Zentrum für Zahn-, Mundund Kieferheilkunde

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1 Numerical Investigations On The Mechanical Behaviour Of The Novel Bar Sys tem SFI-Bar By Cendres+Métaux Report to the company CENDRES+MÉTAUX SA Bözingenstrasse 122 CH-2501 Biel/Bienne Dipl.-Math. Ludger Keilig1,2 Professor Dr.rer.nat. Christoph Bourauel1 Professor Dr.med.dent. Helmut Stark2 1 2 Stiftungsprofessur für Oralmedizinische Technologie und Abteilung für Zahnärztliche Propädeutik - Experimentelle Zahnheilkunde Zentrum für Zahn-, Mund- und Kieferheilkunde Welschnonnenstrasse 17 D Bonn -1-

2 Table of contents 1 Introduction Material Two Implant Solution ( 2I ) Two Implant Solution with parallel implant divergency ( 2I-LL ) Two Implant Solution with opposing implant divergency ( 2I-LR ) Four Implant Solution ( 4I-Side and 4I-All ) Inclination of the loading by 15 degrees in the model 2I-LR Survey of generated FE models Methods Results: Behaviour of the Bar System and the Implant Attachment Simulation 2I (500 N loading of the bar) Simulation 2I-LL (500 N loading of the bar) Simulation 2I-LR (500 N loading of the bar) Simulation 4I-Side (500 N loading per side-bar) Simulation 4I-All (500 N loading per bar) Inclination of the loading by 15 degrees in model 2I-LR Results: Loading of the Implants in the Technovit Bed Simulation 2I (500 N loading of the bar) Simulation 2I-LL (500 N loading of the bar) Simulation 2I-LR (500 N loading of the bar) Simulation 4I-Side (500 N loading of each buccal bar) Simulation 4I-All (500 N loading of each bar) Simulation 2I-LR-B Conclusions and Discussion

3 1 Introduction Employing numerical simulations the mechanical behaviour of the bar-system SFI-Bar (Cendres+Métaux) mounted on idealised implants was to be analysed. The overall aim of the study was to estimate the biomechanical fitness of the whole system aid of the numerical res ults. Within the scope of this problem two major aspects were to be discussed: On the one hand to analyse the implant stress due to loading of the bar, on the other hand to assess the stability and the critical points in the design of the bar system. The following situations were analysed to reach this goal: Two Implant Solution : The anchorage of the bar on two implants was simulated. A loading of the bar with vertical forces of up to 500 N was realised using a strut. Four Implant Solution with loading of the side bars: The anchorage of three bars on four implants following the course of the jaw bone was analysed. With the aid of a strut the two side bars were loaded with a total force of 1000 N, resulting in a 500 N load of each side bar. Four Implant Solution with loading of all bars: The anchorage of three bars on four implants was investigated. All bars were loaded with a total force of up to 1500 N, corres ponding to a force of 500 N per bar. Additionally, the influence of implant divergencies on the loading behaviour was analysed. For that purpose the implants together with the mounted bar were tilted by an angle of 15 and subsequently loaded with the same forces. A further misalignment of the implants con sisted of a simultaneous tilt in two planes of space. This was a simultaneous tilt of the im plants towards each other together with a tilt of the whole system into the buccal direction. The additional tipping of the implants of 15 into the buccal direction was realised by rotating the direction of the forces by an angle of 15 towards the occlusal direction. Thus the total force of 500 N was split up into a component of 482 N of vertical force and 128 N of lingual force. The implants were embedded in a block of resin (Technovit) as this material is used in material testing experiments and the numerical results thus could be compared with the results of measurements in a materials testing machine. The results section of this report consists of the two parts Behaviour of the Bar System and the Implant Attachment and Loading of the Implants in the Technovit Bed. -3-

