3D finite element analysis of immediate loading of single wide versus double implants for replacing mandibular molar.

PURPOSE: The purpose of this finite element study was to compare the stresses, strains, and displacements of double versus single implant in immediate loading for replacing mandibular molar.
MATERIALS AND METHODS: Two 3D FEM (finite element method) models were made to simulate implant designs. The first model used 5-mm-wide diameter implant to support a single molar crown. The second model used 3.75-3.75 double implant design. Anisotropic properties were assigned to bone model. Each model was analyzed with single force magnitude (100 N) in vertical axis.
RESULTS: This FEM study suggested that micromotion can be controlled better for double implants compared to single wide-diameter implants. The Von Mises stress for double implant showed 74.44% stress reduction compared to that of 5-mm implant. The Von Mises elastic strain was reduced by 61% for double implant compared to 5-mm implant.
CONCLUSION: Within the limitations of the study, when the mesiodistal space for artificial tooth is more than 12.5 mm, under immediate loading, the double implant support should be considered.

INTRODUCTION

To support complete arched fixed implant supported restorations for completely edentulous patients, threaded root form osseointegrated implants were designed.[1] In partially edentulous areas, to support single implant supported crowns and fixed partial dentures, this type of implant is used.[2] Many in vitro and animal studies attempted to predict the biomechanical and clinical behavior of dental material and the technique associated with implant-supported prosthesis.[345] In vitro methods include conventional in vitro model analyses,[6] photoelastic analyses,[478] and finite element analyses.[9] In vitro studies are less complicated and less expensive than clinical trials and produce results relatively quickly compared to randomized controlled trials.[10] Finite element method FEM analysis has been used to provide analytical solutions to problems involving complex geometric forms.[9]

Posterior teeth have two or three roots, having 450-533 mm2 total anchorage area in good-quality bone,[11] whereas the surface area of a 3.75-mm implant varies from 72 to 256 mm2, depending on its length. The molar has a crown surface area of approximately 100 mm2, whereas a 3.75-mm implant has cross-sectional area of 10.9 mm2 The masticatory forces are exerted at an angle mesiodistally and buccolingually, creating bending and torquing vectors[12] on the implant, whereas the tooth can dissipate the occlusal forces efficiently. The cross-sectional area of two 3.75 mm implants is 21.9 mm2 and of two 4-mm implants is 19.6 mm2, whereas for a single 5-mm implant, it is 19.6 mm2.[13] For the placement of implant with a wide diameter, the dimension of the buccolingual width of the bone should be more.[14] The wide implant is primarily a means of salvaging a procedure when the previous implant failed, a site had been overenlarged, or the operator desired to place an implant in a recent extraction socket.[1516] Hence, high abutment fracture and loosening of screws are seen in implants used as single molar replacements. Although placing of double implant is technically more demanding than using wide implants, double implants more closely mimic the anatomy of roots being replaced, and double the anchorage surface area and also reduce the rotational forces. Usage of double implants instead of single wide-diameter implant might help us to reduce the risk of implant failure and increase the ability of posterior implant to tolerate occlusal forces.[13]

Immediate functional loading of dental implants has been advocated by several authors in order to minimize the delay between surgical and prosthetic phases.[1718] Immediate loading is the placement of the prosthetic restoration in functional or nonfunctional loading immediately or within 48 h of surgical procedures. Short-term prospective studies on immediate loading of wide-body implants supporting single mandibular molars have reported a cumulative survival rate of 96%.[1920] To our knowledge, there are no studies till date that compared single wide-diameter implant with double implant under immediate loading conditions. The purpose of this finite element study was to compare the stresses, strains, and displacements of double versus single implant in immediate loading for replacing mandibular molar.

