This study was conducted to determine the most secure implant positioning on the marginally resected mandible to support a fixed complete denture through finite element analysis. Three or 4 implants were placed at near, middle, or far positions from the resected margin in a simulation model with a symmetrical marginal defect in the mandibular symphysis. The height of the residual bone was 5, 10, or 15 mm. The 4 possible implant patterns for 3 or 4 implants were defined as (1) asymmetrically isolated position 1 to position 2, (2) asymmetrically isolated position 1 to position 3, (3) asymmetrically isolated with greater-length position 1 to position 2, and (4) 2 implants symmetrically positioned on each side of the defect. The von Mises stress in the resected and peri-implant bone with respect to the occlusal force was calculated. Initially, because the peri-implant bone stress around the isolated implant at the near position was greater than at the middle and far positions regardless of the residual bone height, the near position was excluded. Second, the von Mises stress in the resected bone region was >10 MPa when the isolated implant was at the far position, and it increased inversely depending on the bone height. However, the stress was <10 MPa when the isolated implant was placed at the middle position regardless of the bone height, and it was significantly lower compared with the far position and equivalent to the symmetrically positioned implants. Furthermore, the use of a greater-length implant reduced peri-implant bone stress, which was even lower than that of the symmetrically positioned implants. These results suggest that the asymmetrically positioned 3-implant–supported fixed denture, using a greater-length isolated implant, placed neither too close to nor too far from the resected margin, can be an effective alternative to the symmetrically positioned 4-implant–supported fixed denture.

Dental implant therapy is an option available to rehabilitate edentulous jaws after tumor ablative surgery. In particularly, the dental-implant–supported fixed complete denture is a powerful tool in cases of a totally edentulous jaw, wherein both soft and hard tissues are compromised. Studies have confirmed that 2-implant–retained overdentures and 3-implant–supported fixed dentures are reliable treatment options in the totally edentulous mandible.1,2  Both treatments, when compared with conventional treatment modalities, result in a similar improvement in oral health–related quality of life.3  Overdentures on 2 implants, inserted in the anterior mandible, are the easiest option in the case of an atrophic mandible,4  although 3-implant–supported fixed dentures are more stable and facilitate greater ease in chewing.3  Recent advancements in digital dentistry and related computer-aided design/computer-aided manufacturing technology are helpful in the accurate diagnosis and treatment planning for implant therapy. Finite element analysis (FEA) also provides useful information regarding the mechanical stress in the bone, implant, and prostheses, which are loaded during mastication, to predict their biomechanical performance.5  It has been reported that FEA can be used to evaluate the mechanical features of various types of implant-related materials and tissues before surgery.6  FEA can also be used to determine the effects of implant position on the stress distribution in the bone and prostheses.7  In cases of a totally edentulous mandible after tumor ablation, the occlusal loading forces influence the resected bone region. The mechanical stress with respect to occlusal forces, depending on the occlusal condition and the residual bone height, could reach >100 MPa in the resected bone region, which is large enough to cause fracture of the bone.4  We previously demonstrated that 4-implant–supported fixed dentures reduced the amount of mechanical stress in the resected bone region when compared with 2-implant–supported removable dentures.8  However, it is sometimes difficult to place 4 implants into the resected mandible because both hard and soft tissues are generally compromised. Moreover, reduced bone volume, especially in terms of height, less keratinized gingiva, and inferior alveolar nerve canal, complicate the process of implant insertion. Therefore, in this study, we evaluated the application of 3-implant–supported fixed dentures in a totally edentulous mandible after tumor ablation using FEA. Our hypothesis was that connecting 3 optimally positioned implants to each other would reduce the amount of mechanical stress against occlusal forces in the resected bone region without causing overloading in the peri-implant bone. Using an established model of a totally edentulous mandible caused by marginal resection, the mechanical stress with respect to the occlusal force in the resected and peri-implant bone region was evaluated to determine the most stable positioning of 3 dental implants to support a fixed prosthesis.

Mandibular defect and dental implant model

Three-dimensional finite element models of the mandible, with symmetric defect on the superior border of the mandibular symphysis, were created using computer-aided design software (3-Matic; Materialise NV, Leuven, Belgium). Three types of defects, in which the height of the residual bone was 5, 10, and 15 mm, were created. Dental implants (3.75 mm in diameter and 10 or 15 mm in length) and a 1-piece superstructure were also created. The implants were placed into the unresected area of the mandible, bilaterally, and were positioned at a distance of 5 mm (N: near position), 15 mm (M: middle position), and/or 25 mm (F: far position) from the defect margin. A total of 3 or 4 implants were positioned, either symmetrically or asymmetrically. All implants were connected to the superstructure, which was loaded.

