The numerical method of structural analysis called Finite element method has been used with satisfaction for about thirty years in the structural analysis of biological systems or bio-mechanical systems resulting from the coupling of prosthetic or implant devices to biological structures (joint prostheses, dental implants, valve prostheses …).
In this part of the chapter dedicated to biomechanics, some results are obtained by simulating different implant situations aimed at the partial or total rehabilitation of the jaws.
The models created are the following:
– partially edentulous hemimandible in which they were inserted, with the same geometric conditions, constraint and load, to investigate the different structural effect resulting on the bone:
– 3 so-called “osseointegrated” implants (fig. 7a)
– 3 implants, with a smaller diameter than the previous ones, arranged in tripods fixed together (fig. 7b)
– 5 needle implants (fig. 7c)
– portion of edentulous maxilla in which they have been inserted, with equal geometric, constraint and loading conditions:
– 4 so-called “osseointegrated” implants (fig. 8 a)
– a combination of screw and bracket systems made integral with each other (fig. 8 b)
– fully edentulous mandible with prosthesis overdenture anchored to the jaw with:
* 2 so-called “osseointegrated” implants positioned in the chin area (fig. 9 a)
* 4 implants, with a smaller diameter than the previous ones, arranged in tripods fixed to each other (fig. 9 b)
Figure 7. a) model of partially edentulous hemimandible, b) portion of partially edentulous hemimandible with 3 so-called “osseointegrated” implants, c) portion of partially edentulous hemimandible with 3 implants arranged in tripod between one another, d) portion of emimandible partially edentulous with 5 needle implants inserted
Figure 8. a) model of an edentulous jaw portion with 4 so-called “osseointegrated” implants, b) edentulous jaw portion model with a combination of screw and stirrup implants inserted together
Figure 9. a) fully edentulous mandible with prosthesis overdenture anchored with 2 so-called “osseointegrated” implants, b) fully edentulous mandible with prosthesis overdenture anchored with 4 implants fixed to each other
In all the models constraint and loading conditions comparable to physiological situations and commonly adopted in the scientific literature were simulated.
In all the models the bone was distinguished, both from a geometric and a mechanical point of view (Young’s modulus, Poisson’s coefficient), in cortical and cancellous.
The results of the simulations, as usual in all the analyzes conducted with this method, are provided both numerically, by means of printouts in which each element that constitutes the model, that is to each “virtual brick” constituting the numerical structure, the modules are associated , that is the values, of the components for example of force, displacement, tension and deformation that result in that particular element from the application of the hypothesized loads and constraints, both with images that illustrate the structures under examination or parts of them colored with different shades distributed according to a logic; the different colors in fact correspond to different ranges of values, respectively of force, displacement, voltage, deformation or other parameters object of analysis, which are reported in a legend associated with the image.
Usually in the biomechanical field, the distribution of tension is analyzed with particular attention, both in biological structures to see how much the coupling with an artificial structure (eg prosthesis, implant) modifies their structural response to external stresses, both in artificial structures for check its stamina. The identification in a structure of the distribution and the extent of the tensions is important as it highlights which are the most stressed areas and therefore more at risk of breakage or, in the case of biological tissues, of necrosis or hypertrophy and which are the areas less stressed that, in the case of biological tissues, could induce atrophy.
With regard to the studies illustrated above, this chapter summarizes the results obtained and the conclusions reached; for a complete analysis of the results achieved and for more details, see the related published articles  .
As regards the partially edentulous hemimandible with different implant systems, in the analysis of the stress state of the different biomechanical systems particular attention was paid to the upper part of the mandibular cortical bone, as it was one of the most stressed parts and was compared the tension values in the interface areas with the implant, which experience indicates as being most affected by bone resorption.
In the example shown (fig. 10) the main stresses on the upper surface of the mandibular cortical bone (implant insertion area in the bone) are compared respectively in the case of use of the so-called “ostointegrated” (traditional) implants and of the implants placed tripod solidarized with each other; a summary histogram follows (fig. 11) in which, for each load situation considered, the maximum compression values found in the bone are shown in both implant situations, with the percentage reduction of the tension value in the most favorable situation.