MATERIALS AND METHODS

Two 3D FEM models were made to simulate implant designs. The first model used 5-mm-wide diameter implant to support a single molar crown and incorporated 44,026 nodes and 23,569 elements. The second model used 3.75-3.75 double implant design consisting of 71,577 nodes and 37,360 elements. The crown dimensions were derived from the average dimensions of mandibular first molar.[21] 3D models were meshed using tetrahedral and octahedral elements and modeled by identifying the exact location of nodes after mathematical calculation by considering the inclination of threads. Each implant design consisted of fixture of 10-mm length, incorporating V threads with a thickness of 0.2 mm, and having a constant pitch length and height of 0.8 mm and 0.3 mm, respectively, as shown in Figure 1a. Tapered implants with crestal diameters of 3.75 and 5 mm were used. Corresponding apical diameters were 2.4 and 3.1 mm, respectively. Abutment of height was 5.5 mm with a metal ceramic crown of dimensions 13.5 mm mesiodistally and 10.5 mm buccolingually [Figure 1b], metal of thickness 0.4 mm, and layer of cement between abutment and crown of thickness 0.3 mm. A smooth surface collar height of 1.8 mm was incorporated. The implant with the crown was placed in a bone block of height 18.5 mm and width 17.4 mm. The bone consisted of 2 mm of cortical bone and the rest cancellous bone [Figure 1c]. Cortical and cancellous anisotropic properties were applied to the bone. The only difference between these two models was the number and diameter of implants. Each model was analyzed with 100 N force applied 45° oblique to the vertical axes directed at central fossa of the crown [Figure 1d]. The boundary conditions were defined by restraining all nodes at the base of 3D models. The modeling analyses were performed using a software program, ANSYS workbench version 11. The material properties were derived from other studies[222324] [Table 1]. Coefficient of friction of 0.6[25] was applied to the bone models.

Figure 1

(a-d) Implant dimensions, crown dimensions, bone block, and loading condition, respectively

Table 1

Material properties assigned to the implant models

RESULTS

For each implant design, the loading process generated immediate movement. The results obtained in this study are shown in Table 2. The two designs experienced significantly different Von Mises stresses, Von Mises elastic strain, and micromotion or total deformation. The total deformation for double implants was 1.3 μmm compared to 3.8 μmm for 5-mm-wide implant [Figures 2 and 3]. The sliding distance of double implants was found out to be 3.6 μmm compared to 7.4 μmm for 5-mm implant [Figures 4 and 5]. The maximum and minimum principal stresses for double implant were 2.676 MPa and −21.58 MPa, respectively, compared to 11.76 MPa and −31.47 MPa, respectively, for 5-mm implant [Figures 6a & b and 7a & b]. The Von Mises elastic strain was 1.6 μmm for double (3.75-3.75) implant compared to 5 μmm for 5-mm implant [Figures 8 and 9]. The Von Mises stress was 47.58 MPa for double implant compared to 186.2 MPa with 5-mm implant [Figures 10 and 11].

Table 2

Results obtained for wide and double implants

Figure 2

Total deformation of double implants

Figure 3

Total deformation of 5-mm implant

Figure 4

Sliding distance of double implants

Figure 5

Sliding distance of 5-mm implant

Figure 6

Figures 6: (a and b) Minimum principal stress of 5-mm and double implants

Figure 7

(a and b) Maximum principal stress of 5-mm and double implants

Figure 8

Von Mises strains of double implants

Figure 9

Von Mises strains of 5-mm implant

Figure 10

Von Mises stresses of double implants

Figure 11

Von Mises stresses of 5-mm implant

DISCUSSION

The present study compared the stresses, strains, and displacements of double versus single implant in immediate loading for replacing mandibular molar. The present study design specifically addressed the problem of long-span edentulous space of more than 12.5 mm.

The finite element method is a computer-based technique in which a structure is broken down into many small simple blocks or elements. The behavior of individual elements is assessed by computer from the solutions. Hence, the stress and deflection of all parts of the structure can be calculated.[26]

Immediate functional loading has gained importance, and comparable results were found in single-stage surgical procedure as compared to the usual two-stage protocol for implant placement.[27] Osseoconductive implant surface, good primary stability, and controlled loading conditions are the expected advantageous results for immediate function.[28] The most commonly lost teeth leading to psychological discomfort to the patient are the mandibular first molars, and thus, they were selected for implant placement. Promising results with immediate function for single mandibular molar replacement are available.[19] In vitro and animal studies provide evidence that immediate loading may enhance bone healing and mineralization.[29]

