Virtual Bone Augmentation in Atrophic Mandible to Assess Optimal Implant-Prosthetic Rehabilitation—A Finite Element Study

: The scope of our study was to analyze the impact of implant prosthetic rehabilitation, in bilateral terminal partial edentulism with mandibular bone atrophy, and potential beneﬁts of mandibular bone augmentation through ﬁnite element analysis. A 3D mandible model was made using patient-derived cone-beam computed tomography (CBCT) images, presenting a bilateral terminal edentation and mandibular atrophy. A virtual simulation of bone augmentation was then made. Implant-supported restorations were modeled for each edentulous area. Forces corresponding to the pterygoid and the masseter muscles, as well as mastication conditions for each quadrant, were applied. The resorbed mandible presented high values of strain and stress. A considerable variation between strain values among the two implant sites in each quadrant was found. In the augmented model, values of strain and stress showed a uniformization in both quadrants. Virtually increasing bone mass in the resorbed areas of the mandible showed that enabling larger implants drastically reduces strain and stress values in the implant sites. Also, although ridge height di ﬀ erence between the two quadrants was kept even after bone augmentation, there is a uniformization of the strain values between the two implant sites in each of the augmented mandible quadrants. of input variables in mandible biomechanics analysis, where a complete mandible was modeled with a full dental arch, strain values reported were similar to those obtained in our study Our results also show that, after the simulated bone augmentation, there is a uniformization of the strain values between the two implant sites in each of the mandible quadrants.


