The Effects of Implant Length and Diameter Prior to and After Osseointegration: A 2-D Finite Element Analysis

The concept of osseointegration is one of a dynamic biological healing tissue process, during which the initial acute trauma results in a direct functional and structural connection between ordered living bone and the surface of a load-bearing implant.1,^–3 

A variety of factors control osseointegration, inadequate control of which compromises the stable anchorage of the implant to the bone tissue.4^,5 These factors can be categorized as surgical (primary stability and surgical technique), tissular (quality and quantity of bone, healing, remodeling), implantological (macrostructure, microstructure, and dimensions), and finally occlusal/mechanical (forces and prosthetic design).6^,7 

Until recently it was thought that the crucial variable for a therapeutically successful outcome was the no-loading healing period of the dental implant (delayed loading). For osseointegration to be properly accomplished, a stress-free environment should be established and the implant should be out of any kind of occlusion. The rationale behind this hypothesis was that mechanical factors interfere with the bone-implant interface, inducing micromovement, which prevents the bone deposition.8^,9 

Until now, the immediate loading protocol has not been well investigated. More and wider randomized controlled studies are needed in order for the case for immediate loading to be evidence based.10 Initially, immediate loading of dental implants in the 1960s resulted in fibrous encapsulation, mobility, and, finally, loss of implants. In later studies, when immediate loading started to be governed by strict protocols, it was found to be effective.11 Ledermann12 published the first case report of a successful screw-type dental implant, which was loaded within 72 hours after the implant placement. Since then, immediate loading has been applied in cases of both full and partial edentulism.13,^–15 In these cases it has often demonstrated survival rates, predictability, and direct bone-to-implant contact comparable to conventionally loaded implants.16,^–19 

It seems that the success of immediate loading procedures is a matter of appropriate patient selection, loading conditions, implant (geometry and surface), and prosthesis design.7^,20,^–22 However, due to the lack of understanding of the relationship between interface biomechanics and bone biology, it is difficult to predicatively comment on any of the previous factors.

Optimizing implant geometry in order to maintain a beneficial stress level at the bone-implant interface is a complex issue.23 There are many studies analyzing the stress distribution generated in the surrounding bone in order to arrive at the optimum shape and thread design.24^,25 However, the macroscopic features of dental implants, such as length and diameter, have never been investigated with reference to immediate loading as parameters that could provide a healthy stress level at the bone-implant interface assuring a normal healing period during osseointegration.

The purpose of the present study is to compare the calculated stresses and strains on a single dental implant and its surrounding bone for different implant lengths and diameters prior to and after the phase of osseointegration. A qualitative evaluation of the results provided useful information about the appropriate selection of implants in terms of geometry according to the timing of loading.

In the present study, a two-dimensional finite elements analysis was preferred to a three-dimensional one because the results are equally accurate in a study limited to qualitative rather than quantitative evaluation of the cases.26 The whole modeling and solution process was performed using the ANSYS software program.

An initial model of a single implant-supported crown substituting a lower second premolar was developed with reference to a posterior cross-sectional area of both cortical and trabecular bone. The selected mandibular bone was replicated as a double-layered block, with dimensions vertical (y′y) 18.75 mm and horizontal (x′x) 11.25 mm. Trabecular bone was located in the lower part of this block and was clearly distinguished from cortical bone by attributing different materials properties, meaning that cortical and trabecular bone were not modeled as a unit. The length and diameter of the implant were assumed to be L = 10 mm and D = 3.75 mm. The implant threads were not modeled. The abutment length was defined at 4 mm in the y′y direction and base and crest width were defined at 5.95 mm and 3.65 mm, respectively. The crown was modeled as a second premolar of the mandible (Figure 1). Since the primary concern of the study was to arrive at a qualitative comparison between the stress/strain values on the implant and its surrounding bone, the entire superstructure between the abutment and the crown was modeled as a homogeneous structure, ignoring, as was done in previous studies, the cement thickness and the metal framework.27^,28 Several other studies have not been able to demonstrate any significant differences in the force absorption quotients of gold, porcelain, or resin prostheses.29^,30 Thus, to preserve simplicity and to reduce computational time, it was assumed that the entire material properties of the superstructure would not have a significant effect on our results.

