Comparison of Stress and Strain Distribution Patterns in Canine Implant and Maxillary Bone in Three Occlusal Schemes Using Finite Element Analysis

Abstract Objectives  This study aimed to compare the pattern of stress and strain distribution in canine implant and maxillary bone in the anterior group function (AGF), posterior group function (PGF), and canine guidance (CG) occlusal schemes by finite element analysis (FEA). Material and Methods  In this in vitro experimental study, a dental implant (10 × 4.1 mm) was inserted at the site of the maxillary canine in a model of the maxilla in Mimics software. The implant was scanned three-dimensionally and the data were transferred to SolidWorks software. The von Mises stress, shear stress, deformation, and strain were calculated in the AGF, PGF, and CG occlusal schemes by FEA. Statistical Analysis  Data were analyzed by ABAQUS software to calculate the stress transferred to the canine implant and maxillary bone in the three occlusal schemes. Results  The maximum and minimum von Mises stress, elastic strain, shear stress, and deformation were noted in the AGF and PGF occlusal schemes, respectively, in all teeth. Conclusion  The PGF showed minimum von Mises stress, elastic strain, shear stress, and deformation in the canine implant and maxillary bone. Thus, it appears than the PGF is the best occlusal scheme for maxillary canine implant followed by the CG scheme.


Introduction
Use of dental implants has greatly increased for replacement of the lost teeth.They can be used for replacement of one single tooth, multiple teeth, or as an abutment for fixed partial denture or implant-supported overdentures. 1,2spite the high success rate reported for single-unit maxillary dental implants, 3,4 they are often associated with mechanical and biological complications. 1,5t has been reported that some occlusal schemes and lateral movements are associated with greater changes in marginal bone level around dental implants.7][8] Also, some authors claim that the group function occlusal scheme increases the possibility of contact with the opposing teeth in nonfunctional lateral movements or nonworking side interferences. 6Nonetheless, several factors affect the magnitude of stress applied to dental implants.The occlusal scheme in lateral movements of the jaw is one such factor, which can be anterior group function (AGF), posterior group function (PGF), or canine guidance (CG).
Finite element analysis (FEA) is an ideal method to analyze the effect of occlusal stress applied to implant components, and evaluate the pattern of stress and strain distribution in dental implant and the adjacent structures.It uses a numerical system to analyze the physical phenomena, load distribution, and behavior of materials in response to load application.While studies have demonstrated that the isotropic bone model can lead to an overestimation of maximum von Mises strain by up to 15% under pure compression and an underestimation of up to 50% under pure torsion when compared with the anisotropic model, 9 it is important to note that the complexities inherent in FEA often necessitate simplifications.In many FEA applications, material properties are commonly assumed to be homogeneous, isotropic, and linearly elastic due to the computational challenges posed by incorporating more complex material behaviors. 10,11FEA is also ideal to find the points of maximum stress and strain accumulation in tissues.
Considering the gap of information regarding the pattern of stress and strain distribution in maxillary canine dental implants in different occlusal schemes, this study aimed to compare the stress and strain distribution patterns in the canine implant and maxillary bone in the AGF, PGF, and CG occlusal schemes by FEA.

Material and Methods
In this in vitro, experimental study, a dental implant (10 Â 4.1 mm) was inserted at the site of maxillary canine in a model of maxilla in Mimics software.To enhance threedimensional (3D) analysis, the complex was divided into smaller elements.Cone-beam computed tomography images taken with 330-µm voxel size, 61 Â 78 mm field of view, high resolution, and scanning time of 12.6 second were used for geometrical reconstruction of cancellous and cortical bone, teeth, and periodontal ligament (PDL) in Mimics software (Materialise Mimics Innovation Suite 21.0).The bones, teeth, PDL, and canine tooth crown were modeled in Mimics and 3-Matic software programs.For this purpose, the cone-beam computed tomography scans with 1-mm slice thickness were transferred to Mimics software.Next, the segmentation tool was used to create masks for the teeth, maxillary bone, and PDL.Then, the "Calculate 3D" command was used to create the 3D model of the components.The data in the STL format were then transferred to Geomagic software and converted to the STP format.Next, the 3D design of a bone-level dental implant (10 Â 4.1 mm; Straumann AG, Basel, Switzerland) was scanned by a 3D scanner.The scans along with the data obtained from Geomagic software were transferred to SolidWorks version 5.1 2019 software.SolidWorks was employed for both creating geometric models and refining them during the image reconstruction process from DICOM and 3D scans, before subsequently inputting into FEA software.The software measurement accuracy was 0.001 mm.All materials were considered homogenous and isotropic.The dimensions of the implanted canine tooth were defined according to the values reported in Wheeler's tooth anatomy and morphology software.The final geometry of the components was then transferred from SolidWorks to ABAQUS FEA software.The mechanical properties (►Table 1) of the components (modulus of elasticity, Poisson's ratio, and density), 12,13 type of analysis (which was dynamic), interactions between the components (the amount of friction), magnitude of compressive and tensile loadings, and boundary conditions were all defined, and meshing of the models was performed.The von Mises stress, shear stress, deformation, and strain were calculated and recorded separately for each occlusal scheme of AGF, PGF, and CG.
In PGF, load was applied laterally to the middle and incisal thirds of the lingual surface of the maxillary canine and the palatal surface of the buccal cusps of the maxillary posterior teeth.
In AGF, load was applied laterally to the lingual surface of the maxillary canine and incisors.
In CG, load was applied to the palatal surface of the maxillary canine.Dynamic load was applied in all three occlusal schemes.Dynamic loads were applied in a two-step process following a time-dependent pattern.In both the vertical load step and the oblique load step, the loads exhibited a ramplike behavior, gradually increasing from 0 to 100 in accordance with the time-dependent characteristics.
To enhance precision while dealing with dynamic loads, we employed C3D10 elements as our primary choice, complemented by C3D15 3D elements, both of which possess polyhedral characteristics.Also, the free mesh model was used due to complex boundaries of the model.Tiny elements were selected due to very low thickness of the implant layer.A 100-N load was applied to simulate functional loads in the three occlusal schemes, and the upper part of the maxilla was considered fixed, as illustrated in ►Fig. 1.The total number of tetrahedral elements was 128,495 and the total number of nodes was 238,154.Data were analyzed by ABAQUS software to calculate the stress transferred to the canine implant and the maxillary bone in the three occlusal schemes.