Introduction
Implant-prosthetic rehabilitation has become a successful and highly predictable method used for restoring the functions of the stomatognathic system and improving the quality of the patient's life [1][2][3].
However, in the partially edentulous mandible with bone atrophy, a favorable bone volume and density is a prerequisite for achieving a successful implant-prosthetic rehabilitation [3,4]. In such cases, the placement of standard length implants is often prohibited by an insufficient height of the alveolar ridge [4]. Modern alveolar bone addition techniques can lead to the successful restoration of bone volume, creating the optimal geometry for the use of a larger dental implant [4]. Yet, in the posterior mandible, bone augmentation has been associated with a higher rate of peri-implant marginal bone loss, donor site morbidity, pain, increased costs, and duration of treatment [4][5][6].
In this case, short implants can be a viable solution in implant-prosthetic rehabilitation of the edentulous mandible with bone atrophy [7][8][9]. The development of surface treatment technologies,  Implant-supported restorations were modeled for each edentulous area, consisting of implant, abutment, abutment screw, cement layer, and splinted ceramic crowns. In the atrophied mandible, implants measured 3.75 mm in diameter (D) and 8 mm in length (L) for implant sites 3.7, 4.5, 4.6, and 3.3 mm D with 10 mm L for implant site 3.6. These measurements were planned according to the available alveolar bone dimensions. In the virtually augmented mandible, all implants measured 4.2 mm D and 11.5 mm L.
Simulations of physiological loading of the 3D models were performed using Simulation Mechanical version 2017 (Autodesk, Inc., San Rafael, CA, USA). For all simulation scenarios, a static model with linear and elastic material properties was selected. The mechanical properties of the assigned materials are presented for each element of the 3D analysis assembly in Table 1.
The mandibular model was fixed in the simulation environment at the temporal-mandibular joint surfaces, with rotation restrictions around the Y and Z axes, to simulate the anatomical articulation of the structure and allow for physiological type rotation in the sagittal plane during mastication ( Figure 3). Because the study model presented bilateral terminal edentation, restrictions were set on each one of the ceramic upper restorations at a time, simulating mastication conditions for each quadrant. Masticatory type forces corresponding to the pterygoid muscles (P) of 145 N and the masseter muscles (M) of 151 N were applied ( Figure 3) [14]. Simulations of physiological loading of the 3D models were performed using Simulation Mechanical version 2017 (Autodesk, Inc., San Rafael, CA, USA). For all simulation scenarios, a static model with linear and elastic material properties was selected. The mechanical properties of the assigned materials are presented for each element of the 3D analysis assembly in Table 1.
The mandibular model was fixed in the simulation environment at the temporal-mandibular joint surfaces, with rotation restrictions around the Y and Z axes, to simulate the anatomical articulation of the structure and allow for physiological type rotation in the sagittal plane during mastication ( Figure 3). Because the study model presented bilateral terminal edentation, restrictions were set on each one of the ceramic upper restorations at a time, simulating mastication conditions for each quadrant. Masticatory type forces corresponding to the pterygoid muscles (P) of 145 N and the masseter muscles (M) of 151 N were applied ( Figure 3) [14].
The failure criteria for materials are generally expressed in terms of stress or strain. The biological response of bone tissue to loads applied depends, according to Frost's "mechananostat" theory, on the strain recorded in the tissue [25,26]. The octahedral shear (equivalent) strain is considered to be the most relevant strain for this theory and to be far more conservative than other types of strain such as maximum compression strain. According to the mechanostat theory, the recommended range of strain is 1000-3000 με. Bellow 1000 με, bone tissue experiences stress shielding, leading to bone atrophy. Above 3000 με, the bone tissue is exposed to pathologic overload, which leads to bone damage and absorption [27]. In the simulations of this study, the octahedral shear (equivalent) strain was tracked.
For calculation of the octahedral shear strain, strain component tensors, γxy, γxz, and γzy, were recorded near the implant site. These tensors were then used to calculate the principal strains, using a modified version of Cauchy's symmetric strain tensor [28] as follows: .
(1) Figure 3. Complete mandible assembly in the simulation environment with applied forces corresponding to pterygoid muscles (P) and the masseter muscles (M) and restrictions at the temporomandibular joint surfaces.
The failure criteria for materials are generally expressed in terms of stress or strain. The biological response of bone tissue to loads applied depends, according to Frost's "mechananostat" theory, on the strain recorded in the tissue [25,26]. The octahedral shear (equivalent) strain is considered to be the most relevant strain for this theory and to be far more conservative than other types of strain such as maximum compression strain. According to the mechanostat theory, the recommended range of strain is 1000-3000 µε. Bellow 1000 µε, bone tissue experiences stress shielding, leading to bone atrophy. Above 3000 µε, the bone tissue is exposed to pathologic overload, which leads to bone damage and absorption [27]. In the simulations of this study, the octahedral shear (equivalent) strain was tracked.
For calculation of the octahedral shear strain, strain component tensors, γ xy , γ xz , and γ zy , were recorded near the implant site. These tensors were then used to calculate the principal strains, using a modified version of Cauchy's symmetric strain tensor [28] as follows: The principal strains obtained, ε xx , ε yy , and ε zz , were then used to obtain the octahedral shear (equivalent) strain as follows: Surface averaging of each octahedral shear strain value calculated for each point was done to avoid numerical artifacts of local peak values.

Results
In the resorbed mandible model, strain values in the bone tissue were found to be highest in both quadrants of the mandible in comparison with the virtually bone augmented model, as shown in Figure 4.