Conditions of FEA

To simulate the stress on the resected and peri-implant bone regions, FEA was performed using Mechanical Finder software (Research Center of Computational Mechanics, Inc., Tokyo, Japan).

The Poisson's ratios of the mandibular bone and implant were 0.40 and 0.19, respectively. The Young's ratio of the implant was 10 800 kgf/mm2 and of the mandible was automatically calculated based on Keyak's formula. According to the number and lengths of the implants, there were 242 033 to 281 384 triangular shell elements and 52 079 to 57 700 nodes.

To limit loading conditions, the mandibular ramus was constrained along the X, Y, and Z directions. The loading force of occlusion was 500 N, and the points corresponding to the bilateral molars and midline were set as loading points, the force at which they were equally loaded (Figure 1). Subsequently, the von Mises stress (measured in MPa) in the resected and peri-implant bone regions was calculated.

Implant position patterns and calculation

The 4 possible implant patterns for 3 or 4 implants were defined as (1) asymmetrically isolated position 1 to position 2 (1 implant vs 2 implants): an isolated implant (length: 10 mm; variably positioned: N/M/F) was placed on one side of the mandible, and 2 were placed on the opposite side (length: 10 mm; variably positioned: NM/MF/NF); (2) asymmetrically isolated position 1 to position 3 (1 implant vs 3 implants): an isolated implant (length: 10 mm; variably positioned: N/M/F) was placed on one side of the mandible, and three 10-mm implants were placed on the opposite side (on each at N, M, F); (3) asymmetrically isolated with greater-length position 1 to position 2 (1 implant with greater length vs 2 implants): an isolated implant (length: 15 mm; variably positioned: N/M/F) was placed on 1 side of the mandible, and 2 were placed on the opposite side (length: 10 mm; variably positioned: NM/MF/NF); and (4) 2 implants symmetrically positioned on each side of the mandible (2 implants vs 2 implants): 2 implants (length: 10 mm; variably positioned: NM/MF/NF) were symmetrically positioned on each side of the mandible. Patterns 1, 2, 3, and 4 had 9, 3, 9, and 3 variations, respectively (Figures 25). The stresses in the resected and peri-implant bone regions were calculated; based on the implant positions, the means of each were compared. For pattern 1, the von Mises stresses in the resected and peri-implant bone regions, with respect to the residual bone height and position of the isolated implant, were measured. Then, the mean stress in the resected bone region was compared among different implant positions.

For patterns 2, 3, and 4, the model with the residual bone height of 10 mm was used for measuring von Mises stress. The mean stresses in the resected and peri-implant bone regions were calculated and compared with the corresponding position of the isolated implant in pattern 1. In addition, for pattern 4, the mean stress was also compared with pattern 3.

This study was conducted according to the principles of the Declaration of Helsinki and has been approved by the Ethical Committee of Yokohama City University Hospital (authorization No. B100101001).

Statistical analysis

In the univariate analysis, mean values were compared using the Student t test. In the multivariate analysis, mean values were compared using analysis of variance and Bonferroni's post hoc analysis. P < .05 was considered to be statistically significant.

Pattern 1: Asymmetrically isolated position 1 to position 2 (1 implant vs 2 implants)

The von Mises stress in the peri-implant bone region was ∼20 MPa when the isolated implant was placed at the near position but ∼15 MPa when placed at the middle or far position, regardless of the residual bone height (Figure 6a). The von Mises stress in the resected bone region was >10 to <25 MPa, <10 MPa, and ∼10 to >15 MPa when the isolated implant was placed at the near, middle, and far position, respectively (Figure 6b). The mean stress in the resected bone region was least when the isolated implant was placed at the middle position (P < .01; Figure 6c).

Pattern 2: Asymmetrically isolated position 1 to position 3 (1 implant vs 3 implants)

When the isolated implant was placed at the near, middle, and far positions, the mean stresses in the resected and peri-implant bone regions for pattern 2 were generally equivalent to the corresponding values for pattern 1 (Figure 7a and b).

