Three-Dimensional Finite Element Analysis of Osseointegrated Implants Placed in Bone of Different Densities With Cemented Fixed Prosthetic Restoration

Osseointegrated dental implants have become a favored mode of treatment for rehabilitation of edentulous regions due to their strategic mechanical properties and excellent anchorage to the jaw bone.¹  Despite such implants having good success rates, many long-term studies have reported multiple complications in terms of fracture of implant components, abutment screw loosening, cementation failure, and marginal bone loss after prosthetic rehabilitation. Some of these complications can be ascribed to stress concentration at various interfaces, which in turn has been linked to the differences in rigidity between the components. In this light, interfacial stress transfer between dental implant, surrounding bone, and the other implant components has become one of the important parameters to determine success or failure of a dental implant treatment.¹ 

A key factor in transfer of load from implants is the quality and quantity of the adjoining bone.²  The availability of bone at the edentulous site is an important criterion in implant placement, and it defines the external (quantity/volume) and internal architecture (quality/ density) of the area under consideration. For osseointegration of endosteal implants to occur, adequate bone quantity (height, width, shape) and quality are needed.³  The density of available bone in an edentulous site is a determining factor in treatment planning, implant design, surgical approach, healing time, and initial progressive bone loading during prosthetic reconstruction.⁴ 

The classification scheme for bone quality proposed by Lekholm and Zarb is considered standard in evaluating patients for implant placement. In this system, the sites are categorized into D1 to D4 (high cortical to cancellous) on the basis of jawbone quality.⁴  Bone density is directly related to the strength of bone. A tenfold difference in bone strength is observed from D1 to D4 bone.³ 

The mechanical distribution of stress occurs primarily where bone is in contact with the implant.⁵  As a result of correlation of bone density, bone strength, and bone–implant contact percent, when a load is placed on an implant, the stress contours in the bone are different for each bone density. Sevimay et al⁴  have shown maximum stresses to be incurred by cortical bone and D1 bone exhibiting a more homogeneous distribution of stress along the implant. In D4 bone the stress noted was minimal, with the maximum seen at the crestal cortical portion of the implant.⁴ 

Implant success is influenced by stresses acting along bone–implant, implant–abutment and abutment–prosthesis interfaces.⁶  Increased clinical failure rates (55%) have been reported in poor-quality bone.⁴ 

Implant stability quotients (ISQs) derived from resonance frequency analysis have been used to document implant stability.⁷  Higher ISQ values are seen in D2 bone than in D3 and D4 bone. This shows the influence of bone density on the stability of an implant. The ISQ values for secondary stability are higher than that of primary stability for each bone type.

A successful implant typically has an ISQ >65. An ISQ <50 may indicate failure or increased risk of failure. Herekar et al⁸  found the mean ISQ for secondary stability to be 82 in D2 bone and around 64.5 in D4, showing that even after osseointegration implant stability was lower in cancellous bone. Trisi et al⁹  showed that, after osseointegration, the amount of micromotion was higher in cancellous bone than in cortical bone.

Though finite element analysis studies have shown the effect of different bone densities on stress distribution in an implant-supported crown, there is a dearth of information in the literature regarding the effect of stress generated by implants placed in bone of different densities on fixed prostheses cemented onto the implants. Studies have also shown the stability of osseointegrated implants to be lower in cancellous bone, indicating that there is more micromovement of implants in cancellous bone than in cortical bone. Hence, the purpose of this 3-dimensional (3D) finite element analysis study is to assess whether the stress and micromovement produced by implants placed in bone of different densities produce affect the prostheses cemented onto them.

Segments of maxillary bone corresponding to the molar/premolar area were modeled from computerized tomography (CT) images for which, the physiological parameters of cancellous and compact bone were evaluated with Materialise Mimics Research 20.0 (Materialise Corporation, Leuven, Belgium) and Solidworks 2016 (Solidworks Corporation, Waltham, Mass). Bone segment conforming to premolar region was modeled as 2 layers, an outer shell representing cortical bone of 2 mm thickness, and an inner volume representing cancellous bone, assumed to be perfectly connected with the cortical layer. Bone segment for the molar region was modeled as a homogeneous cancellous bone. Gingival soft tissues were not modeled. The length of bone segment in the mesial-distal direction was approximately 35 mm, and the average height was about 26 mm.¹⁰  The model was constructed as a homogeneous and isotropic block possessing linear elasticity. Two distinctly different bone qualities (D2 and D4) were used in this model since these bone qualities are often encountered in the posterior maxilla.⁴ 

