mm/regular hexagon) showed the largest areas and the most intense stress, and model B (implant 5.0 mm/regular hexagon) showed a more favorable stress distribution.
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The highest tensions were observed in the application of lateral load.
