Evaluation of Stress in Tilted Implant Concept With Variable Diameters in the Atrophic Mandible: Three-Dimensional Finite Element Analysis

The loss of alveolar bone height and width after tooth extraction is an unavoidable process. Implant-supported dentures have been frequently used to rehabilitate edentulism since the 1960s. However, an edentulous ridge with horizontal and/or vertical atrophy may restrict the placement of implants with standard diameter and length because of anatomic limitations.^1–4  Replacement of bone loss may require complex surgical procedures such as bone augmentation, onlay graft techniques, ridge split, and nerve lateralization for the atrophic mandible, prolonging the treatment process.^1,4,5  The optimal treatment modality in edentulous atrophic jaws still remains under investigation.^1,6 

There are many options for the rehabilitation of the jaws without using invasive surgical procedures. In recent years, clinicians who seek more conservative alternatives tend to use short and narrow-diameter implants (NDIs) in the atrophic mandible.^4,7–9  However, some authors still have concerns about the stress transmission between the bone-implant interface of NDIs, which may lead to early failures.¹⁰  Also, higher stress values between short implants and surrounding bone tissue were reported.¹¹ 

The concept of a fixed prosthesis supported by 2 vertical and 2 tilted implants in the atrophic mandible was introduced by Malo and colleagues.¹²  This technique helps to reduce stress distribution, additional cost, and operation time.¹²  In addition, the use of short implants as a posterior anchorage may offer an alternative treatment option by eliminating the cantilever effect in the case of an insufficient vertical alveolar ridge.^13,14  Since the 1960s, the advantages of using 4 or 6 implants in completely edentulous mandibles have been reported.¹⁵  However, the beneficial biomechanical properties of using NDIs or short implants in these cases are not clear.^5,16,17  Furthermore, studies investigating the effect of diameter and number of implants on the stress transmission along the bone and implant interface are limited.^14,18 

Atrophy of the jaw can occur in both the vertical and transversal directions.¹⁹  Thus, the use of NDIs and/or short implants can be considered as an alternative treatment modality to avoid augmentation procedures.^5,20  The purpose of the present study is to compare the stress distribution of 4 different models with variable implant diameters and numbers under static loading in the atrophic mandible using 3-dimensional finite element analysis (3D FEA).

Four different types of dental implants with variable widths and lengths were analyzed: 3 different bone-level tapered implants (∅ 3.3, 4.1, 4.8 mm in width and 10 mm in length; Roxolid, Institute Straumann AG, Basel, Switzerland) and 1 tissue-level short implant (∅ 4.1 mm in width and 4 mm in length; Roxolid, Institut Straumann AG). The implants were made of titanium-zirconium (Ti-Zr) alloy (Roxolid). The simulated restorations consisted of cobalt-chromium (Co-Cr) alloys (Wirebond C, BEGO Medical, Bremen, Germany) as the framework and feldspathic porcelain (Ceramco II, Dentsply Ceramco, Burlington, NJ) as the superstructure. The details of the designs are shown in Figure 1.

A case of appropriate quality from the clinical computerized tomography records were selected and used as a reference for the modeling. Meshes were formed with 10 noded (brick type) elements as much as possible to maximize the sensitivity of the analysis. The implants and abutment components used in the study were scanned 3-dimensionally with an Activity 880 digital scanner (Smart Optics Sensortechnik GmbH, Bochum, Germany). The Rhinoceros 4.0 program (McNeel, Seattle, Wash) was used as a 3D modeling software. The same denture, modeled via the Rhinoceros, was used for each model to ensure the standardization of the loading process. Mandibular bone structure was determined as type II based on the Lekholm and Zarb classification.²¹  An outer shell of bone structure representing the cortical bone layer was designed with an average thickness of 2 mm, and the rest (an inner volume) consisted of cancellous bone tissue. The length of the mandibular arch in the mesial-distal direction was approximately 40 mm, and the height in both the anterior and posterior regions was about 16 mm. All models were situated to the 3D space with correct coordinates and the model-merging procedure was completed.

After finishing the model-merging procedure, models were transferred to Algor Fempro (ALGOR, Pittsburgh, Penn) software in .stl format for analysis. All materials were assumed to have a linearly elastic, isotropic behavior and homogenisoty.¹¹  In agreement with data available in the literature, the Young's modulus of the mandibular cortical bone was assumed to be 13 700 MPa, the Young's modulus for mandibular cancellous bone was set to 1370 MPa, and the Ti-Zr alloy had a Young's modulus and Poisson's ratio of 100 000 MPa and 0.3, respectively.^22–24  Young's modulus and Poisson's ratio values of all materials are given in Table 1.

Boundary conditions of the study were modeled as fixed in all directions. Modeled structures were simulated as tightly bonded. Complete osseointegration between implant and bone was assumed. A static oblique occlusal load of 200 N with 45° inclination in the buccal-lingual direction was applied bilaterally at the top of the distal buccal cusp of the prosthesis for each model.

Different treatment options were applied to the atrophic mandible in 4 study models. Implants with 10-mm length were placed in the anterior mandible, between the mental foramens, while short implants were placed behind the foramens. All models are shown in Figure 2.