Results
The maximum and minimum elastic strain and shear stress (►Fig.2) values were noted in the AGF and PGF occlusal schemes, respectively, in all teeth.
As shown in ►Figs.3-5, the maximum total deformation in all teeth was recorded in the AGF occlusal scheme, and the minimum total deformation was seen in the PGF occlusal scheme.
The maximum level of von Mises stress in the CG scheme was recorded in the teeth adjacent to the canine tooth (first premolar and lateral incisor) and the lowest stress was recorded in the first and second molar teeth.Also, maximum elastic strain in CG was noted in the lateral and central incisors, the first and second premolars, and the first molar in the cervical region.The lowest elastic strain was the same in all teeth.Maximum shear stress in CG was noted in the lateral incisor, canine, and first premolar.The lowest stress was the same in all teeth.Regarding total deformation, maximum deformation was noted in the lateral incisors and the first premolars.Thus, maximum stress was recorded in teeth adjacent to the canine tooth.
In the AGF, the maximum von Mises stress was recorded in teeth adjacent to the canine tooth, such that the central and lateral incisors and the first and second premolars showed the highest stress.Also, the lowest stress was recorded in the occlusal three-fourths of the crown of the first molar and the entire second molar.The amount of elastic strain in the AGF was the same in all teeth, but the first premolar and first and second molars of the other side of the jaw showed minimum stress.Also, the maximum shear stress in the AGF was recorded in the lateral incisor, canine, and first premolar teeth.Regarding total deformation, maximum deformation was noted in the lateral and central incisors.Thus, maximum stress was recorded in the teeth adjacent to the canine tooth in the AGF.
In the PGF, the maximum von Mises stress was noted in the first premolars and lateral incisors.Also, elastic strain was higher in the first and second premolars than the other teeth, and was the same in the remaining teeth.Shear stress was the same in all teeth.Also, maximum deformation was noted in the first premolar.
►Table 2 presents the von Mises stress values applied to maxillary canine implant restoration in different occlusal schemes.As shown, the maximum and minimum von Mises stress values in canine implant restoration were noted in the AGF and PGF, respectively.Moreover, ►Table 2 indicates the von Mises stress values applied to maxillary canine implant fixture in different occlusal schemes.As shown, the maximum and minimum von Mises stress values in maxillary canine implant fixture were noted in the AGF and PGF, respectively.
►Table 3 presents the total deformation of restoration in different occlusal schemes.As indicated, the maximum and minimum total deformation of canine restoration occurred in the AGF and PGF, respectively.In addition, ►Table 3 indicates the total deformation of implant in different occlusal schemes.As indicated, the maximum and minimum total deformation of canine implant occurred in the AGF and PGF, respectively.
Regarding the peri-implant bone, the site of maximum stress accumulation in bone around the implant was the same in all occlusal schemes, and close to the implant neck.Maximum total deformation in the peri-implant bone was recorded in the AGF, and minimum total deformation was noted in the PGF (with a small difference with CG).The maximum and minimum von Mises stress values the in periimplant bone were recorded in the AGP and CG, respectively.The maximum and minimum shear stress values in the

