This study aimed to evaluate the effects of different tapering angles of an immediately loaded wide-diameter implant on the stress/strain distribution in bone and implant after implant insertion in healed or fresh molar extraction sockets. A total of 10 finite element (FE) implant-bone models, including 8.1-mm diameter implant, superstructure, and mandibular molar segment, were created to investigate the biomechanical behavior of different implant taper angles in immediate and delayed placement conditions. The degrees of implant taper ranged from 2° to 14°, and the contact conditions between the immediately loaded implants and bone were set with frictional coefficients (μ) of 0.3 in the healed models and 0.1 in the extracted models. Vertical and lateral loading forces of 189.5 N were applied in all models. Regardless of the degree of implant tapering, immediate loading of wide-diameter implants placed in molar extraction sockets generated higher stress/strain levels than implants placed in healed sockets. In all models, the von Mises stresses and strains at the implant surfaces, cortical bone, and cancellous bone increased with the increasing taper angle of the implant body, except for the buccal cancellous bone in the healed models. The maximum von Mises strains were highly concentrated on the buccal cortical struts in the extracted models and around the implant neck in the healed models. The maximum von Mises stresses on the implant threads were more concentrated in the non-tapered coronal part of the 11° and 14° tapered implants, particularly in the healed models, while the stresses were more evenly dissipated along the implant threads in other models. Under immediate loading conditions, the present study indicates that minimally tapered implants generate the most favorable stress and strain distribution patterns in extracted and healed molar sites.

Introduction

Over the past decade, the primary stability of implants was tremendously improved through modifying the surgical protocol, implant surface characteristics, and design. The ability to achieve and maintain a high primary stability has caused a paradigm shift in the way implants were traditionally placed and loaded. Shortening the treatment time has introduced new terms in the oral implant vocabulary. Terms such as “immediate” or “early” placement and loading were used to describe the different treatment modalities that attempted to meet patients' demands for a shorter period of intervention.14  One of the most popular protocols combines immediate implant placement with immediate restoration/loading (the bimodal approach, Figure 1).3  Immediate placement was defined as placing the implant in a fresh extraction socket on the same day of surgery,1  and immediate restoration/loading referred to placing the implant restoration within the first 48 hours after implant placement.4  The bimodal approach offered the shortest treatment time, optimal soft tissue outcomes, and high rates of short-term success.511  However, meta-analytic studies showed a higher failure risk associated with immediate placement/loading of single implants compared with the conventional protocol, so practitioners were advised to remain cautious in embracing the immediate placement concept.2,3 

Figure 1.

Time frame of different implant placement and loading protocols.3 

Figure 1.

Time frame of different implant placement and loading protocols.3 

Implant design is one of the factors that may influence the biomechanical behavior of an oral implant and hence its primary implant.12  The earliest traditional implant was cylindrically parallel in design. The paralleled shape, however, was not applicable in all clinical situations. Therefore, other implant designs and thread geometries were introduced to achieve a better stability in different anatomic and bone conditions. The tapered (root analogue) implant was initially marketed by Friatec Corporation to be inserted immediately into an extraction socket.13,14  The tapered implant design has a wide diameter coronally and a tapered implant body resembling the shape of an extraction socket. Such a design may enhance the immediate placement by offering an implant surface that engages the walls of the tapered socket and minimizes the need for bone graft. In addition, tapered implants can be placed in non-extraction sites where wide-diameter implants offer a more favorable distribution of loading forces.15  Moreover, it has been suggested that tapered implants may improve esthetics, allow implant insertion between 2 adjacent teeth,16  and avoid the risk of perforation due to anatomic concavities.17 

The tapered design was modeled to enhance the primary implant stability in poor bone quality by transferring the compressive forces to the cortical bone, as the cortical bone is expected to handle higher stress/strain values than cancellous bone.18,19  Likewise, wide implants have also been reported to improve the primary stability by increasing the surface area of contact between the bone and the implant.20  However, the surgical technique of placing tapered wide implants can be sensitive and is mainly influenced by the degree of implant taper and bone density as excessive compression of bone can be created during implant insertion. Such compressive forces, if exceeding the physiologic limits of bone, can lead to osseous necrosis and compromised stability.21,22 

The tapering angle can be one of the basic design features that differentiate the increasing number of commercially available tapered implants in the market. From a biomechanical point of view, the optimal design for immediate loading is the one that has a tapering angle that can enhance the primary stability by allowing an even bone compaction, favorable magnitude and distribution of strains along the cortical and cancellous bone levels, and uniform stresses at the implant surface without any detrimental compressive or wedging effects. It is now well accepted that a certain level of intraosseous strain can enhance early osteogenesis at the bone-implant interface.2325  Thus, an implant configuration that can achieve the desired level of micro-strains may have a profound influence on the early phase of peri-implant osteogenesis, which is crucial for the long-term success of immediately loaded implants.