4 2 Material Finite element models of the Two Implant Solution and of the Four Implant Solution have been generated. Additionally two specific situations with implant divergencies have been gen erated for the Two Implant Solution. Due to extreme calculation and modeling times, the di vergencies have not been generated for the Four Implant Solution. This can be justified, as the simulation results of the Two Implant Solution reflected a minor influence of the divergen cies on the loading behaviour of the SFI-Bar-system. The different FE models are dis-played in Figure 1 (Two Implant Solution) and Figure 2 (Four Implant Solution) and are de-scribed in more detail in the following. 2.1 Two Implant Solution ( 2I ) Model 2I initially was generated with an element size at the outer surface of 0.3 mm. The resulting FE model consisted of 190,000 elements and 36,000 nodes (see Figure 1a). It was subsequently used as a basis for the calculation of the models with divergencies. 2.2 Two Implant Solution with parallel implant divergency ( 2I-LL ) Model 2I without Technovit embedding was used as a basis for modelling the implant diver gencies. Both implants with mounted implant adapter and bar were rotated parallelly by 15 degrees (Figure 1b). The transformation of the implants had to be performed in a separate simulation in order to ensure a perfect fit of the geometries of the different components (a) (b) (c) Figure 1: Representation of the FE model of the Two Implant Solution: 2I (a), 2I-LL (b) and 2I-LR (c). -4-

5 Figure 2: Representation of the FE model of the Four Implant Solution. without any penetration. Subsequently the ambient Technovit embedding was remodelled. The complexity of the model was similar to that of 2I. 2.3 Two Implant Solution with opposing implant divergency ( 2I-LR ) Again, model 2I without Technovit embedding was used as a basis for modelling the im plant divergencies. Tilting both implants by 15 degrees against each other was performed with mounted bars (Figure 1d). Subsequently the ambient Technovit embedding was remod elled. The complexity of the model was similar to that of 2I. 2.4 Four Implant Solution ( 4I-Side and 4I-All ) According to model 2I model 4I was generated with an element size of 0.3 mm at the out er surface. This resulted in an FE model with 390,000 elements and 72,000 nodes (Figure 2). Due to the size of the model and the long time required to solve the corresponding simula tions, it was decided to omit the simulations with implant divergencies. This was justified by the simulations of the Two Implant Solution, as the respective results showed only a minor in fluence of the divergencies on the loading behaviour of bar and implant. This will be dis cussed further below. For the model of the Four Implant Solution, two different simulations have been preformed. In the simulation 4I-Side both buccal bars were loaded with a force of 500 N on each bar. In the simulation 4I-All all three bars were loaded with 500 N each. 2.5 Inclination of the loading by 15 degrees in the model 2I-LR Finally, one specific simulation was performed, in order to simulate a simultaneous implant inclination in two planes of space: Model 2I-LR was used to simulate the opposing inclina tion of the implants with simultaneous tilt of both implants towards the buccal direction. The buccal inclination was realised by rotating the force vector by 15 degrees into the lingual dir -5-

6 ection in model 2I-LR. The force magnitude was kept at 500 N, resulting in 482 N occlusal and 128 N lingual forces. The corresponding simulations are denoted 2I-LR-B. 2.6 Survey of generated FE models The dimension of the developed FE model, i.e. the number of elements and nodes in the model, has a decisive influence on the calculation time of the respective simulations. The number of nodes directly defines the number of equations in the system of equations that is to be solved for the simulation. The dimension of the FE models developed in the context of this study strongly depended on the level of detailed representation assumed in the course of the surface discretization. A detailed surface representation was necessary for correct modelling of the bar anchorage at the abutment and the different implant threads. A sensitivity analysis was performed using model 2I with a finer mesh with a surface ele ment size of 0.1 to 0.2 mm. While the original model 2I required a computation time of one to six hours, the finer mesh increased the calculation time to up to 36 hours. A further critical aspect in the simulations was the contact problems within the bar system. A simplification of the models was realized by implementing the joints as rigid connections, if possible. However, especially at the transition from implant abutment to bar anchorage the dynamic characteristics of the bar mounting had to be modelled. As any reference values did not exist, the contact properties, especially the frictional coefficient in the screwed state, had to be determined in a sensitivity analysis by varying the contact parameters in a series of simulations. -6-