Results
In the resorbed mandible model, strain values in the bone tissue were found to be highest in both quadrants of the mandible in comparison with the virtually bone augmented model, as shown in Figure 4.
There was also a considerable variation between strain values among the two implant sites in each mandible quadrant in the resorbed mandible. Moreover, where the 3.3D/10L implant was used in implant site 3.6, strain values obtained were the smallest, as opposed to the other implant sites where the 3.7D/8L implants were used.
After simulation of bone augmentation, strain values decreased in all implant sites. In each quadrant, differences in strain values between each implant site also decreased ( Figure 4). Stress was concentrated at crestal bone level in all simulated cases, as shown in Figure 5. The highest values of stress were recorded in the resorbed mandible model. Between the two quadrants of the resorbed model, there is still a considerable variation of stress values. In the virtually bone augmented mandible mode, as stress and strain values decreased, the area of distribution increased as more bone was engaged. The values of stress between the two quadrants of the augmented model were similar ( Figure 5). There was also a considerable variation between strain values among the two implant sites in each mandible quadrant in the resorbed mandible. Moreover, where the 3.3D/10L implant was used in implant site 3.6, strain values obtained were the smallest, as opposed to the other implant sites where the 3.7D/8L implants were used.
After simulation of bone augmentation, strain values decreased in all implant sites. In each quadrant, differences in strain values between each implant site also decreased ( Figure 4).
Stress was concentrated at crestal bone level in all simulated cases, as shown in Figure 5. The highest values of stress were recorded in the resorbed mandible model. Between the two quadrants of the resorbed model, there is still a considerable variation of stress values. In the virtually bone augmented mandible mode, as stress and strain values decreased, the area of distribution increased as more bone was engaged. The values of stress between the two quadrants of the augmented model were similar ( Figure 5).

Discussion
The long-term survival of implant-supported restorations depends on bone quality and quantity as well as implant dimensions [29,30]. High-stress concentration areas in addition to high strain values owing to excessive implant loading are related to bone resorption [30][31][32][33][34]. Bone homeostasis is achieved, according to Frost's "mechanostat theory", when bone tissue responds favorably to the forces transferred through the implant and strain values fall between 1000 με and 1500 με [25,26]. Bone remodeling occurs when strain values are in the 1500 με-3000 με interval, but above these values, the risk of bone resorption or even fracture rises significantly [25,26].
The results of our study showed that, by virtually increasing bone mass and allowing for larger implants to be used, strain values decreased in both quadrants. Although strain values for both resorbed and bone augmented mandible were far under the lower limit of the bone homeostasis interval, the variability of muscle forces in current literature, as well as an additional effect of other masticatory muscles, must be taken into account [35].
Studies that have reported values above the lower limit of the homeostasis interval have used sections of the mandible bone and applied a set value of force directly on the abutment or, in some cases, on the ceramic upper restoration [36][37][38][39]. This is considered an oversimplification in the analysis and, although it may show a trend of the strain values in the bone tissue, it may also lead to artifacts or unreliable results [35][36][37][38][39][40]. Moreover, there is currently a high variability regarding the magnitude of forces applied directly on implant-supported restorations having a large influence of the strains exerted on the bone tissue [40].
In a study on the importance of input variables in mandible biomechanics analysis, where a complete mandible was modeled with a full dental arch, strain values reported were similar to those obtained in our study [35]. Our results also show that, after the simulated bone augmentation, there