Wide-diameter implants were used initially to replace standard-diameter implants.[14] The wide-diameter implants were introduced due to their high mechanical stability as compared to that of the standard-diameter (3.75) implants. This has led to better success with excellent osseointegration due to increased surface area at the bone–implant interface.[30] Despite encouraging data obtained from finite element analysis and animal studies, the initial experience with machined-surface wide-body implants showed lower success rates than those reported for standard-sized implants. A failure rate ranging from 10 to 19% in the mandible and from 9 to 29% in the maxilla was presented by earlier clinical studies.[3132] Furthermore, an augmented marginal bone resorption was observed around the wide-body implants placed in the posterior mandible, as compared to the standard-sized implants.[32] Clinical reports have stated wide implants tend to fail more frequently[33] when the posterior edentulous ridges are narrow. The placement of wide implants will further lead to bone loss in these situations.[34]

With respect to the implants’ length and width, the crown size restored to one implant has certain discrepancies. When the size of the crown exceeds the implant's long axis, cantilevers are generated. This leads to screw loosening and eventually implant fatigue. The ideal replacement is with two implants for a single molar. According to Saaduon et al.,[35] a minimum of 12.5-14.0 mm of interdental space is needed to successfully replace double standard implants for a missing molar.

For immediate loading situations, the coefficient of friction was set to 0.6. In this frictional contact, tensional forces are not transferred by contact zones, but they transfer only pressure and tangential frictional forces.[36] Under delayed loading, the FEA models bonded the implants perfectly to cortical and cancellous bones. They showed optimal osseointegration at bone–implant interface.[3738] However, the conditions are different under immediate loading conditions. Here, certain minor displacements at the bone–implant contact surface are present. Frictional contact is incorporated in this study to simulate the immediate load and to stabilize the implant.

This study focused on the values of Von Mises stress and Von Mises strain on the surrounding bone.[36] The property of transverse isotropy was given to the cortical and cancellous bone and modeled as homogenous materials. The elements were 10-node tetrahedral structural solid p-elements (ANSYS solid 148) with three translational degrees of freedom at each node. Boundary conditions included constraining all three degrees of freedom at each of the nodes located at the most external mesial or distal aspect of the model. Loading was simulated by applying a vertical load of 100 N to the most coronal part of the crown through the long axis of the restoration and implant.[39] It should be noted that great spectra of vertical loads/forces have been reported for patients with endosseous implants (mean range: 91-284 N), and the loads appear to be related to the location of the implant, as well as to food consistency. In finite element analysis, a combined load (oblique occlusal force) along with the usual axial loads and horizontal forces (moment causing loads) is used, as oblique force gives local stresses in the cortical bone,[34] which is more realistic in directing occlusal forces than the others. In this study, 45° oblique loads were considered and the location for force applications was on central fossa. Measured bond strengths of many base metal–porcelain combinations are comparable to those of noble alloy–porcelain combinations.[40] Co–Cr alloys have high tensile strength (552-1034 MPa) and high elastic modulus (200.000 MPa). The Co–Cr alloy used in the present study was also used by Williams et al.[41] These authors stated that Co–Cr alloy allowed more uniform distribution of stress within the framework, providing more efficient and durable load transfer. Porcelain is a commonly used material for occlusal surfaces.[42] Cibirka et al.,[42] in an in vitro simulated study, compared the force transmitted to human bone by gold, porcelain, and resin occlusal surfaces and found no significant differences in the force absorption quotient of the occlusal surfaces among these three materials. Therefore, porcelain was used for the occlusal surface.

The process of loosening failure in implants is one of the important determinants for the lack of primary stability.[43] Relative micromovements of about 100 or 200 μm delivered by physiologic loads in bone–implant interface may be detrimental.[44] These relative micromovements in the bone–implant interface need accurate evaluation, as they are of more concern in preclinical and clinical contexts.[26] Micromotion of dental implant under immediate loading is reflected by evaluation of the gap distance and sliding distance. The gap distance and sliding distance for double implant were significantly less compared to those for single wide implant, with 12% and 51% reduction, respectively. The micromotion of double implant compared to that recorded for single wide implant was decreased by 65.78%. This FEM study suggested that micromotion can be controlled better for double implants compared to single wide-diameter implants. When the mesiodistal space for artificial tooth is more than 12.5 mm, the double implant support should be considered. When the load was applied directing the implant axis, initial stability of double implant was clearly superior.