7 3 Methods As a boundary condition, the models were tightly fixed during the simulations at the collateral outer surfaces of the Technovit embedding (see Figure 3). This kind of bearing ensured a mobility of the model in the direction of force application. Additionally fixing the model at the lower surface might have corrupted the results. In all simulated loading cases, load was applied via the bar system, in order to model the loading in a materials testing machine. Initially, simulation of a strut for load application was planned, thus that the simulations were as realistic as possible compared with materials test ing. However, the contact analyses necessary for the corresponding simulations proved to be too complex and time-consuming and thus were rejected. Instead point loads were applied at the two end points of the bar. Basically, this kind of loading corresponds to the loading with a strut, as it simulates the situation with even a minimal deflection of the bar. Figure 3: Representation of the boundary condition with model fixation at the collateral outer surfaces of the Technovit embedding (model 2I-coarse ). -7-

8 4 Results: Behaviour of the Bar System and the Implant Attachment Description of the results of the FE simulations is done using a colour-coded representation. The coding of the respective figure is given in the colour bar on the left side of each figure. A uniform scaling was used in various figures in order to simplify a comparison of the different results. Values beyond the scaling of the respective colour coding result in a representation in grey of the corresponding area. This will be described in the associated text. All presented results and figures refer to the maximum loading of the bar system. Results of the loading below these maximum forces can be interpolated from the presented results. Only the stresses are displayed. As all components except the implant embedding are made of the same material (Titanium Grade 5) and the loading is below the proportional limit, the strains are directly proportional to the presented stresses and may be calculated from these results. 800 MPa 0 MPa Figure 4: Colour-coded representation of the stresses in the bar and its anchorage. The left column shows a 3D view of the whole system, the right column shows a cutting plane through the bar system. The upper row displays the results of the simulation 2I, the middle row those of the simulation 2ILL. The lower row displays the stress distributions for the model 2I-LR. -8-

9 800 MPa (a) (b) (e) (c) (f) (d) (g) (h) 0 MPa Figure 5: Colour-coded representation of the stresses in the implant abutments. The upper row shows the abutments of the Two Implant Solution (a: 2I, b and c: 2I-LL, d: 2I-LR ), the lower row shows the abutments of the Four Implant Solution (e and f: middle and terminal element from 4I-Side, g and h: middle and terminal element from 4I-All ). 4.1 Simulation 2I (500 N loading of the bar) The results of this simulation are presented in the upper row of Figure 4 (overview) and in Figure 5a (implant abutment). Stresses in the area of load application were above 800 MPa. This is a direct consequence of the simulated kind of load application and may be omitted as it is not significant. On the undersurface of the bar, especially in the middle underneath the hollow, regions with increased stresses could be identified. Maximum stresses were in the order-of-magnitude of 350 MPa, which is about half the yield stress of Titanium Grade 5. On the interior surface of the implant adaptor slightly increased stresses of about 300 MPa could be determined (see Figure 5a). 4.2 Simulation 2I-LL (500 N loading of the bar) The results of this simulation are displayed in the middle row of Figure 4 and in Figures 5b and c. Stresses were below those determined for model 2I, however the location of the maximum stresses did correspond to the previous simulation. Underneath the hollow in the bar, stresses of about 200 MPa could be determined. At the upper border of the outward in clined implant adapter (left implant adapter in the figures, details in Figure 5b) stresses at the -9-