Subsequently, the initial model was modified in order to study the effects of implant length and diameter before and after osseointegration. Although the model contained three parameters—length, diameter, and the phase of osseointegration—the latter was not studied individually but always in combination with either the length or diameter of the implant. The finite element mesh of the initial model, consisting of 1707 nodes and 507 elements, was varied in line with modifications made to the model. The selected types of elements were target 169, contact 171, and plane 82. Constraints were applied at the outer surface of the bone in order to prevent free body motion. The loading condition was performed by the application of a static vertical force of 118.2 N to every node of the cusp, simulating the oblique direction of masticatory forces.31 The relative mechanical properties were attributed according to the materials and were selected based on previously published studies using finite element analysis (FEA).32^,33 The material properties required for the structural analysis were Young's modulus and Poisson's ratio (Table 1).

Considering the length of the implant and the phase of osseointegration as independent variables, the implant diameter of the initial model was kept stable (3.75 mm). The influence of implant length was simulated using implants with lengths of 8 mm, 10 mm, 12 mm, and 14 mm. The influence of the phase of osseointegration was simulated assuming a different type of bond at the interface between bone and implant. Prior to osseointegration, the bone-implant interface was characterized by sliding of the entire surfaces, using different assumed coefficients of friction for cortical and trabecular bone.34^,35 After the osseointegration, the contact surfaces of implant and surrounding bone were always bonded, with no sliding permitted (fixed bond). The influence of implant length prior to and after osseointegration was simulated by eight finite element models (models 1–8), as shown in Table 2.

Considering the implant diameter and the phase of osseointegration as independent variables, the implant length of the initial model was kept stable (10 mm). The influence of diameter size was simulated using implants with diameters of 3 mm, 3.75 mm, 4.5 mm, and 5 mm. The influence of the phase of osseointegration was simulated as previously reported. The influence of implant diameter prior to and after osseointegration was also simulated by 8 additional finite element models (models 9–16), as shown in Table 3.

The present study provides the stress/strain distribution on both the surrounding bone (cortical and trabecular) and implant. The influence of implant length and diameter prior to and after osseointegration was produced by evaluating the exhibited maximum von Mises stress values for the implant and the maximum von Mises strain values for the surrounding bone. Both the calculated stresses and strains are presented as a colored band, each color representing a particular stress/strain level in the deformed state. The von Mises stress and strain values for each model were compared with a reference model, in order to compare the effects of implant length and diameter qualitatively prior to and after osseointegration. The standard model being taken as the initial model prior to osseointegration (Model 2: L = 10 mm, D = 3.75 mm, prior to the osseointegration). The resulting values were computed as a percentage of the relative stress of the value for the reference model.

Figures 2a through d present the stress state of the implant, while Figures 2e through h present the strain state of surrounding bone produced by finite element analysis of Models 1 through 4, respectively, for the same diameter but different lengths loaded during the healing phase. Table 4 shows the maximum von Mises stress and strain values for every implant length on implant and cortical/trabecular bone, respectively. The stress and strain distribution on the implant and peri-implant bone tissue of Models 5 through 8 is presented in Figures 3a through d and Figures 3e through h, respectively, for every implant length after the healing phase of osseointegration. Table 5 shows the maximum von Mises stress and strain values obtained for every model, after the phase of osseointegration.

Figures 2a through d and 3a through d show that the areas where maximum stress was produced appeared at the abutment-implant interface. The distribution of the von Mises stresses in the implant is similar for all the models both prior to and after osseointegration. Moreover, the calculated stress values in Tables 4 and 5 reveal that there was a tendency towards reduced maximum stress values in the implant with increasing implant length, prior to and after osseointegration. The plotting of relative stress (in terms of percentages of those in the reference model) on the implant against implant length for both osseointegration phases is shown in Figure 4. More specifically, the relative stress prior to osseointegration showed an increase of 4% when a shorter implant was used while use of longer implants (12 mm, 14 mm) led to reductions of 6.8% and 18.4%, respectively. After osseointegration, the use of short implants (8 mm, 10 mm) resulted in 6.8% and 11.8% stress decreases, respectively. Longer implants (12 mm, 14 mm) resulted in stress reductions of about 18.4% and 30.1%, respectively. All the maximum von Mises stresses on the implant for each implant length prior to osseointegration were higher than the measured von Mises stresses after osseointegration. Furthermore, the largest reduction was obtained for 14-mm implants for both phases.