The Adin Touareg–S, spiral dental implant (Adin Dental Implant System Ltd, Afula, Israel) was selected for the simulation. It is a tapered implant with a spiral tap that condenses the bone during placement for immediate stability. It features an aluminum oxide blasted/ acid etched surface treatment, and its unique design provides good primary stability even in Type IV bone. Two implants of 4.2 × 10 mm, abutments, and connecting screw were subjected to micro-CT scanning at the Indian Institute of Science, Bangalore, India. (Figure 1) The 3D geometric model of the implants and components was constructed from DICOM (Digital Imaging and Communications in Medicine) format CT slices of 0.7 mm thickness through image segmentation and 3D reconstruction using Materialise Mimics Research 20.0. Each component of the dental implant system was then assembled and reconstructed using the computer-aided design software Solidworks 2016.

The model consisted of 2 implants, abutments, and connecting screws, each secured in the second premolar and second molar regions of the bone. The inter-implant distance was kept as 20.6 mm, and the implants were connected by a 3-unit fixed prosthesis. A bonded type of contact was used to describe the interfaces—abutment–implant, connecting screw, and implant–bone. Bonded contact was incorporated to ensure that there was no movement between each component. The bonded type simulated perfect osseointegration, in which the implant and the surrounding parts were fully integrated so that neither sliding nor separation in the implant–bone interface was possible.¹¹ 

The simulated 3-unit fixed prosthesis model consisted of framework material made from cobalt-chromium. The mesiodistal width of the prosthesis was 26 mm (Table 1). The thickness of metal used in the study was 2 mm. A 3D finite element model of 3-unit implant-supported fixed dental prosthesis replacing the maxillary first molar with maxillary second premolar and second molar as the abutments was designed.

After construction of the model, mesh generation was done, using ANSYS pre-processor (ANSYS 19.1, ANSYS, Canonsburg, Penn; Figure 2) and the model was divided into elements and nodes (Figure 3; Table 2). The fixed prosthesis was meshed with an element size of 0.5 mm. Material properties were defined and assigned to each component of the framework, cementing medium, abutment, implant, and bone section (Table 3).

Finite element simulations for the implants were developed considering static and dynamic axial loads that were applied uniformly on the entire fixed prosthesis. For static analysis a load of 115 N was applied. For dynamic analysis time-dependent masticatory load a sinusoidal cyclic load (0 N-115 N-0 N) was applied (Figure 4).

Stresses were calculated using von Mises criteria (equivalent stress) and calibrated in megapascals. Deformation was calibrated in millimeters. These were represented in color-coded maps from blue to red (showing minimum to maximum stress/deformation), depicted as contour lines with different colors connecting stress/deformation points between certain ranges. These values were obtained for static and dynamic loading conditions

The von Mises stress distribution and deformation in static and dynamic loading for different components (Tables 4 through 7) were as follows.

As shown in Figures 5 through 8, maximum von Mises stress was noted in the upper part of the implant at its neck in relation to D2 bone versus D4 in both loading conditions (8.64 MPa in dynamic and 6.52 MPa in static), with the amount of stress being much higher in the dynamic loading condition. The maximum amount of deformation was seen in relation to the coronal part of implant in approximation to the abutment under both loading conditions. This was higher in D4 (2.22 × 10^–3 mm) bone than D2, in both dynamic and static loading.

As shown in Figures 9 through 12, von Mises stress noted at the implant–bone interface was concentrated apically in D4 bone and was distributed more homogeneously in D2 bone, showing that cortical bone endured more stress than cancellous bone. This interfacial stress was higher in static than in dynamic loading. As for the deformation at the bone–implant interface, maximum amounts were seen in D4 bone at the crestal region, which was much higher than in D2 bone. This was almost similar in static and dynamic loading.

As shown in Figures 13 through 16, maximum von Mises stress was seen toward the apical portion of the abutment closer to the implant in relation to D2 bone, in both loading conditions. The stress was higher in static loading (20.24 MPa) than in dynamic loading (18.14 MPa)

Deformation values (2.5 × 10^–3 mm) for abutment was higher in D4 bone. This was significant along the coronal portion of the abutment, which was in line with the load applied and was comparable in both loading conditions.

As shown in Figures 17 through 20, although maximum von Mises stress was recorded in D2 bone, there was an even distribution of stress along the connecting screw in both densities of bone. It was notably higher in static loading (10.3 MPa) than dynamic loading. The maximum amount of deformation happened at the coronal portion of connecting screw in contact with the abutment in D4 bone (2.33 × 10^–3 mm) and was almost similar in both loading conditions.

