Biomechanical Study of Implant Treatment For Maxillas With Different Bone Quality

1. Introduction

In the case of implant treatment, four to eight implants were treated for a patient with edentulous maxilla or mandible [1-3], depending on the bone density and structural stability of the patient. Thus, occlusal forces during daily activities and unexpected forces such as bruxism [4,5] are supported by those inserted implants and the mechanical stresses were directly transmitted into the jaw bones. In the case of bruxism, the buccal mandibular movement causes the risk of implant fracture as the result of the bending overload [5]. It is therefore expected that a jaw bone with implants is facing much severer mechanical situations than a jaw bone with teeth. This kind of mechanical stress has been considered to cause bone absorption around the implants [6-8], resulting in the loosening and the subsequent removing of the implants. Therefore, finite element analysis of jaw bones with implants has actively been conducted in order to understand such mechanical conditions in the vicinity of the implants [9-10].

In the computational analysis of jaw bones, mandibles have mainly been investigated by constructing their three-dimensional models [11-15] and few attempts have been made to assess maxillas computationally. In general, structure of maxillas is more complex than that of mandibles [16], and it makes resulting in an increase of the risk of the surgical treatments [17]. For example, hollow structures named sinus maxillaries exist in the maxilla, and the bone tissue under the sinus is thin structure that makes the placement of implants difficult. In the vicinity of sinus maxillaries, an implant is usually tried to be inserted into the rear or front part of the sinus maxillaries, or inclined to avoid the sinus maxillaries.

In the field of computational mechanics, CT-image based modeling has actively been developed to construct the models of detailed bone structures considering their three-dimensional shapes, and has effectively been applied to the clinical problems in orthopedics [18-21] and dentistry [22-28]. In this modeling procedure, detailed bone models are constructed from CT-images by extracting the cross-sectional areas corresponding to the bones. Furthermore, the remodeling mechanism has been tried to be simulated by using various theoretical approaches in the bone tissue [29-34]. These approaches can be divided into two categories, macroscopic and microscopic approaches. One of the macroscopic approaches is based on a mechanical hypothesis in which the bone remodeling can be controlled by strain energy density [29-31,33]. On the other hand, one of the microscopic approaches tries to understand the remodeling mechanism by using the biomechanical responses of bone tissue related osteocytes [34].

In this study, two different types of maxilla models varying in the shape and the bone quality were constructed using the CT images of the edentulous maxilla of a male and a female patient. Total six implants were inserted into each of the maxilla models. Finite element analysis was performed to assess the effects of the implant treatment on the distribution of the strain energy density in the maxillas.

2. Materials and methods

2.1 Finite element models and analysis

Two different types of maxilla models were constructed by using the CT images of the jaw bones of an 84 years old male and a 65 years old female. The total number of the CT images and the slice distance were 80 and 0.5 mm for the male and 37 and 1 mm for the female. Mechanical Finder (RCCM, Inc.), a software for finite element modeling and analysis of bone structure, was used in this study. Four-nodes tetrahedral elements were used to construct a finite element model of the maxilla. The total number of elements and nodes were 134223 and 630675 for the male model and 110052 and 505919 for the female model. Figure 1 shows the three-dimensional solid models. The models had the limited upper and side boundaries because only the limited regions of maxilla in which implants were supposed to be inserted were chosen by the dentist in charge and taken by CT in order to minimize the effects of X-ray radiation to the patients.

Figure 1: Computational models. The upper side is 84 years old male model, the lower side is 65 years old female model. The left side is a finite element model of edentulous maxilla, the right side is maxilla models with prosthesis.

The bone mineral density, , corresponding to each element was estimated from the averaged CT value (Hounsfield units) using the following formula [35]:

The Young’s modulus of the element was then calculated from the corresponding bone density by using the relationship by Keyak, et al. shown in Table 1 [18].

Table 1: Relationship between bone density and Young’s modulus [18].

For each maxilla model, a prosthesis model consisting of six implants and a curved support was developed as shown in Figure 2. The diameter of all implants was chosen to be 3.75mm. The curved supports were determined so that they fitted to the curved shapes of the maxillas. The material of the implant and the curved support was assumed to be pure titanium with the Young’s modulus of 106 GPa and the Poisson’s ratio of 0.3. Figure 1 shows these prosthesis models were attached to the maxilla models. In a real structure of maxilla, gingiva usually exists in the space between the maxilla and the curved support and neglected in this modeling. The boundaries between maxilla and implants were assumed to be perfectly bonded. The length of each implant was set to be maximized in each implantation position as shown in Table 2. In Table 2, the number in the parenthesis expresses the insertion length of the implant within maxilla.

Figure 2: Prosthesis models consisting of implants and curved support.

Table 2: Length of each implant. The number in parenthesis is the insertion length.

Figure 3 shows the boundary condition. In the restraint condition, the top of the maxilla model was totally fixed as shown in Figure 3(a). In the loading condition I, a distributed load of 200N was applied to the bottom surface of the prosthesis in the +Z-direction as shown in Figure 3(b). The value of 200N has been reported as an actual load subjected to jaw bones during an occlusion condition [36]. In the loading condition II, a partially distributed load of 100N was applied to the left half surface of the prosthesis in the +X-direction as shown in Figure 3(c). It is noted that the horizontal loading simulates a bruxism condition.