The maximum developed strains on peri-implant bone tissue were found at the interface of cortical-trabecular bone, before and after the healing phase. Prior to the osseointegration, the strain distribution pattern inside the bony socket presented a gradual widening when the length of the implant was increased, while after osseointegration the strain distribution pattern was similar for all the models examined. Moreover, there was a similar tendency, for both trabecular and cortical bone, of strain decreasing when longer implants (12 mm, 14 mm) were used, for either phase of healing. In contrast, no difference in the strain values for both bone structures appeared when short (8 mm, 10 mm) implants were analyzed, for each healing phase. The plot of relative strain on bone tissue (expressed in percentages of the reference model) with implant length for both osseointegration phases is shown in Figure 5.

Prior to osseointegration, loading of the implants with lengths of 12 mm and 14 mm led to a relative strain reduction of 7.8% and 14.7% on the trabecular bone, while the reduction reached 58.9% and 61.6% in the cortical bone for the same implants. After the osseointegration, the obtained reduction for same implant lengths was 38.4% and 41.8% for the trabecular bone and 58.8% and 61% for the cortical bone, respectively. The highest reduction was obtained for the 14-mm implant for both healing phases. After the osseointegration, the maximum von Mises strain values for each implant length were higher for the cortical bone than the obtained strain values prior to osseointegration. The opposite was the case for the trabecular bone. It should also be noted that the difference in the calculated relative strain values for cortical bone was about 0.6%, while the difference in the obtained relative values for trabecular bone were 30% to 40%.

Figures 6a through d and Figures 6e through h show the stress and strain field on implant and peri-implant bone for Models 9 through 12, respectively, due to the effect of implant diameter prior to osseointegration. The maximum von Mises values are presented in Table 6. The stress/strain patterns in the investigated structures caused by the variation of implant diameter after osseointegration (Models 13–16) are presented in Figures 7a through d and Figures 7e through h, respectively, while the maximum values obtained for the observed stress and strain on implant and bone tissue, respectively, are shown in Table 7.

According to Figures 6a through d and 7a through d, no difference in the developed stress field on implant structure was observed for the phase prior to and after osseointegration. The finite element analysis shows that the variation in diameter had a varying effect on stress/strain distribution, significantly different from the pattern produced by varying length. The relative stress (expressed in percentages of the reference model) on the implant, plotted against implant diameter, is shown in Figure 8. There was a tendency towards decreased stress on the implant with progressively larger diameter implants when the implants were loaded during the healing phase. The maximum reduction was obtained for the 5-mm–diameter implant (8.2%). On the contrary, when the implants were loaded after the osseointegration, the maximum von Mises stress pattern did not behave similarly with increasing diameter. Specifically, the least reduction was obtained for the 3.75-mm diameter implant, while the highest reduction occurred with the 4.5-mm diameter implant. However, the measured von Mises stress values for the implant were always lower compared with the measured values prior to osseointegration for each diameter.

The stress pattern generated in peri-implant bone tissue was also similar for all the models investigated, with the maximum von Mises stresses concentrated in the area around the upper part of implant, on the cortical-trabecular interface. The relative strain (expressed in percentages of the reference model) on bone tissue plotted against implant diameter is shown in Figure 9. During the healing phase, the reduction of implant diameter to 3 mm resulted in a strain reduction of about 2% and 56.1% for the trabecular and cortical bone, respectively—although the most marked intraosseous strain effect occurred with an implant diameter of 4.5 mm. Here the reduction was about 6.5% for trabecular and 58.4% for cortical bone. Further increase in implant diameter to 5 mm caused increased stress on the bone tissue, 0.1% and 54.9% for the trabecular and cortical bone, respectively. After osseointegration, all the strain values obtained in trabecular bone for each implant diameter were lower than those calculated for the same implant diameter during the healing phase. The maximum difference was obtained for the 5-mm implant. The calculated strain values for cortical bone were higher than those calculated during the healing phase, except the value exhibited by the 5-mm implant, which was lower after the end of healing phase. At this point, it must be noted that the cortical bone exhibited small relative differences between the two phases (1%–4%), while the trabecular bone exhibited much higher relative differences (30%–40%).