10 inner surfaces of up to 350 MPa were determined. Stresses in that region at the second im plant adapter were below 100 MPa (Figure 5c). However, in the neck of the fixation screw, in creased stresses of 250 MPa (left adapter) to 400 MPa (right adapter) could be observed. The increased loading on the right side is a result of the direct contact of the ball connector and screw in the respective region. 4.3 Simulation 2I-LR (500 N loading of the bar) The results are displayed in the lower row of Figure 4 and in Figures 5d. Stresses were com parable to those determined in simulation 2I-LL. The stresses on the undersurface of the bar were about 200 MPa. Stresses in the implant adapter and the fixation screw on both sides were nearly identical (Figure 5d) and did correspond to the values of the outwardly in clined implant abutment from 2I-LL (Figure 5b). 4.4 Simulation 4I-Side (500 N loading per side-bar) The stress distribution in the middle and end segments of this model are shown in Figures 5e and f. The left column of Figure 6 shows the mechanical loading of the whole system as a cut through the front and one side bar and a 3D view of these two bars. As expected, there were no excessive stresses in the front bar (Figure 6a and e). At the underside of the side bars stresses up to 450 MPa could be determined. Stresses in the implant adapters of all four anchorages were around 350 MPa. The overall behaviour of the buccal bars and the corresponding adjacent implant abutments was quite similar to the results seen in the simulation 2I. 4.5 Simulation 4I-All (500 N loading per bar) The stress distribution in the middle and end segments of this model are shown in Figures 5g and h. The right column of Figure 6 again shows the loading of the whole system as a cut through the front and one side bar and a 3D view of these two bars. Magnitude and distribu tion of stresses are almost identical in all three bars (see Figure 6b and d). The stresses at the underside of the bar were about 450 MPa. The bars themselves as well as the terminal implant abutments showed a behaviour similar to the results of 2I or the buccal, loaded bars of 4I-Side. However, both frontal implant abutments showed increased stresses of up to 600 MPa, as they receive a combined load from both adjacent bars

11 800 MPa 0 MPa (a) (b) (c) (d) (e) (f) (g) (h) Figure 6: Colour-coded representation of the stresses in the bars and in the abutments for the Four Implant Solution. The left column presents the stresses in the simulation 4I-Side, the right row presents the results of the simulation 4I-All. The first line shows a cutting plane through the frontal bar, the second line a cutting plane through a buccal bar. In the third and fourth line 3D views of the frontal and the buccal bar, respectively, are presented. 4.6 Inclination of the loading by 15 degrees in model 2I-LR The upper left of Figure 7 shows a cut through the loaded bar system. It is obvious that the results do not differ significantly from those presented for model 2I-LR. The 3D view of the bar (Figure 7, left below) displays a slight shift of the maximum stress, caused by the inclined load application. A change compared to the simulation 2I-LR can be seen in the region above the implant adapter (Figure 7, right). Due to the changed loading direction, the adapter is bent, resulting in stresses up to 500 MPa. It is to be stated that the model had to be ideal ised: A rigid connection was modelled between the screw thread of the implant adapter and

12 800 MPa 0 MPa Figure 7: Colour-coded representation of the stresses in the bar and in the abutment in the simulation 2I-LR-B. The left column presents the stresses in the bar, the right column presents the results in the implant abutment. The upper row shows the stress distributions in a cutting plane through the model, the lower row shows a 3D view of the model. the thread of the implant. A more realistic and detailed modelling of the contact would prob ably reduce the loading of the neck, however increase the loading of the thread itself

13 5 Results: Loading of the Implants in the Technovit Bed Again the figures presented here use a colour coded representation of the results of the FE simulations. The coding used can be found on the left side of each figure. To enable a com parison between the different figures, a uniform coding has been used as far as it was pos sible. If calculated values were outside the given scale (indicated by the grey areas within the figures) this will be noticed in the corresponding text. 5.1 Simulation 2I (500 N loading of the bar) Results of this simulation are presented in the upper rows of Figure 8 (stresses) and Figure 9 (strains). There is a clearly symmetric distribution of stresses and strains around the implants on the left and on the right side. This symmetry can also be seen in the embedding. 100 MPa 0 MPa Figure 8: Colour-coded representation of the stresses in the implants and the surrounding Technovit. The left column shows the distribution across a cutting plane, the right column shows a 3D view. The results of the simulation 2I are shown in the first row, the simulation 2I-LL in the second row and the simulation 2I-LR in the last row