Discussion
The occlusal scheme is an important factor that needs to be addressed to improve the prognosis of dental implant treatment. 14,15FEA is a reliable method for assessment of stress and strain distribution patterns. 16This study compared the stress and strain distribution patterns in canine implant and maxillary bone in the AGF, PGF, and CG occlusal schemes by FEA.FEA provides standard models, and has been previously used for assessment of different occlusal schemes. 17The present results revealed a significant difference in the amount of stress applied to the maxillary canine implant and maxillary bone in the three occlusal schemes, and maximum stress was noted in the AGF, while minimum stress was recorded in the PGF scheme.The level of stress in the CG scheme was close to that in the PGF.
The maximum level of von Mises stress in the CG scheme was recorded in teeth adjacent to the canine tooth (first premolar and lateral incisor) and the lowest stress was recorded in the first and second molar teeth.In the AGF, the maximum von Mises stress was recorded in the teeth adjacent to the canine tooth, such that the central and lateral incisors and the first and second premolars showed the highest stress.The lowest stress was recorded in the occlusal three-fourths of the crown of the first molar and the entire second molar.In the PGF, the maximum von Mises stress was noted in the first premolars and lateral incisors.
The results of most previous studies on stress distribution in dental implant, tooth, and bone were in agreement with the present findings.Himmlová et al, 18 Anitua et al, 14 Pellizzer et al, 15 and Takahashi et al 19 reported maximum stress accumulation in the implant neck, and also at the framework-abutment interface, and the terminal end of framework.In the surrounding bone, maximum stress distribution is often in the cortical bone around the implant neck.However, some other studies reported different results.Hidaka et al 20 and Roque et al 21 reported maximum stress distribution in the posterior region.Difference between the present results and those of Hidaka et al 20 and Roque et al 21 can be due to insertion of posterior implants close to the hinge axis of the jaws.Thus, in designing implant-supported fixed partial dentures, the amount of load applied to tooth, bone, and implant should be considered.Bone quality should be well assessed while selecting the treatment type, implant type, and implant site.The implant system used in the posterior region should well resist the masticatory forces. 17ürker et al 17 evaluated the amount of load applied to bone  and implant in different occlusal schemes and reported that the CG applies lower stress than the AGF and PGF.In the present study, the PGF applied minimum stress to canine implant and maxillary bone, and the AGF resulted in maxi-mum stress accumulation in canine implant and maxillary bone.Thus, their results were different from the present findings, which may be due to the difference in the study design and methodology.In this study, we have meticulously evaluated the mechanical parameters (stress and strain) for all model components, ensuring none of them exhibit yielding behavior.Nevertheless, we propose that in future research the PDL be examined using viscoelastic and hyperelastic materials to enhance result precision when compared with the use of elastic materials.Furthermore, we recommend parallel clinical assessments in future investigations to validate numerical outputs from the software by comparing them with experimental data, thus confirming the credibility of our simulation results.

Conclusion
The PGF showed minimum von Mises stress, elastic strain, shear stress, and deformation in canine implant and maxillary bone.Thus, it appears than the PGF is the best occlusal scheme for maxillary canine implant followed by the CG scheme.

Ethical Approval and Consent to Participate
The present study was a finite element study and, therefore, no ethical approval was required.

Fig. 1
Fig. 1 Loading and boundary condition in three occlusal schemes.(A) Canine guidance.(B) Anterior group function.(C) Posterior group function.

Fig. 2
Fig. 2 Strain and stress distribution.(A) Elastic strain in canine guidance occlusal scheme.(B) Elastic strain in anterior group function occlusal scheme.(C) Elastic strain in posterior group function occlusal scheme.(D) Shear stress in canine guidance occlusal scheme.(E) Shear stress in anterior group function occlusal scheme.(F) Shear stress in posterior group function occlusal scheme.
Comparison of Stress and Strain Distribution in Canine Implant and Maxillary Bone in Three Occlusal Schemes Fathi et al.peri-implant bone were recorded in the PGF and CG, respectively.The maximum and minimum elastic strain in the periimplant bone were recorded in the AGF and CG, respectively.
Comparison of Stress and Strain Distribution in Canine Implant and Maxillary Bone in Three Occlusal Schemes Fathi et al.
Comparison of Stress and Strain Distribution in Canine Implant and Maxillary Bone in Three Occlusal Schemes Fathi et al.

Table 1
Mechanical properties of the components Comparison of Stress and Strain Distribution in Canine Implant and Maxillary Bone in Three Occlusal Schemes Fathi et al.

Table 2 von
Mises stress values applied to maxillary canine implant restoration and fixture in different occlusal schemes (in MPa) European Journal of Dentistry © 2023.The Author(s).

Table 3
Total deformation of restoration and implant in different occlusal schemes (in mm) Comparison of Stress and Strain Distribution in Canine Implant and Maxillary Bone in Three Occlusal Schemes Fathi et al.
European Journal of Dentistry © 2023.The Author(s).