FEA allows the estimation of the stress/strain state of extremely geometrically complex systems such as the dental implant–bone system. The more detailed the representation of its structural integrity, the more reliable the numerical results obtained. Thus, the prediction of dental implant success36^,37 is increased. However, as with every other theoretical analysis, there are limitations stemming from the inadequacy of accurately representing the detailed geometry of the bone and implant superstructure, the boundary conditions, and the material properties of the structures involved, especially at the bone-implant interface.38 Due to these inadequacies, a comparative evaluation of the numerical results under the same limitations is preferable. In the same way, a qualitative description of the biomechanical behavior of the whole system, rather than an attempt at a quantitative analysis, is also preferred.39 

Under immediate loading conditions, finite element modeling is difficult to replicate due to the complex time-dependent situation existing at the bone-implant interface.40 However, a coefficient of friction is assumed at the bone-implant interface, representing a specific moment during the healing phase. On the other hand, a fixed bond is assumed as representing full osseointegration. Since the implant design influences force transmission and the stress/strain concentration in peri-implant bone,41 both implant length and diameter have been extensively studied in scientific literature. The implant diameter and length are responsible for microstrains, stresses, and eventually for micromotions generated at the bone-implant interface.42 According to the differentiation hypothesis demonstrated by Frost,43 this induced local mechanical environment regulates the proliferation and differentiation of the osteoblasts responsible for the peri-implant bone tissue formation. This mechanical environment may be beneficial for the bone-implant interface, within certain limits. A threshold for tolerated micromotion has been identified beyond which bone deposition cannot be achieved. Micromotion of less than 30 microstrains (μɛ) at the implant-bone interface does not interfere with osteogenesis,44 while an even wider range (50 μɛ–100 μɛ) has also been reported as not being detrimental.45 Furthermore, there is a physiologic spectrum of microstrains (500 μɛ–3000 μɛ) that promotes mature bone formation, while higher peak strains result in immature bone mineral formation and a fibroblastic cell pattern.46 

The necessity for simplification and the reduction of risk in surgical protocol when there is inadequate bone volume has led to the use of short and/or narrow implants.47^,48 A research-based re-evaluation of this has begun with the investigation of the biomechanical performance of implant dimensions at the bone-implant interface.

Until now, implant length has not been considered a significant factor contributing to osseointegration, because the applied stress is distributed mainly on cortical bone rather than on the rest of bone-implant interface, independent of implant length.49 Furthermore, implant length seems also to be a weak contributing factor to primary stability.50 In 2006, Misch et al tried to find the connection rationale between the high failure rates of posterior-placed short dental implants with the hypothesis that implant length does not influence success rates. Increased crown height, high bite forces, and bone density are the factors that affect the implant-bone interface and not the implant length.51 This is why the posterior sites of the jaw have been avoided for the application of immediate loading.52 Also, there are studies suggesting that the implant length cannot be considered in isolation, but only in conjunction with the height of the mandibular cross-section when considering the effect on strain concentration around an implant.23^,53^,54 

The present study indicates that the strain distribution pattern is independent of increased implant length prior to and after osseointegration. The maximum von Mises strains are concentrated at the trabecular-cortical interface for all the models considered, while the induced strains in the remaining bone-implant interface are always lower. These results are comparable to those reported by Lum49 and Himmlova et al.31 

The literature contains no studies defining with clarity the relationship between implant length and success rates. It has been reported that increasing implant length affects success rates up to a limit,49 while other studies report that implant length does not significantly affect survival rates,55,^–57 yet other studies correlate short implants either with increased failures58^,59 or with similar outcomes to those reported with longer implants.60,^–62 Renouard et al, trying to explore the high failure rates of short implants, revealed that the surgical protocol used for short implant insertion did not include factors such as the evaluation of the bone quality and the implant surface.63 

As far as concerns the impact of implant length on immediate loading protocols, the only available data come from clinical experience and limited human studies.64 However, these results indicate the use of implants longer than 10 mm, and some authors suggest the use of even longer implants, equal to or longer than 14 mm.65,^–67 Ottoni et al in a controlled study reported 10 failed implants in the experimental group (immediate loading), while the control group (conventionally delayed loading) produced only one failure when inserting implants of various lengths (10–15 mm) with a standard diameter (3.75 mm, 4.5 mm). No statistical significant correlation was found between length and the cumulative survival rates, while the failures were significantly correlated with the insertion torque.68 