14 0,25 % 0,00 % Figure 9: Colour-coded representation of the strains in the implants and the surrounding embedding. The results are presented in the same order as for the stresses in the previous figure. Only in a small area at the upper side of the implant, stresses of around 100 MPa could be found. These areas were at the inner side of the structure. In the remaining area of the implants stresses were below 40 MPa. These stresses are clearly below the yield limit of the implant material (Titanium Grade 4). This assures a sufficient margin even for loads above the simulated forces. Corresponding to the low stresses within the implants the strains were low as well. The strains in the embedding were at up to 0.25 per cent. These highest strains were located at the outer side of the implants. Strains below the implants, that is in the direction of loading, were at 0.13 per cent. 5.2 Simulation 2I-LL (500 N loading of the bar) The results of this simulation are displayed in the middle rows of Figure 8 (stresses) and Fig ure 9 (strains). Neither the stress distribution nor the strain distribution around the left and the right implant are symmetric. However, increased stresses were observed in regions similar to the simulation above

15 The left, inwardly tilted implant showed similar results as both implants in the simulation 2Icoarse, with stresses of up to 100 MPa at the inward top side of the implant and stresses well below 50 MPa in all other areas. The right, outwardly tilted implant showed slightly re duced peak stresses at 80 MPa at the outward side of the implant. Nonetheless, these stresses were well below the material limits. Strains in the embedding around the implant showed a similar asymmetry as the stresses within the implants. At the outer side of the left implant the strains were slightly reduced, while they increased to approximately 0.3 per cent at the outer side of the right implant. 5.3 Simulation 2I-LR (500 N loading of the bar) The results of this simulation are displayed in the lower rows of Figure 8 (stresses) and Fig ure 9 (strains). In this simulation a clear symmetry was visible for both, stresses and strains, between the left and the right side of the model. Stresses as well as strains in the implant and in the embedding around the implant were nearly identical to the situation in the left half of the model 2ILL. 5.4 Simulation 4I-Side (500 N loading of each buccal bar) The stress distribution in this model is presented in the left column of Figure 10, the strain distribution in the same column of Figure 11. Overall the magnitude and the location of the calculated stresses in the implants in this simu lation were lower than in the simulation 2I. The only difference to the simulation 2I was that there was no stress peak at the inner upper side of the frontal implants. The areas with higher stresses were located at the side opposite to the loaded bars (see cut through two buccal implants, Figure 10, middle row left). Strains in the embedding were at up to 0.35 per cent. These were located on the outward side (with respect to the buccal bar) of the implants. Magnitude and location of the strains around the implants were nearly the same for all implants. 5.5 Simulation 4I-All (500 N loading of each bar) The stress distribution in the model of this simulation are presented in the right column of Fig ure 10, the strain distributions can be seen in Figure

16 Stresses in both frontal implants in this simulation were in the range of 40 to 70 MPa in a large area, without the typical stress peak at the top that could be seen in most of the previ ous simulations (see Figure 10, upper row, right). Stress distributions in both terminal im plants were almost identical to the situation observed in the simulation 2I, with a stress peak at 100 MPa at the inward top and stresses below 50 MPa in the remaining areas (see Fig ure 8). As the two frontal implants were loaded via both adjacent bars, the stress distribution differs from the terminal implants. The observations made for the implants can be lifted to the strains in the embedding around the implants. Maximum strains around the distal implants were at 0.25 per cent. The distribu tion as well as the magnitude of strains around these implants were the same as in the simu lation 2I. Strains around the two frontal implants were up to 0.55 per cent and thus twice as high as strains around the distal implants. 100 MPa 0 MPa Figure 10: Colour-coded representation of the stress distribution in the implants and in the surround ing Technovit for the Four Implant Solution. The left column shows the results of the simulation 4ISide, the right column shows the results of 4I-All. The first row shows a cutting plane through both frontal implants, the second row shows a cutting plane through two buccal implants. The last row shows a 3D view inside the model

17 0.25 % 0,00 % Figure 11: Colour-coded representation of the strain distribution in the implants and in the surround ing Technovit for the Four Implant Solution. The left column shows the results of the simulation 4ISide, the right column shows the results of 4I-All. The first row shows a cutting plane through both frontal implants, the second row shows a cutting plane through two buccal implants. The last row shows a 3D view inside the model. 5.6 Simulation 2I-LR-B Stress and strain distributions within the plane parallel to the bar did not change significantly compared to the simulation 2I-LR. This complies with the assumptions made for the corres ponding simulations, and consequently will not be further discussed