In implant biomechanics, the finite element (FE) method has been extensively used to simulate clinical scenarios that would be more complicated to examine using other methods. Most of the previous FE studies have extensively evaluated implant design parameters in a fully osseointegrated implant model.2628  However, the biomechanical role of these parameters in immediate/early placement and loading scenarios has not been adequately studied in the literature. The aim of this study was therefore to analyze, using a nonlinear FE approach, the influence of the implant's tapering angle on the strain values in the cortical and cancellous bone and the stress distribution in immediately loaded wide-diameter implants placed in the molar sites under 2 different placement protocols (healed ridges vs extraction sockets).

Materials and Methods

FE model design

Three-dimensional models of a posterior mandibular segment with wide-diameter implant and superstructure were created using a personal computer (AMD Athlon 64 ×2 processor, Sunnyvale, Calif) and a computer-aided design program (SolidWorks 2009, SolidWorks Corporation, Concord, Mass). The dimensions of the mandibular bone segment were 27 mm in height and 12 mm in buccolingual width, and it consisted of a spongy center of cancellous bone surrounded by a 2-mm layer of cortical bone.29  A molar extraction socket was modeled to simulate the immediate placement protocol. The socket dimensions were based on the anatomy and geometry of the roots of mandibular molars. The bone-implant models were created according to the tapering angles of the implant bodies (2°, 5°, 8°, 11°, and 14°) and the type of implant insertion (healed vs extraction site). Roman numerals (I–V) were used to describe the different tapering angles (Figure 2) and either “h” or “e” was used to designate a healed or extraction site, respectively. Thus, a total of 10 different implant models were available for analysis. Each implant had an 8.1-mm diameter, a length of 11 mm, and a thread pitch of 0.8 mm. For simplicity, a 5-mm high abutment was assembled to the implant as one-piece unit and an all-ceramic provisional crown was modeled over the titanium abutment. A rigid bond was assumed along the prosthesis-abutment interface, and the thickness of the cement was excluded from the model.3032 

Figure 2.

Geometry of the tapered implant models (I–V).

Figure 2.

Geometry of the tapered implant models (I–V).

Material properties and interface conditions

The material properties of the bone, implant, and prosthetic crown (Table 1) were presumed to be linear, elastic, homogenous, and isotropic.33,34  A nonlinear face-to-face contact model with a coefficient of friction (μ) of 0.3 was used to simulate the contact condition in the healed ridges between the surface of immediately loaded implant and bone before osseous integration.35,36  A lower coefficient of friction (μ) of 0.1 was selected in the extracted models to account for the blood interface, which acts as a lubricant between the immediately loaded implant and bone. The frictional contact elements were used to allow for contact pressure and shear movement.37 

Table 1

Mechanical parameters of materials used in the finite element model35,36 

Mechanical parameters of materials used in the finite element model3536
Mechanical parameters of materials used in the finite element model3536

Constraints and loads

The analysis was performed using FE software (SolidWorks Simulation version 2009 for Windows, Concord, Mass). A loading force of 189.5 N38  was applied vertically and obliquely (45°) to every node of the cusp to simulate immediate masticatory conditions in the molar region. The direction of the load applied in all the models is shown in Figure 3. An automatic mesh was generated, and the models consisted of 42 274 to 62 087 elements and 9665 to 13 263 nodes, depending on the implant taper and placement protocol. The boundary conditions were applied by constraining the 3 degrees of freedom at each node located at the mesial and distal aspects of the bone segment. The maximum von Mises stress at the implant and the maximum displacement in bone were reported. All the stress/strain distribution patterns were illustrated using contour maps.

Figure 3.

Implant-bone model under a loading force of 189.5 N.

Figure 3.

Implant-bone model under a loading force of 189.5 N.

Results

The influence of the tapering design of an immediately loaded oral implant inserted in healed or extracted molar models was evaluated by calculating the maximum von Mises stresses at the implant and the maximum von Mises strains on the adjacent bone. The maximum von Mises stress/strain values at the implant, cortical level, and cancellous level are summarized in Table 2.