Histologic and histomorphometric reports validated the formation of mineralized tissue and the establishment of osseointegration, by counting the direct bone-to-implant contact around short implants, retrieved from both animals and humans.69,^–72 Degidi et al, making biopsies on immediate loaded short implants (8 mm, 9.5 mm) retrieved from humans after short periods of function, revealed newly formed bone lamellae, while the extent of the bone-to-implant contact was about 60% to 70%.73^,74 A comparative study of the evaluation of the bone-to-implant contact between nonsubmerged immediate loaded and submerged implants revealed a higher percentage of contact for the immediate loaded implants.75 Varying degrees of integration have been obtained from retrieved transitional implants by evaluating the removal torque values.76 

In the present study, the results obtained from the correlation between implant length and intraosseous strains are in line with the results obtained from clinical studies, suggesting that by increasing implant length, lower strain status is induced at the implant-bone interface. However, it seems that the use of implants shorter than 10 mm does not imply a less desirable strain status. The generation of decreasing maximum von Mises strains for each increase in implant length led to the suggestion that implants longer than 10 mm should be preferred for both phases of healing phase. All the investigated models, in both healing phases, showed the greatest reduction when using an implant with a length of 14 mm.

Furthermore, it seems that the cortical bone undergoes almost the same strain deformation during each healing phase. In contrast, the deformation in trabecular bone presents the higher difference between the two phases, by undergoing significantly higher deformation prior to osseointegration. So, it can be assumed that phase of osseointegration affects the strain distribution in trabecular bone, independently of the examined design parameters. Despite this fact, the generation of different degrees of deformation at the bone-implant interface may not similarly affect each osseointegration phase. This is an area requiring further investigation.

In regard to the analysis of stress on the implant, it should be noted that the bone-implant interface is an area of great importance for implant survival and success, notwithstanding the significance of the implant-abutment interface for the vitality of implant-supported superstructure. This interface is associated with complications generated in the system, jeopardizing its predictability.77^,78 Applied loading develops a highly deformed state at implant-abutment interface. Exceeding the proportional limit due to stress concentration may lead to joint opening.79 Many factors contribute to the mechanical integration at the implant-abutment interface80^,81 although there is no study concerning the effect of length on the stress field in the implant.

The present study confirms that maximum stress concentration under loading is found at the implant-abutment interface. Incremental increase in implant length causes a gradual reduction of maximum von Mises stress at the abutment-implant interface, something observed for both healing phases—although loading of the implant after the phase of osseointegration produces a lower stress state on the overall superstructure.

Apart from standard diameter implants (3.75 mm, 4 mm), extensive use of narrow (3 mm, 3.3 mm) and wide (5–7 mm) implants is now being made and even “mini” implants (<2.7mm) are available.82 Wide implants are preferred in cases where immediate placement, bone engagement, and initial stability are indicated,83^,84 although the disadvantages of overinstrumentation and heat generation need to be taken into account.83 Narrow implants are preferred in cases where less than 5 mm of space is available or transitional implants are indicated but carry with them the handicap of lower fracture resistance.85 It has been reported that a 3.3-mm–diameter implant is about 25% more prone to fracture than a 3.75-mm implant.47 

The biomechanical rational behind the use of wide implants is the alleviation of the increased stress generated at the neck of the implant.31 This is supported by biomechanical studies using FEA, which report that the stress distribution around the neck of narrow implants is not comparable to wide ones.86 Against this must be set clinical studies evaluating potential vertical alveolar bone loss that are not in line with the biomechanical results and indicate that the pattern of marginal bone loss seems not to be significantly correlated with the diameter of the implant and its load-bearing capacity.47^,57^,87^,88 

The literature contains studies attempting to correlate the implant diameter with survival rates, but the results are often contradictory. No correlation between the two parameters is revealed from several studies,57^,89^,90 while others demonstrate that the increased implant diameter (5 mm) is correlated with high failure rates. The high failure rates of wide-diameter implants are often associated with the presurgical/surgical protocol and the tendency of the compromised areas to be confronted with wide “rescue” implants.91 Clinical studies evaluating narrow implants fail to specify their clinical performance with clarity, although the combination of narrow and short implants seems to demonstrate the highest failures.92,^–95 