As shown in Figures 21 through 24, the amount of stress exhibited by cementing medium in relation to D4 (1.071 MPa) bone was higher in dynamic loading; in static loading, it was greater in D2 bone (2.28 MPa). These maximum stresses were recorded at the apical portion of the cementing medium, in contact with the abutment. Among all the components, the value of stress noted in the cementing medium was the minimum.

As for the deformation, the maximum value was seen in the D4 region in both static and dynamic loading conditions, and the amounts were also almost similar. Though in dynamic loading the deformation was highest at the coronal portion of the cementing medium in contact with the abutment, in static loads, the cement over the entire abutment was reported to exhibit deformation.

As shown in Figures 25 through 28, maximum von Mises stress was noted in relation to D2 bone, which was almost double that noted in D4 bone. This was similar in both loading conditions (12.32 MPa in dynamic and 13.57 MPa in static). The areas of stress concentration were seen at the most apical and coronal interfaces of the abutment and the prosthesis.

The maximum amount of deformation was seen in relation to D4 bone in both loading conditions, and this occurred at the distocoronal half of the prosthesis along the second molar region.

Maximum von Mises stress in the entire unit (Figures 29 through 32), taking into consideration all the components, showed that the highest stresses were concentrated at the apical part of the abutment in close proximity to the implant in relation to D2 bone under both loading conditions. The maximum deformation for the entire unit was noted at the abutment–prosthesis interface in relation to D4 bone along the distal coronal surface of the unit in relation to second molar region.

Complex clinical situations can be simulated well with finite element method; hence, its use in implant biomechanical analysis has become the standard. A finite element model is defined by several characteristics, such as dimension (1-dimensional, 2-dimensional [2D], 3D), number of element nodes, and the associated approximation functions. In this study, 3D models were used over 2D models, owing to their closeness to reality in geometric modeling accuracy, load application, and boundary conditions. The more detailed the representation of its structural integrity, the more reliable the numerical results obtained.

For the success of dental implants, reliability and durability of interfaces (implant–bone, implant–abutment, abutment–prosthesis) and the stresses concentrating at these interfaces play a pivotal role.¹⁴  Stresses around osseointegrated dental implants are influenced by many biomechanical parameters, such as loading condition, type of implant and prosthesis, implant geometry, surface texture, density and volume of adjoining bone, and contact established at the bone–implant interface.¹⁵  In treatment planning for implant placement, density of bone is a key factor to consider. Density of bone is categorized into D1 to D4 (highly dense cortical to soft cancellous type).⁵  As stated by Misch,³  D1 bone is 10 times stronger than D4 bone. The rigidity and hence the elastic moduli of cortical (D1) bone is significantly greater than cancellous (D4) bone.

Several studies have been performed to analyze the stresses produced around a single tooth implant, its distribution along the bone–implant interface. and the way stresses are distributed in cortical and cancellous bones. It has been demonstrated that the highest stresses are concentrated in the cortical bone and that the stresses tend to concentrate in areas where there are significant differences in elastic moduli of adjacent materials. Analysis on the influence of bone quality on the distribution of stresses in an implant-supported crown has shown maximum von Mises stress to be concentrated in the crestal cortical portion in all 4 densities (D1–D4) of bone, with no stress within the spongy bone. In D3 and D4 bone qualities, the highest values of von Mises stresses tend to concentrate at the neck of the implant and are distributed locally. But in the case of D1 and D2 bone densities, the stress distribution is more homogeneous and is seen in the entire bone. Hence, under the influence of loading, stress in the compact bone is greater than stress in cancellous bone, and this mechanism of stress transmission to the bone is directly proportional to the Young modulus. Hence, stresses incurred by more rigid bone—that is, cortical bone—is higher than soft cancellous bone.¹⁶ 

Studies have demonstrated significant differences in displacement of implants in different bone densities, with more micromotion occurring in less dense bone when subjected to occlusal loading.¹⁷  This is well correlated to the secondary stability quotient, which is higher in D2 bone than in D3 and D4 bone.⁸  It is predicted that placing implants in bone with greater thickness of the cortical shell and greater density of the core has resulted in less micromovement of the implants after loading.¹⁸ 

Comparative studies on stress distribution in implant-supported fixed prostheses under static and dynamic loading have shown that the amount of von Mises stresses induced by dynamic loading on the dental prosthesis is almost double that of static loading. The maximum stresses are mostly incurred at interfacial regions that included the framework–abutment interface, the interface between the abutment and the implant, and the coronal portion of the implant in contact with the crestal cortical bone. These interfacial regions comprise the areas where differences in modulus of elasticity are exhibited.¹⁴ 

A review of the literature has identified studies demonstrating the influence of varied bone densities on stress and deformation in single implant-supported prostheses. Taking into consideration the differences in stress and deformation exhibited by osseointegrated implants in different bone densities, the current study sought to evaluate the distribution of these factors in an implant-supported fixed prosthesis that was cemented onto implants placed in 2 different densities of bone (D2 and D4). This was evaluated under both static and dynamic loading conditions using a 3D finite element analysis method.

