With improvements to the implant surfaces, designs, and placement-related procedures, such as guided bone regeneration or osteodistraction,1,2 implants have become the more predictable treatment options for partially and totally edentulous patients. Compared with the edentulous mandibles, the edentulous maxillae require careful evaluation for the site and number of implant placement because of a lower bone density and anatomical limitations, such as the maxillary sinus, which renders a lower survival rate of implants than mandibles.3–6
Although it would be desirable to use an implant for each missing tooth, it is usually difficult to carry out this concept because of financial and anatomical restrictions. There have only been few studies on the minimum number of implants required to provide occlusal support for fixed prostheses, particularly in edentulous situations. Recently, several systems, such as the Novum system (Nobel Biocare AB, Göteborg, Sweden)7–9 or the all-on-four immediate-function concept with Brånemark system implants (Nobel Biocare AB)10,11 have been proposed to provide support for edentulous patients with a minimum number of implants. However, little is known about the rationale of implant placements for these situations in terms of the biomechanical stress.
Finite element analysis has become an increasingly useful tool for the prediction of the effects of stress on the implant and the surrounding bone.12 A key factor for the success or failure of a dental implant is the manner in which stresses are transferred to the surrounding bone environment.13–15 Finite element analysis allows researchers to predict stress distributions in the contact area of the implants with cortical bone and around the apex of the implants in trabecular bone.
The aim of this study was to determine the influences of the number and location of posterior implants, especially in molar region, on the stress, and deformation, when loaded in edentulous maxillary bone using a three-dimensional finite element model (3D FEM).
Materials and Methods
Finite Element Model
A computed tomography (CT) scanner (LightSpeed QX/i, GE Healthcare, Chalfont, St. Giles, UK) was used to collect scans of an edentulous maxilla from a dry skull and then these data were reconstructed into a 3D model. Specifically, the CT scan data in DICOM (Digital Imaging and Communications in Medicine) format and a specially designed software (Mechanical Finder version 5.2 Extended Edition, Research Center of Computational Mechanics, Inc., Tokyo, Japan) provided morphological data for the dry skull with the edentulous maxilla (Fig. 1). Bone density information was calculated from the CT values. A 3D FEM was created with 123,613 nodes, 126,416 shells, and 545,505 solids using 1.0 to 3.0 mm on a side. Instead of using uniform material properties of cancellous bone for the inner part, as in conventional FEMs, the real weight density of each solid was calculated from the CT values. Regarding material constants, Young’s modulus and Poisson’s ratio were used as in previous studies,16 and yield stress values in the model were determined using Keyak’s equation.17
Analyses with the FEM
The original dry skull model by the FEM software was further modified to allow implants to be installed into the bone at designated sites, and remeshing of the surrounding bone structures. Thus, implant installation models were created (Fig. 2).
Titanium cylindrical implants without threads were also simulated as the configuration of 14 unsplinted implants throughout the dental arch (US14), 14 splinted implants (S14), 6 splinted implants (canine, premolar, and molar regions, S6), 4 splinted implants (all-on-four configuration, S4), and 6 anterior implants (between canines on both sides, A6). In the S4 model, longer implants placed bilaterally in the positions of second premolars were distally tilted at a 45-degree angle along with the anterior wall of the maxillary sinus to avoid a cantilever.10,18 Two mesial implants were placed vertically in the positions of the lateral incisors. The other implants in the US14, S14, S6, and A6 models were fixed vertically to the occlusal plane.
In consideration of the anatomical conditions, diameters (D) and lengths (L) of the titanium implants were decided as follows (Fig. 3): for the US14, S14, S6, and A6 model: incisor, D: 3.2 mm × L: 10 mm; canine and first premolar, D: 3.4 mm × L: 10 mm; second premolar, D: 3.4 mm × L: 9.0 mm; first molar, D: 4.0 mm × L: 6.0 mm; and second molar, D: 4.0 mm × L: 5.0 mm; for the S4 model: incisor, D: 3.75 mm × L: 10 mm; and molar, D: 4.0 mm × L: 15 mm. The surfaces of the implant body and the host bone shared nodes at the interface.
The occlusal table was set parallel to Camper’s plane with a 32 mm distance from the anterior nasal spine. Distributed loads of 200 N in the bilaterally vertical direction were applied on the buccolingual midline of occlusal table of the superstructures. Additionally, distributed loads of 200 N in the unilaterally 60-degree inclined palatobuccal direction were applied on the buccolingual midline of occlusal table of the superstructures. The amount of the load was distributed gradually increasing from the mesial to distal teeth. Calculations using these models were analyzed by compressing stress, which is a minor principle stress, and by the deformation of the mandible in relation to the occlusal support position.
The largest principle stresses were found in the bone surrounding the neck of the implants in the incisor alveolar ridge of the US14, in the canine and premolar area of the S14 and S6 models, and in the bone around the most posterior implants in the S4 and A6 models (Fig. 4). In contrast, the largest amount of deformation was found in the bone surrounding implants in the anterior alveolar ridge of all models (Fig. 5).
The S6 model was subjected to similar amount of stress and deformation to the US14 and the S14. The S4 model was subjected to approximately two times the amount of stress, and the A6 model was subjected to approximately 2.7 times the amount of stress when compared with the model with posterior supports (S6 model). Similarly, the A6 model showed approximately 1.4 times the deformation when compared with the model with posterior supports.