Regarding an immediate loading protocol, no critical diameter of the immediate loaded implant has been proposed and the obtained data are limited. Only Degidi et al associated an average increased risk with implants exceeding 5.25 mm in diameter.96 Previously, Lorenzoni et al, in a 1-year follow-up case series-study, had reported the 100% survival rates of immediate loaded implants with diameters 3.85 mm to 5.5 mm located in the anterior maxilla.97 

In the present study, the pattern of strain distribution seems to be similar for every diameter selected, both prior to and after the healing phase. The area of maximum von Mises stress concentration is identical for all the selected models and is located around the upper part of the implant. This means that the pattern of the generated field is independent of increased diameter for both healing phases.

The correlation between implant diameter and maximum von Mises strain values shows a different pattern for each phase of osseointegration without, however, permitting clear conclusions. Nevertheless, it seems that implants with a diameter of 4.5 mm have the best biomechanical performance when they are loaded prior to the end of osseointegration. Further increase to 5 mm results in greater strain values indicating that wider implants are not always preferable when the immediate loading protocol is applied. The cortical bone around conventionally loaded implants, for every diameter, shows biomechanical behavior similar to cortical bone around the immediate loaded implants of the same diameter. In contrast, trabecular bone presents a high relative difference between the two phases, being highly deformed prior to osseointegration. With the completion of osseointegration, increasing diameter up to 5 mm results in a gradual reduction of the strain values, indicating that wide implants should be selected when the rest of the requirements are fulfilled. Implants with a reduced diameter of 3 mm have a similar biomechanical performance for both healing phases, despite the fact that the calculated strain values are higher for the phase prior to osseointegration.

As far as the analysis of stress on the implant is concerned, it should also be noted that the abutment-implant interface is the most deformed area under loading. It has been hypothesized that wide diameter implants would experience less deformation at the implant-abutment interface than standard-diameter implants because of an increase in platform surface area. However, studies have revealed that 3.75-mm implants and 6-mm implants demonstrate similar fatigue patterns under certain cycles for the same abutment-implant interface, while the fatigue pattern is differentiated according to the type of the interface.98 All the models in this study, independent of the variable considered, present the factors conducive to higher stresses at the abutment-implant interface location. No clear conclusions can be drawn, however, on the basis of this study about the correlation between the stress distribution on an implant and its diameter. It seems that prior to osseointegration the use of progressively longer implants is accompanied by stress reduction. However, implants with diameters of 3.75 mm and 4.5 mm have almost the same biomechanical performance. Whereas, after osseointegration, the best biomechanical performance is achieved by the 4.5-mm–diameter implant, but no specific tendency can be observed between strain variability and increasing diameter. Of course, this lack of specificity is in accordance with the present literature. However, it is clear that for every implant diameter, the maximum von Mises stress values are lower for loading after the phase of osseointegration.

The results of this study suggest that:

• Increasing implant length from 10 mm to 14 mm results in strain reduction on bone tissue during immediate (prior to osseointegration) and delayed (after osseointegration) implant loading. However, it seems that implants shorter than 10 mm do not alter the strain field.

• No specific correlation has been identified between implant diameter and strain distribution on bone tissue. Within a certain range of implant diameters, strain reduction is observed. It seems that wide implants (>5 mm) should not be selected for immediate loading protocols.

• Delayed implant loading results in significant strain reduction on trabecular bone, while almost no difference is observed for cortical bone, compared with immediate implant loading. It seems that the phase of osseointegration does not have an impact on cortical bone, while it significantly affects trabecular bone, something independent of the design parameter examined.

• Bone tissue around the upper part of implant experiences maximum stress concentration during immediate and delayed loading for every implant length and diameter.

• The abutment-implant interface experiences the maximum stress concentration prior to and after osseointegration.

• Increased implant length results in stress reduction on the implant in both immediate and delayed loading. For a given implant length, the stresses are lower after the phase of osseointegration.

• No specific correlation has been identified between implant diameter and strain distribution on an implant, although it is clear that there is a stress reduction for conventionally delayed loaded implants compared to immediate loaded implants.

• Well-controlled load experiments in vivo are necessary for the estimation of the time-dependent reaction of bone tissue around dental implants.

This research is supported by the RTD PENED-2001 Programme of the General Secretariat for Research and Technology of Greece (http://www.gsrt.gr).