The voltage values shown in the figures and in the histogram are expressed in MPa and correspond to one of the main voltages, that is to the indicative of the maximum compression acting at the point considered. The color scale is not comparable because the extremes of the scale vary: the negative value indicated in correspondence with the blue color is indicative of the maximum value of main tension found. Negative values indicate a state of compression, while positive values indicate a state of traction
Figure 10. Comparison between the biomechanical system with so-called “osteintegrated” implants and solidarized tripod implants: maximum main tension distribution on the upper surface of the mandibular cortical bone resulting from the application of a compression load equal to 200 N applied on 2 ° prosthetic tooth
As regards the portion of edentulous maxilla with different implant systems, the analysis of the results was carried out by considering different areas: the outer surface of the cortical bone, the interface surface between the cortical bone and the transecular bone and the diametric sections of each plant (fig. 12). To allow a synthetic view, the trend of the Von Mises equivalent voltage alone has been reported, that is of a voltage indicative of the seriousness of the overall stress condition.
Figure 12. Distribution of the equivalent stress state in the two plantar types stressed by a compression load equal to 40 N
In both cases the stresses are fairly well distributed, however affecting the entire portion of bone analyzed despite the fact that the load was localized. Tensions are reached that could cause bone fracture only in very localized points: the interface area between the screw and implanted bone in the case of traditional implants and the interface area between the ‘staples’ of the bracket and cortical bone for the second type of planting.
The reached tensional levels are quite similar for the two different modalities of intervention, however the following differences are recognized: the external surface of the cortical bone is more loaded in the case of implantation with bracket as evidently the brackets rest directly on this surface, not however, ‘dangerous’ voltages are reached thanks to the fact that in the model the lower surface of the bracket perfectly copies the bone; the trabecular bone is slightly loaded at the interface surface with the cortical bone since the cortical bone, having a higher elastic modulus, bears most of the load. In the case of implants with stirrups there may be tension concentrations at the points where the screws, implanted obliquely, pierce the trabecular bone to go to rest on the cortical bone; however, tensions remain modest; as regards the sections, the values reached by the voltages are similar for the two extreme sections, while, as far as the two ‘internal’ sections are concerned, in the case of traditional systems there are important concentrations of tension at the points where the screw enters the cortical bone and likewise in the areas of discontinuity between the original cortical bone and implanted bone, considered in this simulation, and at the distal end of the screw.
Finally, as regards the completely edentulous mandible with an overdenture, the objective of the study was to compare two different implant support systems to identify the best solution from the point of view of the biomechanical behavior of the bone-implant system. Particular attention was paid to the distribution of tension in the bone, both cortical and cancellous, in order to understand in which situation the most favorable structural conditions for the bone occur. Figure 13 shows the equivalent voltage distribution of Von Mises in the two cases considered: osseointegrated implant support (Fig. 13 a) and implant support arranged in tripod with solidarized implants (Fig. 13 b). The analysis of Von Mises stresses that the voltage peaks occur, for both implant solutions, in correspondence with the implant that is closest to the application of the hypothesized load. The voltage peak occurs at the implant insertion area in the bone, in the distal side.
Figure 13. a) Von Mises tensions in cortical bone: traditional implant solution; b) Von Mises tensions in cortical bone: implant solution with solidarized implants
The implant support realized with four solidarized implants, in the hypothesized constraint and loading conditions, has been shown to determine tension peaks in the cortical bone, in correspondence with the area of insertion of the implant more loaded in the bone, of lower modulus of 34 % compared to those determined, in the same constraint and load conditions, by a traditional implant support achieved by two implants. The application of the implant solidification bar has resulted in a 5% reduction in voltage peaks. It should be noted, however, that the simulated structural situation is that of complete osseointegration: it is believed that its contribution to the reduction of stress peaks may increase if a condition of primary stability is considered.
In conclusion, with regard to the applications illustrated above, the finite element structural analysis method has proved to be adequate in the simulation of complex systems such as those that are created in the rehabilitation of the jaws and to be able to contribute with considerable time savings, materials and costs, compared to clinical trials, which obviously continues to remain precious and necessary, to the development of new prosthetic and implant systems.