Table 2

Maximum von Mises stress/strain values on the implant and surrounding bone in the finite element model

Maximum von Mises stress/strain values on the implant and surrounding bone in the finite element model
Maximum von Mises stress/strain values on the implant and surrounding bone in the finite element model

The tapered implants generated more stress/strain values at the implant, cortical bone, and cancellous bone in the simulated extracted sites than in the healed sites. At each tapering angle, the maximum von Mises stress values at the immediately loaded implants in the extracted models were almost doubled compared with those in the healed models. Moreover, the increase in the implant taper angle resulted in higher stress values in the extraction and non-extraction models. Hence, the lowest stress value was recorded in the 2° tapered implant in the healed model (9.9 MPa; Figure 4a), and the highest stress value was recorded in the most tapered implant in the extracted model (35.3 MPa; Figure 4b). At the abutment-implant interface, the maximum von Mises stress values were considerably high when the taper angle was more than 8°. In the healed model, the peak values of von Mises stresses occurred at the first 3 threads of the tapered implants in models IV and V, but the stress values were more evenly distributed along the implant threads in other models.

Figure 4.

The von Mises stress distribution on wide-diameter implants at different implant tapering angles.

Figure 4.

The von Mises stress distribution on wide-diameter implants at different implant tapering angles.

In the cortical bone, the maximum von Mises strains were generated at the cortical bone around the implant neck in healed model V (0.0003679ɛ; Figure 5a) and at the cortical buccal strut adjacent to the implant neck in extracted model V (0.003383ɛ; Figure 5b). In the cancellous bone, the healed models showed a different behavior in the strain distribution, as the highest von Mises strain value occurred in the buccal side of the cancellous bone around the least tapered implant (0.001654ɛ; Figure 6a), while the strain distribution in the cancellous bone in the extracted models followed the stress/strain patterns along the implant surface and the cortical bone, with the highest von Mises strain value being generated around the apical part of the most tapered implant (0.007120ɛ; Figure 6b).

Figure 5.

The von Mises strain distribution on the cortical bone around the implant neck at different implant tapering angles.

Figure 5.

The von Mises strain distribution on the cortical bone around the implant neck at different implant tapering angles.

Figure 6.

The von Mises strain distribution on the cancellous bone at different implant tapering angles.

Figure 6.

The von Mises strain distribution on the cancellous bone at different implant tapering angles.

In the healed models, reducing the tapering angle from 14° to 2° decreased the maximum von Mises stress at the oral implant and the maximum von Mises strain at the cortical bone around the implant by 50.7% and 32.2%, respectively. Alternatively, the value of the maximum von Mises strain at the cancellous bone decreased by 54.2% by increasing the tapering angle to 14° (Figure 7a). In the extracted models, the reduction in maximum von Mises stress at the implant was less—only 39.1% reduction as the implant taper angle decreased to 2°—whereas the strain values along cortical and cancellous bone were reduced by 68.9% and 55.2%, respectively (Figure 7b). Thus, the degree of implant tapering may have more influence on the strain patterns along the simulated extracted sockets than the healed sites.

Figures 7 and 8.

Figure 7. The percentage decrease in the stress/strain profile caused by different tapered implant designs. Figure 8. Influence of implant taper angle on the von Mises stress distribution along the oral implant threads.

Figures 7 and 8.

Figure 7. The percentage decrease in the stress/strain profile caused by different tapered implant designs. Figure 8. Influence of implant taper angle on the von Mises stress distribution along the oral implant threads.

The plotting of the maximum von Mises stress values at the implant threads for each model showed that the maximum values were more located in the coronal parallel-sided part of the implant. The first 3 threads of the tapered implants in healed models IV and V showed considerably higher stress values than the rest of the implant threads (Figure 8a). A similar pattern was observed in the extracted models. However, the difference between the stress values along the threads was small, and there was more gradual change between the coronal and apical aspect (Figure 8b).

Discussion

The current FE study estimated the influence of different tapering angles on the stress/strain profiles of immediately loaded wide-diameter implants and the simulated bone models that represented a healed or a fresh molar extraction socket. The FE analysis was carried out to examine the optimal implant tapering angle that can provide a beneficial and uniform stress/strain distribution at the bone-implant interface. The von Mises values were used in calculating the stresses and strains in the bone and the implant models, which is often the most commonly reported value in FE studies as it summarizes the overall stress profile at a point.39,40 

This study demonstrated that increasing the degree of implant taper can result in higher stress/strain values in an immediate loading scenario in healed and extracted molar models. The only exception was the cancellous bone in the healed sites, in which increasing the implant taper angle reduced the strain values. As the implant tapering increased in the healed models, the area of maximum von Mises stress was more concentrated at the parallel coronal part of the implant, particularly at the implant-abutment interface, and the strain values are more coronally shifted toward the adjacent cortical bone. It is worth noting that the anatomic shape of the extracted molar sockets may not allow uniform contact between the tapered implant body and the bony socket walls. Thus, the maximum contacts were observed at the most coronal part and around the apical part of the oral implant. This explains the stress/strain distribution patterns at the implant, cortical, and cancellous regions in the extracted models.