Figure 3: Boundary conditions applied to maxilla model.

3. Results

3.1 Distribution of Young’s modulus

Figure 4 shows the distributions of Young's modulus on the vertical cross-sectional areas at the implant ①. It is clearly observed that higher moduli were distributed in the cortical bone regions. It is also noted that the female model exhibited lower modulus than the male model. The variations of the modulus along the dashed lines A-A' and B-B' are plotted in Figure 6. One modulus value was plotted at each element along the lines. It is clearly seen that higher moduli were distributed in the cortical bone regions and the female model exhibited much lower distribution of the modulus than the male model.

Figure 4: Elastic modulus of finite element model. (A) is 84 years old male model. (B) is 65 years old female model. (C) is distribution of elastic modulus along each dashed line in (A) and (B).

3.2 Distribution of strain energy density

Figure 5 shows the maximum values of the strain energy density in maxilla in the vicinity of the implants. In the case of loading condition I, for both models, the highest maximum value existed in the vicinity of the implant ①. Compared with the maximum value of the strain energy density in the implant ①, there was a 68.8% difference between male and female model. Similarly, in the case of loading condition II, the highest maximum value existed in the implant ①, and then, three implants (implant ①, ②, ③) were most affected. However, for both models, the maximum values in the implant ② and ③ are smaller than that of the implant ①. Compared with maximum value in the implant ①, there was a 67.3% difference between male and female model. In the case of the female model, the length of the implant ① was the shortest (see Table 2) and the distance between the implant ① and ② was the longest (see Figure 2(b)), therefore the implant ① was influenced by higher load and moment than the others. In the case of the male model, on the other hand, the insertion length of the implant ① was the shortest as shown in Table 2 because of the shorter width of the right-side bone than the left-side as shown in Figure 1(a). This shortest insertion length of implant might cause the highest strain energy density.

Figure 5: Comparison of maximum strain energy density in the vicinity of implants.

The distribution of strain energy density in the cross-sectional areas of the implants ① for a male and female model is shown in Figure 6. It is clearly seen that the distribution of the strain energy density was mainly concentrated around the inserted implants.

Figure 6: Distribution of strain energy density in the vicinity of the right molar implant. The upper side is 84 years old male model, the lower side is 65 years old female model. The left side is loading condition I, the right side is loading condition II.

4. Discussion

In the female model, the implant ① exhibited higher strain energy density than that of the male model. Considering the lower bone density and weak bone structure of the female model, such high concentration of the strain energy density may cause damage and subsequent bone absorption around the implant ①. It is recommended to modify the implant ① to reduce the concentration of the strain energy density. One of the effective approaches is thought to lengthen the implant ①, however, the sinus maxillaries located above the implant prevents such lengthening. Therefore, an inclined insertion of implant was applied to the model. Figure 2(c) shows the modified prosthesis model introduced to the female model. The length of the implant was changed from 9 to 15 mm, and it was inclined by 45 degree to avoid the sinus maxillaries.

Figure 7 shows the maximum strain energy density in the vicinity of each implant. It is clearly observed that the strain energy density around the implant ① was dramatically reduced by the modified female model. It is successful that the maximum value of the strain energy density in the implant ① under the loading condition I and II decreased 75.4%, 45.7% by being modified the implant ①, respectively. Figure 8 shows the distribution along the indicated lines around the implant ①. It is noted that the distribution in the modified female model was comparable to that in the male model.

Figure 7: Maximum strain energy density in the vicinity of implants of modified model.

Figure 8: : Distribution patterns of strain energy density along the lines around the implant ①.

It should be noted that lengthened and inclined implant effectively improves the safety of the implant treatment; however, much higher surgical skill is required for the dentist. It is also noted that in an actual implant treatment, the number of the implants may unwillingly be reduced due to the structural weakness of the maxilla. Therefore, risk assessment by the computational method is recommended to minimize the number of the implants and to optimize the positions and the lengths of the implants for patients.

In actual medical treatments, threshold level of strain energy density could be very useful in order to predict the risk assessment for bone absorption using the computational analysis during the preoperative planning. Further study needs to be done to find such threshold level and establish the computer aided preoperative procedure.

5. Conclusion

Three-dimensional finite element models of edentulous maxillas of a male and female patient were developed using their CT-images. For each model, a prosthesis model, including six-implants and a curved support was attached to the maxilla. Finite element analysis was then performed to assess the effects of the implantation on the concentration of the strain energy density that has been considered to be a macroscopic parameter controlling bone absorption around the implants. The conclusions are summarized as follows:

1. In both the maxilla models, strain energy density was severely concentrated around the implant ①, and the concentration in the female model was higher than in the male model, suggesting bone absorption around the implant ① of the female model.
2. The high concentration of the strain energy density around the implant ① was thought to be attributed to the shortest insertion length of the implant, resulting in the smallest contact area with bone tissue. For the female model, furthermore, the longer distance between the implants ① and ② was also considered to result in the higher moment subjected to the implant ①.
3. The implant ① of the female model was replaced by a longer and inclined implant. The concentration of the strain energy denisty was then successfully reduced.

6. Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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