Patterns 3 and 4: Asymmetrically isolated with greater-length position 1 to position 2 (1 implant with greater length vs 2 implants) and 2 implants symmetrically positioned on each side of the mandible (2 implants vs 2 implants)

The von Mises stresses in the resected bone region were 13.1 MPa, 8.5 MPa, and 10.7 MPa when the isolated implant with greater length (15 mm) was placed in the near, middle, and far positions, respectively, whereas the stress in the resected bone region was 8.7 MPa when the paired implants were placed symmetrically (Figure 8a). In addition, the von Mises stress in the resected bone region was reduced compared with the corresponding values for pattern 1 (using a 10-mm implant) when the isolated implant with greater length (15 mm) was placed either at the near or far position (Figure 8a). The von Mises stresses in the peri-implant bone region were 18.6 MPa, 13.2 MPa, and 13.6 MPa when the isolated implant with greater length was placed at the near, middle, and far positions, respectively (Figure 8b). The mean stress was reduced when using an implant with greater length, irrespective of the position, compared with the corresponding values for pattern 1 (Figure 8b). In addition, the stress around the implant with a greater length at the middle or far position was generally equivalent to the corresponding values in a symmetrical pattern (Figure 8b).

Based on an initial analysis, it was deduced that an implant could not be inserted at the near position because the peri-implant bone stress was >20 MPa, irrespective of the bone height. Hence, a secondary analysis, regarding the stress on the resected bone, was conducted. This analysis showed that when an isolated implant was placed at the far position, the von Mises stress increased inversely depending on the bone height. However, when an isolated implant was placed at the middle position, the von Mises stress was stably low, irrespective of the bone height, thus suggesting that the middle was the most appropriate position for placing an isolated implant. Furthermore, the use of an implant with a greater length as an isolated implant could reduce the peri-implant bone stress to even lower than that of a symmetrically positioned paired implant. Therefore, the results of the present study demonstrated that in cases in which it is challenging to place 4 implants in the resected mandible, a 3-implant–supported fixed prosthesis could act as a reasonable alternative option.

Two distinct processes of bone modeling and remodeling maintain bone tissue. The mechanical stress influences both bone resorption and formation. According to the Mechanostat theory,9,10  bone resorption and bone formation thresholds exist, which are considered to be approximately 1–2 MPa and 20 MPa, respectively. A low intensity of mechanical stress on the bone tissue causes bone resorption, whereas overloading promotes additional bone formation. However, overloading may also lead to microcracks, which possibly result in negative bone responses, such as infection, necrosis, and fracture. With regard to the intensity of the mechanical stress that leads to microcracks, studies have reported approximately 60 MPa in the compact bones of young adults.4,9  The bone strength decreases by up to 50% in certain health conditions,1113  thereby indicating that the threshold for damage could be <30 MPa in generally or locally compromised bone tissue. Moreover, Cicciù et al6  reported that the threshold varied depending on the loading direction and bone types such as the cortical and cancellous bone.

In the mandible, the occlusal loading point and an anatomically compromised bone, such as in postoperative condition, directly affect the outcomes of mechanical stress, which in the case of an unbalanced bite force could reach approximately 100 MPa in the resected region.4  Furthermore, the mandibular symphysis, which was evaluated in this study, is the location at which the mechanical stress due to the occlusal force is concentrated and is even more concentrated after ablation. Cicciù et al14  conducted an FEA analysis and reported that the mechanical stress in the mandibular symphysis of a totally edentulous mandible was approximately 80–90 MPa in a 4-implant–supported overdenture, even though the denture was supported with a bar attachment, whereas that in a 6-implant–supported fixed denture was only 20–30 MPa. This indicates that the use of a fixed prosthesis, when compared with an overdenture, reduced the von Mises stress by up to 70%–80%. Therefore, it is necessary to connect implants appropriately to reduce stress and achieve stability and balance of the occlusion, particularly in the resected mandible. In our previous research, we reported that the mechanical stress in the resected region of a totally edentulous mandible was reduced by up to 50% when 4 implants were connected to support the fixed complete denture.8 

In this study, the results demonstrated that 3-implant–supported fixed complete dentures remain effective in reducing the amount of mechanical stress acting on the resected region. However, this beneficial effect depends on the exact positioning of the implant, which is isolated from other implants. The isolated implant should be positioned far from the resected area but not at the farthest point in the arch. We observed that placing this isolated implant at the middle position of the arch reduced the von Mises stress irrespective of residual bone height. When in the middle, the mean stress value was <10 MPa, which was significantly smaller than when the isolated implant was placed at the near or far position. Placing the isolated implant at the near and far locations was inadequate for supporting the fixed complete dentures. In particular, an implant placed near the resected region, when loaded, may have an adverse effect on the area.