18 6 Conclusions and Discussion In all considered loading cases, the simulations using the model of the Two Implant Solution reflected relatively low stresses taking the relatively high forces into account. Basically, the stresses were below 400 MPa at a loading of 500 N, thus being clearly below the yield stress of Titanium Grade 5. Obviously, the safety margin for loading of the bar system is sufficiently large. With respect to the divergencies simulated in the models, no significant variations in the mag nitude of the determined stresses could be observed. The only region with an increased stress compared to the non-inclined implants was the neck of the fixation screw. As the im plant inclination of 15 degrees represents the maximum possible tilt of the implants, a direct contact of the fixation screw and the ball connector. Assuming unfavourable conditions, the screw could be deformed thus that a prospective unscrewing might be impossible. We as sume that slightly reduced implant inclinations (< 13 ) will reduce this increased loading of the screw. Consequently we recommend that the maximum implant divergencies should not be utilised. Comparing the two configurations with different divergencies ( 2I-LL and 2I-LR ) reflects that the simulation 2I-LR delivers no additional results. Both implant abutments in the simu lation 2I-LR displayed the same stress magnitude and distribution as the one implant abut ment in 2I-LL that was outwardly inclined. The highest stresses of 550 MPa, reported in this study were observed in the simulation 2ILR-B, located in the region of the neck of the implant adapter. The yield stress of Titanium Grade 5 is reported to be 795 MPa. Thus even under the assumption of an extreme loading of 500 N per bar, as done in the current study, a permanent deformation of the bar is not to be expected. Such a high loading might occur during grinding, only under the precondition that there is no or insufficient support on the mucosal surface. The stresses in the implants were quite low for all simulated loading cases. Only few situ ations resulted in stresses slightly above 100 MPa. Thus the stresses were far below the giv en limits of the material (Titanium Grade 4). Consequently, even a loading of the system with forces beyond the simulated ones will not result in permanent deformation or even fracture of the implants. There is a sufficient safety margin. Considering the strains in the Technovit embedding allows certain conclusions regarding the loading of the alveolar bone, as the material parameters roughly match those of the bone (Young s modulus: 2,300 MPa, Poisson s number: 0.3). In literature, values can be found for bony structures without a differentiation between cortical and spongious bone that read as follows: Young s modulus 2,000 MPa, Poisson s number Under these preconditions, the strains in the simulated bone were within the physiologic limit2. 1 Abé H, Hayashi K, Sato M (Hrsg.), Data Book on Mechanical Properties of Living Cells, Tissues, and Or gans. Springer Verlag Frost HM, A Determinant of Bone Architecture. The Minimum Effective Strain,

19 No significant changes in the magnitude of the determined stresses and strains could be ob served with the divergencies. Only the implant that was inclined to the outward in the simula tion 2I-LL (right implant, middle row of Figure 9) resulted in a increase of the strains in the implant bed as compared to the model 2I. Comparing both models with divergencies ( 2ILL and 2I-LR ) reflects that there are no additional findings in the simulation 2I-LR with re spect to the results from 2I-LL. Both implant abutments in 2I-LR displayed same results with respect to magnitude and distribution of stresses as the outwardly tilted abutment in 2ILL. Discussing the simulation of the Four Implant Solution reflects a change in the position of increased strains in the Technovit embedding. Moreover, a change in the mechanical charac teristics of the mounted bar system was obvious. For the implants, the highest stresses of approximately 250 MPa calculated in the above sim ulations could be observed in the simulation 2I-LR-B in the lingual upper area of the im plants. The yield stress of Titanium Grade 4 is 700 MPa. According to the simulations above a plastic deformation of the implants is not to be expected, even for the assumption of an ex cessive load of 500 N. After considering the support of a prostheses on the mucosa, loads of this magnitude will even in the case of bruxism only seldom be expected. Bonn, 24/05/ Dipl.-Math. Ludger Keilig Prof. Dr.rer.nat. Christoph Bourauel Prof. Dr.med.dent. Helmut Stark