The results of the current analysis suggest that a tapering angle of 2° can provide a significantly lower strain level at the cortical and cancellous bone in the extraction site, indicating a better biomechanical behavior of minimally tapered implants inserted in molar extraction sockets (Figure 7a), whereas in the healed socket, a tapering angle of 8° can result in a more favorable strain distribution in cortical and cancellous bone (Figure 7b). The high stress/strain patterns caused by use of high tapered implants can be attributed to the increased wedging effect that may ultimately lead to micro-cracks and bone damage.41  The use of a relatively small tapered angle (≤8°) may direct the maximum stress levels away from the abutment-implant interface, which is the area most susceptible to loading as excessive loading forces can cause joint opening, thus jeopardizing implant survival regardless of the implant diameter.42 

Although an optimal implant taper angle under an immediate loading condition has not been proposed in the literature, previous FE studies27,43  have investigated the effect of implant taper in models where complete osseointegration and a fully bonded bone-implant interface were assumed. Petrie and Williams27  created 16 FE models to examine the influence of 3 implant parameters (implant diameter, length, and taper). The implant tapering angles used in the models ranged from 0° to 14°. The authors predicted that wide, long, and non-tapered implants can provide the most favorable strain patterns at the peri-implant crestal bone. Siegele and Soltesz43  evaluated 4 implant shapes (cylindrical, tapered, screw, and conical). The FE analysis suggested that conical or tapered implant design produces higher crestal stresses than the cylindrical one. Likewise, this study showed that implants with small tapered angles also offer a favorable stress distribution along the implant threads and reduce displacement of the surrounding bone in an immediate placement loading scenario.

It has been suggested that wide implants increase the contacted surfaces between implant and adjacent bone and thus minimize the micro-movements and enhance the implant stability. Nevertheless, wide-diameter tapered implants are not necessarily the optimal choice in certain anatomic sites, such as molar extraction sockets, where bone may be damaged due to the high degree of compression that take place on the buccal strut during insertion and subsequent immediate loading. This is evident in the high insertion torque generated as tapered implants engage the cortical bone layer. The resultant compressive forces may lead to osseous necrosis and bone resorption limited to the cortical bone layer.21,22 

The FE analyses have been extensively used to help researchers and clinicians modify implant designs and solve complicated problems. However, the FE study has several limitations that need to be acknowledged:

  1. 1.

    Homogenous and isotropic material properties were assumed.

  2. 2.

    The complicated geometry of implant and bone was difficult to accurately model. Hence, an arbitrary model was created based on actual dimensions of mandibular bone cross-section.

  3. 3.

    The study was limited to one tapering design in which the implant had a coronal non-tapered part and an apical tapered part with different tapering angles. There was no attempt to study an opposite geometry of a coronally tapered implant with parallel-sided apical part.

  4. 4.

    The effect of the implant's tapering angle in immediate protocols was analyzed independently of other factors (ie, bone quality, implant length, and implant diameter). Nevertheless, it provided more insight analysis on a particular design parameter in an immediate loading model.

  5. 5.

    A time-dependent model44  of immediate loading was not considered. The current FE analysis, however, offered several advantages, including the use of 3-dimensional FE models instead of 2-dimensional models to represent 2 common modalities of implant placement (extracted vs healed sites) and the adoption of nonlinear contact analysis to simulate the complicated relationship between the prepared osteotomy and the oral implant under immediate loading.

Conclusions

Despite the limitations due to the assumptions used in the FE models, the following clinically relevant conclusions can still be drawn from this analysis:

  • The von Mises strains caused by immediate loading of immediately placed wide tapered implants were mainly concentrated in the cortical buccal strut around the implant neck where bone is at high risk of resorption.

  • Tapered implants of approximately 8° and less may provide the most favorable choice in the healed molar sites in terms of minimizing stresses around the implant neck and strains in the peri-implant alveolar bone.

  • An implant taper angle of 2° allowed the maximum anatomic contact between the implant threads and the molar extraction socket walls and showed the lowest stress and strain levels among all tapered implant designs.

  • In immediate implant placement, the tapered implant was designed to duplicate the shape of natural single-rooted anterior tooth. However, a strongly tapered implant may not be biomechanically advantageous in a multi-rooted extraction socket, even when a wide diameter is considered. Therefore, it would seem advisable to avoid the use of strongly tapered implants for immediate placement/loading in molar sites.

  • • 

    Further studies are still needed to evaluate other implant geometries that allow even and minimal stress/strain distribution along the implant surface and adjacent bone in different implant placement and loading protocols.

Abbreviations

     
  • FE

    3-dimensional

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