The ultimate stress of the cortical bone has been reported to be higher in compression (170 MPa) than in tension (100 MPa).[45] The maximum principal (tensile) and minimum principal stresses (compressive) for double implants and 5-mm implant were within the limits of ultimate stress.

Seong et al.[4] reported least mesiodistal (MD) strain with 5-mm implant design compared to double implants. Authors stated that deeper analyses of experimental results, specifically related to MD strains were required. The results of the present study implied the opposite. Better mesiodistal support for double implant compared to artificial crown arrangement is suggested using the principles of engineering.[5] Double implants more closely resemble the naturally occurring anatomic forms of mandibular molar.[10] Rangert and Sullivan[46] recently suggested that as a result of bending moments, molars replaced by one implant may fracture. They suggested that compared to single-standard 3.75-mm implant, wide implants or multiple implants may withstand the occlusal forces on molars better. In engineering terms, endosseous implants act like a bar elastically supported by the surrounding bone. If the applied load is better distributed across the implant and the host bone, the better will be the bony support of the implant. But this only applies if all of the host bone is tightly bound to the implant. Compressive and tensile strains are more evenly distributed under delayed loading protocol, which results in a bonded bone implant interface BII because of osseointegration. Concentration of stresses at the areas where the implant surface contacts the bone during lateral loading is seen under immediate loading conditions. Immediate loading shows abnormally low strains appearing at noncontact sites.[47] Consequently, in immediate loading protocol, Von Mises stresses and strains were found, especially from middle to apical third of the implant. The Von Mises stress for double implant showed 74.44% stress reduction compared to that of 5-mm implant. The biologic response resulting in resorption and remodeling of the bone tissue is stimulated by strains at bone–implant interface.[45] The physiologic loading zone has been reported to be in the 1000-3000 microstrain range.[48] The Von Mises elastic strain was reduced by 67.96% for double implant compared to 5-mm implant. The reduction in Von Mises strain in double implant compared to single wide-diameter implant is roughly comparable to the experimental results of the study by Seong et al.[4] The application of force is directed to the central fossa, which extends along the junctions of slopes of all cusps except mesial and distal cusps. In FEM analysis, the force cannot be directed at a point; so, there was dissipation of force along the central fossa as well as to the distal triangular minor fossa, which can be well appreciated from double-implant models, with the distal implant showing the maximum stress and strain compared to the mesial implant, but within limits. Minimum of 7-mm ridge width throughout its length is required by wide-diameter 5-mm implant.[16] Screw loosening occurred primarily in the single-implant situation and may also be an indicator of overload. Strengthening the screw joint may induce higher stress to implant–bone interface.[12] Therefore, the use of two implants for the reduction of implant–bone stress is a biomechanically more advantageous solution. It not only minimizes the mechanical problems such as screw loosening but also lowers the stress on implant and bone.[13]

Nevertheless, there were some limitations in the study. The dynamic loads of chewing movements of the mandible were not applied and would cause changes in stress patterns. Flexure of posterior mandible during the opening and closing of mandible, along with loads applied were not considered.

Finally, biologic factors, such as potential difficulty in maintaining proper oral hygiene with the double-implant design, which resembles a molar with an advanced furcation invasion, were not considered, and oral hygiene problems may outweigh any mechanical advantages to this approach.[10]

CONCLUSIONS

Because every molar is not equally wide and long, it is impossible to provide optimal support using only one implant; however, two implants replace the missing tooth roots more naturally in position and direction. Within the limitations of this FEM analysis, the following conclusions were drawn for immediate loading of mandibular molar, replacing edentulous space of more than 12.5 mm.

Double (3.75-3.75) implants were better in eliminating stresses and strains than 5-mm-diameter implant

The micromotion was reduced, enhancing primary stability for double implants, and was lower than 100 μm, reducing crestal bone loss and leading to better osseointegration

The double implants give wider support to a molar restoration in both the mesiodistal and the buccolingual dimensions. This should help to preserve and maintain crestal bone and should also provide better support against buccolingual and mesiodistal bending by eliminating the mesiodistal cantilever.