From the results, it is noted that when a uniform static or dynamic load is applied onto a 3-unit fixed partial prosthesis cemented onto 2 implants placed in 2 different densities of bone (D2 and D4), the stress values are higher for all the components in relation to D2 bone region, which is a highly cortical bone.

This result, showing stress values being higher in dense cortical bone, is in accordance with findings of previous studies. Ichikawa and colleagues¹⁶  demonstrated that under the influence of loading, the stresses tended to concentrate in denser bone, and this was directly proportional to the elastic modulus. The higher the elastic modulus, the more rigid the material and, hence, the greater the stress incurred.¹⁶  Sevimay et al⁴  showed the maximum stresses to be located within the cortical bone surrounding the implant, with no stress within the spongy bone. The study by Kitagawa et al¹  also showed that von Mises equivalent stress increased as the Young modulus of cortical bone increased. Thus, cortical bone that exhibits higher elastic modulus than cancellous bone tends to sustain more stress.⁴  We found similar results in the present study, where the stresses incurred by the implant, implant components, and bone in relation to D2 (cortical bone) are much higher than that in D4 (cancellous bone).

The results obtained for deformation showed that applying a uniform static or dynamic load on a 3-unit fixed partial prosthesis cemented onto 2 implants placed in 2 different densities of bone (D2 and D4) causes more deformation of the unit in relation to D4 (cancellous bone) region. This was in agreement with a study by Karl et al,¹⁷  where a single implant was placed in different bone densities and the level of micromotion was calculated. That study found that the amount of micromotion of osseointegrated implants was higher in less dense bone.¹⁷  In yet another study by Herekar and colleagues,⁸  the secondary stability of implants in denser bone was reported to be higher than that in softer bone, implicating the displacement of implants to be greater in cancellous bone when subjected to loading.

Evaluation of von Mises stress of the individual components showed that the maximum stress was borne by the apical portion of the abutment in approximation to the implant and bone. This is seen in relation to the D2 region in both static and dynamic loading. Despite these results showing a relative similarity to the study by Djebbar et al,¹⁴  who had explained with finite element analysis that the maximum stresses were incurred at interfacial regions that included the framework–abutment interface, the interface between the abutment and the implant at the connection between the shank and first thread of the abutment, and the coronal portion of the implant in contact with the crestal cortical bone, certain differences are noted compared with the present study. The reason could be attributed to the mode of retention of the prosthesis, where, in the current study, it is by means of a provisional cementing medium compared with the previous study by Djebbar et al,¹⁴  where it was by screw retention. Hence this can be explained in terms of rigidity/resiliency of the structures overlying the abutment. In a study by Sertgöz,¹⁹  it was demonstrated that using resilient materials for the superstructure increases the stresses within the prosthetic components. In yet another study by Eskitascioglu et al,²⁰  it was shown that the stresses were concentrated on the metal framework, and minimal stresses were transmitted to the underlying structures. Hence, these studies explained the use of rigid materials as superstructures to prevent prosthetic failure of other components.²¹  In the current study, though the framework incorporated a rigid chrome-cobalt material, the cementing medium at the interface of the framework and the abutment was a highly resilient material with a very low Young modulus (0.22 GPa) compared with that of the titanium abutment and the metal framework. Hence, when occlusal loads were applied, though the framework tended to dampen the stress, the cementing medium could cause concentration of stresses on the abutment. The interpretation of more stress at the apical portion of the abutment along the interface with implant can be attributed to the difference in elastic modulus of the implant–abutment interface and the crestal cortical bone.