The results of the present study also suggest that the intensity of mechanical stress in the resected region was equivalent when either 3 or 4 implants were used to support the fixed complete dentures, although the amount of mechanical stress around the isolated implant increased. As mentioned earlier, mechanical stresses of between 1–2 and 20 MPa, that is, between the bone resorption and bone formation, respectively, are considered to be appropriate, although the actual tolerable amount of stress in the peri-implant region remains unclear.15  In the present study, the relationship between the implant and bone was set to be totally connected (ie, 100% osseointegration). However, if the values assuming 100% osseointegration were converted into 50% osseointegration, then the mechanical stress in the peri-implant bone would increase 1.3- to 1.4-fold.16  Consequently, the mechanical stress around the isolated implant in the present study would possibly reach >20 MPa for any implant position, which may be too excessive for the bone tissue to handle. In this study, the implant length had an influence on the mechanical stress in the peri-implant bone. The greater the isolated implant length, the lower the mechanical stress. When the isolated implant with greater length was placed at the middle or far positions from the resected margin, the stress in the peri-implant bone was <15 MPa, approximately 90% of that observed for shorter implants, which is considered not to be an excessive load. It has been reported that an increase in the implant length reduces the stress on the cancellous peri-implant bone,17  suggesting that selecting an implant with greater length to be placed in an isolated position could be considered for fabricating functional 3-implant–supported fixed complete dentures. However, a systematic review indicated that a thicker diameter implant, in comparison with an implant with greater length, can more effectively reduce the peri-implant bone stress.18  Although an implant with a thicker diameter can be a more effective option, it requires a wider keratinized mucosa, which is not easily available in the resected region.

A tilting implant could also reduce the mechanical stress in the peri-implant region. In a study using FEA, the authors determined that tilted implants reduced the stress around the bone and implants.19  On the other hand, it has also been reported that no significant difference exists between axial and tilted implants with respect to marginal bone loss during the early to mid observation period.20  If the mechanical stress around the isolated implant is excessive despite using a greater length, thicker diameter, or tilting implant, more than 4 implant-retained overdentures may be used as alternatives. The mechanical stress on the peri-implant bone for the 4-implant–supported overdentures was reduced compared with that for the 2-implant–retained overdentures in the FEA, suggesting that increasing the number of implants reduces the mechanical stress around each implant.21  Furthermore, the retention system of overdentures influences the stress on the peri-implant bone. The Locator or Equator systems are advantageous in terms of overall load distribution of the mechanical stress with respect to the chewing stresses simulated using FEA.22  These retention elements decrease the peak interfacial shear stresses between the bone and the implant surface as compared with the traditional universal attachment system.23 

It is necessary to consider the effects of prosthodontic components on the stress distribution. The mechanical stress on the implant-supported fixed complete denture is distributed to the superstructure (crown), abutment, connection screw, as well as the fixture and bone tissue. FEA studies revealed that this distribution is dependent on the materials, implant design, and loading direction,6,24  suggesting that the mechanical stress in the bone tissue with respect to the occlusal force can be reduced by altering the characteristics and design of implant-related denture components and implant position. Cicciù et al6  analyzed the von Mises stress in the bone tissue when the 4-implant–supported fixed complete denture was loaded and reported that the mechanical stress in the cortical bone varied in terms of the von Mises stress according to the thread shape and design of the implants and the loading direction. Therefore, it is also necessary to consider the implant design and material strength of the prosthodontic components to reduce the mechanical stress in the peri-implant and resected bone tissue. Interestingly, even by only changing the thread shape of the straight-designed implant, the part of the bone, cortical or cancellous, that is mainly loaded is changed.6  Moreover, the mechanical stress in the cortical bone increases due to the lateral force, whereas the stress on the cancellous bone decreases due to the lateral force rather than vertical force.6  Although only the stress in the resected and peri-implant bone was evaluated in the present study, further investigation considering the bone quality and prosthetic components is warranted.

Within the limitations of this study conducted using FEA, asymmetrically positioned 3-implant–supported complete dentures could be an alternative method for reducing the mechanical stress in the resected bone region of the mandible. However, it is important to consider the position and length of the isolated implant to avoid overloading in the peri-implant bone region. The isolated implant should be placed neither too close nor too far from the resected margin. Moreover, the application of an implant with greater length in this location may decrease the mechanical stress on the peri-implant bone.

This study was supported in part by a Grant-in Aid for Scientific Research (C) (No. 16K11758) from the Japan Society for the Promotion of Science.

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There is no conflict of interest in this study.