The differences in principle stress and deformation under the inclined load in each model were more remarkable than in the vertical load. The S4 model was subjected to approximately four times the amount of stress, and the A6 model was subjected to approximately five times the amount of stress when compared with the model with posterior supports (Fig. 4). Similarly, the S4 model showed approximately 1.3 times the deformation, and the A6 model showed approximately 1.6 times the deformation when compared with the model with posterior supports (Fig. 5). However, the S6 model was subjected to similar amount of stress and deformation to the US14 and the S14.
The biomechanical loads of implants must be precisely evaluated and interpreted to clinically predict host bone responses and the longevity of the entire implant-supported system.19–23 There are several methods for the biomechanical analysis of implant restorations. Models using strain gauges have some advantages. For example, measurements of strain at the surface of abutments can be performed with strain gauges, and the comparison of results between intraoral applications and experimental models.24–26 However, stress in the implants themselves and in the bone surrounding the implants cannot be easily evaluated by strain gauges. Strain gauges cannot be attached to an area narrower than their own size. In this case, attachment is therefore limited to the smooth surface, and any stress to the inner portion of the tooth cannot be measured. For such parameters, 3D FEMs exhibit more advantages than strain gauge measurements and are considered to be more effective. The stress values of the FEM in this study correlated significantly to that of the strain gauge measurements (Pearson correlation test, P < 0.001, R2 = 0.82).27
Results obtained using simplified jaw shapes or homogeneous structures of cancellous bone should be carefully evaluated with 3D FEMs.28 Here, we used a 3D FEM created directly from CT data of a dry skull. We believe that the 3D morphology and bone density data collected from this CT analysis of a dry skull provide a more precise evaluation of deformation and stress distribution than has been previously reported in other studies using simplified models.
However, there are some limitations with the 3D model in this study. First, all interfaces in the models were assumed to be fully bonded, and the implants were of a simple cylindrical shape to make the calculations easier. Second, we regarded the implant and the abutment as a single and solid structure in this study, and the internal (or external) design of the implant collar, implant-abutment interface, abutment screw, and gold (or fixation) screw were not included.
Many clinicians are of the opinion that the selection of the implant positions and the scheme of prosthesis splinting are critical for the longevity and stability of an implant prosthesis. Kregzde29 used a 3D simplified FEM of jaw bones, teeth, and various implant numbers, positions, and prosthesis designs to attempt optimization of the stress distribution to the implants. He found that stresses induced in the implants and in the host bone were sensitive to the scheme of prosthesis splinting and implant positions. However, his study included simplified models rather than modeling real cancellous and cortical bone.
Implant-supported fixed prostheses with cantilevers add additional factors that can influence stress distribution. These factors include cantilever length, cross-sectional beam shapes, and, recently, a system for additional support of the distal extension of the cantilever.12 With a 3D FEM of a bilateral distal cantilever-fixed prosthesis supported by six implants in the mandible, previous studies30,31 reported that maximum stresses would occur at the most distal bone-implant interface on the loaded side and that these stresses would significantly increase with an increase in cantilever length. Here, we found that both the six splinted implants in the anterior maxilla and the four splinted implants resulted in a larger stress concentration in the bone surrounding the most distal implants when compared with the superstructure with posterior supports.
In contrast, the stress distribution patterns indicated that the six splinted implants of the bilateral canine, premolar, and molar model were almost equally efficient to the 14 unsplinted implant models in the maxilla, suggesting that posterior occlusal support may be important for preventing bone resorption.
Four splinted implants in bilateral lateral incisors and second molars without posterior occlusal support were expected to create more stress and deformation, especially from the lateral force. In terms of stress distribution, the results of this study demonstrated that it is better to establish posterior occlusal support in the maxilla, where a larger occlusal force is expected in relation to the largest closing muscle vectors of the masseter and the median pterygoid.
In this study, evaluation of stress by the FEM of a real anatomical model was primarily qualitative rather than quantitative. The literature reports that the critical threshold for bone resorption should be approximately 50 MPa32 or 200 MPa.33 The anticipated stress by the lateral force in the FEM without posterior supports was beyond these critical threshold values. Clinical significance in a life-like anatomical model cannot be defined. However, this model evaluated here, which includes bone density data from CT, provides potentially more information than oversimplified models, such as the curved beam model18,30,31 or a model with a smaller number of solids.29
The results of loading in this 3D FEM analysis suggest that the six splinted implants configuration in bilateral canine, premolar, and molar regions (S6) has a similar stress and deformation pattern when compared with naturally positioned unsupported implants (US14) in the edentulous maxilla. Additionally, significantly lower stress and deformation were observed in this configuration (S6) when compared with four splinted implants including two tilted longer ones (A4) or six anterior implants (A6).
The authors claim to have no financial interest, either directly or indirectly, the products or information listed in the article.
This research was supported by a general subsidy for research from Osaka University. The authors thank Joanne Madsen, MA, for reviewing the grammar and syntax, and Robert Renner, DDS, Professor Emeritus, State University of New York at Stony Brook, for providing an expert’s review of the prosthodontics.
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