The maximum deformation for the entire unit was noted at the abutment–prosthesis interface in relation to D4 bone along the distal coronal surface of the unit in relation to the second molar region in both static and dynamic loading conditions. This can be explained in terms of shear modulus of the cementing medium. A study by Stegaroiu et al²²  showed that materials like resin with low shear modulus caused more bending of the prosthesis, thus causing more stress transmission to the implant–abutment units and bone. This can be correlated with the present study wherein the cementing medium with an extremely low shear modulus could cause excess movement between the abutment and the prosthesis. Added to this, the D4 bone being less rigid could augment the deformation occurring at this interface, hence causing failure of the prosthesis. Other interfaces, implant–abutment and implant–bone being more rigid than the abutment–prosthesis interface apparently exhibited lesser deformation. The comparative evaluation for static and dynamic loading conditions indicated an unpredicted pattern in distribution of stress and deformation of the entire unit in relation to D2 and D4 bone. Though the maximal stress was seen at the region of the abutment in both loading conditions in relation to D2 bone, the stress values were comparatively higher in static than dynamic loading. This is in contrast to the studies by Kayabashi et al⁶  and Djebbar et al,¹⁴  where the stress levels were higher in dynamic than static loading.

But these studies were done on screw-retained prostheses, and the load was applied only to a section of the prosthesis. The present study was done on cement-retained prostheses, and the load was applied uniformly on the entire prosthesis simultaneously. Hence, in static loading, due to the constant high load application, the unit would recuperate to normalcy at a lower rate, thereby increasing the concentration of stresses. This could have led to higher stress values in static than dynamic loading. As for deformation, the amount was higher in dynamic loading in relation to D4 bone along the abutment-prosthesis interface.

Finite element analysis was considered for this study, as this was a new conception. Biomechanical aspects are difficult to evaluate using clinical observation/experimental approaches with little information and sample variations, hence finite element analysis was chosen as a complementary tool for understanding the detailed mechanical responses for such biological investigations.²³ 

Implants placed in bone of 2 different densities and connected by a fixed prosthesis is not an uncommon occurrence. The biomechanics of this condition follows the same mechanism as that of a natural tooth with a good foundation support connected to a periodontally weaker tooth or an implant connected to a tooth. These scenarios can be explained by means of a cantilever mechanism, where the cantilevered end simulates a periodontally weaker tooth. In these situations, studies have shown higher stresses to be concentrated in teeth with good periodontal support or the implant (in case of tooth implant-supported prosthesis), which is in the region away from the cantilever.²⁴  Deformation occurs along the cantilevered end. Hence, the entire unit acts like a Class I lever. The current study, which involved placing implants in 2 different bone densities also follows a similar pattern wherein the implant in relation to a less dense region (D4) acts like a cantilever and stress concentrates in denser regions (D2).

Diagnosis and treatment planning are of paramount importance in these conditions. It would be ideal to incorporate longer healing periods and progressive loading protocols in such situations.²⁵  With regards to the prosthetic phase, planning has to be done such that, under occlusal load, the less rigid and weaker elements are protected from deformation. Indirectly, this can also be achieved by preventing excess stress concentration in the more rigid components. Prosthetic planning in terms of implant protective framework and superstructure can be considered wherein the prosthesis in relation to D4 bone does not undergo a substantial amount of deformation, thereby protecting the underlying implant and its components.

Taking into consideration the mode of retention, in the current study, a provisional cement with a very low modulus of elasticity was incorporated. Since the results have shown maximum deformation happening at the abutment–prosthesis interface, it can be connected to the cementing medium causing this deformation. So, when planning the type of retention for the prosthesis, use a cement with a higher modulus of elasticity or a screw-retained prosthesis, thereby eliminating the cementing medium.

Implants were assumed to be perfectly osseointegrated to bone. However, a 100% ratio of osseointegration between the implant and bone does not occur in a clinical setting. The prosthesis has been designed as a metal framework, without incorporating the superstructure, to minimize the number of components and hence the material properties. This can reduce the accuracy of the results obtained.

Within the limitations of this study, the following conclusions can be drawn:

1. von Mises stress was greater in D2 than D4 bone, and in D2 bone the component with higher stress was the abutment. Stress was more concentrated along the apical region of the abutment in proximity to the bone and implant.

2. Deformation greater in D4 than D2 bone, and in D4 bone the abutment–prosthesis interface underwent more deformation.

3. When comparing static and dynamic loading, the overall stress values were higher in static load in the D2 region for all components, except at the implant region, where stress was marginally higher in dynamic loading. As for deformation, it was higher in dynamic loading in D4 bone for all components, except along the region of abutment, cementing medium, and abutment prosthesis interface, where it was marginally higher under static loading in D4 bone.

Abbreviations

CT:

computerized tomography

ISQ:

implant stability quotient

The authors declare no conflicts of interest.