Discussion
The long-term survival of implant-supported restorations depends on bone quality and quantity as well as implant dimensions [29,30]. High-stress concentration areas in addition to high strain values owing to excessive implant loading are related to bone resorption [30][31][32][33][34]. Bone homeostasis is achieved, according to Frost's "mechanostat theory", when bone tissue responds favorably to the forces transferred through the implant and strain values fall between 1000 µε and 1500 µε [25,26]. Bone remodeling occurs when strain values are in the 1500 µε-3000 µε interval, but above these values, the risk of bone resorption or even fracture rises significantly [25,26].
The results of our study showed that, by virtually increasing bone mass and allowing for larger implants to be used, strain values decreased in both quadrants. Although strain values for both resorbed and bone augmented mandible were far under the lower limit of the bone homeostasis interval, the variability of muscle forces in current literature, as well as an additional effect of other masticatory muscles, must be taken into account [35].
Studies that have reported values above the lower limit of the homeostasis interval have used sections of the mandible bone and applied a set value of force directly on the abutment or, in some cases, on the ceramic upper restoration [36][37][38][39]. This is considered an oversimplification in the analysis and, although it may show a trend of the strain values in the bone tissue, it may also lead to artifacts or unreliable results [35][36][37][38][39][40]. Moreover, there is currently a high variability regarding the magnitude of forces applied directly on implant-supported restorations having a large influence of the strains exerted on the bone tissue [40].
In a study on the importance of input variables in mandible biomechanics analysis, where a complete mandible was modeled with a full dental arch, strain values reported were similar to those obtained in our study [35]. Our results also show that, after the simulated bone augmentation, there is a uniformization of the strain values between the two implant sites in each of the mandible quadrants.
Stress values in the bone augmented model exhibited the same pattern. This is because of the increase of implant diameter and length, as well as an increase in bone volume. Besides the dimensional factor of the implants, attention needs to be given to the virtually augmented bone dimensions. The increase of bone volume seems to minimize the position effect of the teeth on the strain values recorded in the bone tissue. The small differences that do exist in strain between each of the implant sites may be because of the position that leads to a specific physiological load [41][42][43]. This may suggest that, in the absence of bone augmentation, further consideration needs to be given to the placement of the implant in atrophic ridges.
In the resorbed mandible model, higher stress values were obtained compared with the simulated bone augmented mandible model. Increasing the implant diameter from 3.3 mm/3.75 mm to 4.2 mm and the length from 8 mm/10 mm to 11.5 mm led to a considerable decrease in stress, as well as a favorable distribution at the crestal level. This is in accordance with several studies that suggest that increasing the diameter and length of the implant leads to lower stress values in the mandibular bone [35,43,44].
In our study, the distribution of stress was found to be similar in the resorbed and bone augmented ridge, as stress was concentrated at the crestal level. This is because of the difference between the elastic modulus of the cortical and cancellous bone. Owing to the increased stiffness provided by a higher elastic modulus in the cortical bone tissue, stress concentrates at the crestal bone level. These findings are consistent with current studies, which suggest that this type of stress concentration is more influenced by the mechanical properties of the bone tissue as well as the type of loading applied [45,46]. Moreover, as high stress and strain values are found at crestal level, which may lead to bone resorption and implant failure, clinicians should carefully plan implant restorations in both augmented and resorbed ridges.
Simulating a bone augmentation in a real clinical case allowed for a comprehensive assessment of rehabilitation possibilities. This method may be further developed as a standardized method of evaluation, allowing for individual patient FEA simulations. However, the diversity of bone augmentation techniques may be challenging to asses in FEA studies. Moreover, from a clinical point of view, it is difficult to evaluate the performance of any bone augmentation technique while ensuring an increased implant success rate [4,6]. The clinical evidence of oral rehabilitation success in mandibular bilateral terminal edentulism with bone atrophy is scarce. However, our results are in accordance with the reported clinical studies, suggesting that bone augmentation may be beneficial to the long-term survival of dental implants [3,30].
Another important aspect of the studied mandible is the absence of an implant restoration of the second molar in the fourth quadrant. The need to replace the tooth with an implant-prosthetic restoration remains a topic of debate [47,48]. However, as the decision to not restore the missing second molar is a common practice, it was important to keep this detail to ensure input variables in the finite element study are as close to clinical reality as possible.

Conclusions
Virtually increasing bone mass in the resorbed areas of a CBCT derived mandible model with bilateral partial edentulism showed that enabling larger implants drastically reduces strain and stress values in the implant sites. Also, although the ridge height difference between the two quadrants was kept even after bone augmentation, there is a uniformization of the strain values between the two implant sites in each of the augmented mandible quadrants. Stress values in the bone augmented model exhibited the same pattern. In the resorbed mandible, values of strain varied greatly between each implant site in the two quadrants, even where implants of the same dimensions were used. These findings suggest that bone augmentation may favorable to the long-term survival of implant-supported restorations. This research may be further developed to offer a comprehensive individualized method of evaluation. This may allow clinicians to assess each patient through individual finite element analysis simulations. Further studies need to address complex rehabilitation cases that reflect real clinical aspects, using patient-specific data to ensure the accuracy and validity of results.