The diameters of the implants were 3.3 mm. The emergence profile of the implants was located in the second incisor and second premolar. This model had 2 vertical and 2 tilted implants and bilateral cantilevers with 11 mm in length. Distally tilted implants were angled at 30°.

The diameters of the implants were 4.1 mm. The location and angulation of the implants were the same as those for model I.

The diameters of the implants were 4.8 mm. The location and angulation of the implants were the same as those for model I.

The diameters of the implants were 4.1 mm. The emergence profile of the implants was located in the second incisor, second premolar, and first molar areas. This model had 2 vertical and 2 tilted implants of 10-mm length and 2 short implants with 4-mm length. Distally tilted implants were inclined 30°. There was no cantilever in the superstructure.

The von Mises stress field was used to analyze the stress of the implants and restorations (for unbending materials). Maximum (tensile) and minimum (compressive) principal stress values were used at the bone-implant interface to define local risk indicators of the activation of bone resorption. The von Mises as well as maximum and minimum principal stress data were evaluated by the range scales. All values were produced numerically in Megapascal units, color coded on any desired location, and compared among the models.²⁵ 

Von Mises, minimum, and maximum principal stress values and images are shown in Table 2.

In all models, stress concentrations of the implants were located at the top threads and the neck of the implants, and the highest stress values were measured on the lingual side of the tilted implant. As the diameters and number of implants increased, the von Mises stress values on each implant were reduced. The lowest stress concentration in all implants was demonstrated in model 4. In addition, the lowest von Mises stress values were obtained in the short implant among the most distal implants (48.7 MPa). The stress value on the tilted implant in model 2 (tilted: 129.5 MPa) was almost halved by the additional use of short implants in model 4 (Tilted: 57.2 MPa; Figure 3).

Cortical bone exhibited a higher stress concentration than trabecular bone. Minimum principal stress values were higher than maximum principal stress values in tilted and short implants in all models. The highest minimum principal stress values were observed in the distal and lingual region of the cortical bone surrounding the most distal implant in all models, whereas the highest maximum principal stress concentrations were located at the buccal region. The highest stress values were obtained in the bone surrounding the most distal implant in all models. Although there was no apparent difference among the first 3 models in terms of minimum principal stress of the tilted implants, stress values decreased as the diameters of the implants increased. Similar to von Mises stress data, the lowest minimum and maximum principal stress values were measured in model 4 (Figure 4).

The angled implant concept is one of the most preferred immediate-function protocols, which allows the rehabilitation of an atrophic edentulous jaw in a single operation eliminating nerve transposition and/or bone-grafting procedures.²⁶  As a result of the placement of the implants with inclination, many biomechanical advantages are obtained by achieving a wide anteroposterior distance, providing better load distribution in the occlusal plane, avoiding a long cantilever distance, and increasing the bone-implant contact with the use of longer implants.^27,28  This protocol, achieved by strategic positioning of 4 implants and maximization of the existing bone volume, has rapidly become popular.²⁸ 

Functional and parafunctional forces in the mouth cause stress in teeth, bones, soft tissues, and dental materials. Reducing the extent of compressive forces and optimizing the stress distribution are vital for increasing the long-term success of restorations. However, the ideal implant combinations and configurations to reduce stress values on both bone and dental materials are not identified yet.²⁹  Therefore, we brought into question whether the increase in implant diameter or the number of implants is more effective in optimizing stress distribution in the atrophic mandibular bone.

FEA is a method to investigate the stress values on complex structures. Actually, stresses arising from loading are impossible to visualize clinically. However, 3D FEA makes it possible to examine stresses around biomaterials and tissues 3-dimensionally and provides insight into the mechanical resistance under loading conditions.^30–32 

Loads in the mouth are rarely transmitted vertically. The highest stress values were obtained under oblique forces in FEA studies of implant-supported fixed prosthesis.^18,33,34  Therefore, occlusal loads of 200 N, 45° angled in the buccal-lingual direction were applied at the distal end of the prosthesis in all models of the present study.

Assuming the ultimate bone strength as a physiological limit, local overloading at cortical bone occurs in compression when the minimum compressive principal stress exceeds 170–190 MPa and in tension when the maximum tensile principal stress exceeds 100–130 MPa.^35,36 

Cortical bone, which has a higher elastic modulus, is usually exposed to greater stresses, unlike trabecular bone. It is also known that chewing forces are maximally transferred to the bone closest to the top of threads of the implants. In further corroboration with existing knowledge and previous studies, the highest values of the compressive stresses were obtained in the crestal cortical bone layer in all models.^35,37  Even so, all stress values were under the estimated physiological limits of ultimate bone strength.

In the recent past, NDIs were considered to fail because of fractures and deformation under chewing forces, particularly if applied to the posterior regions of the mouth. Therefore, dental implants with standard diameters have been widely used for the tilted implant treatment concept.³⁸ 

On the other hand, Ti-15Zr (Roxolid) alloy has recently been brought into clinical practice, owing to its advantageous mechanical properties when compared with Ti-6Al-4V alloy. The tensile strength of Ti-Zr alloy is 953 MPa, which makes the implant more resistant against the excessive loads.³⁹  In the present study, although von Mises stress values decreased in parallel to the increase in the diameters of the implants, only a negligible difference was found between the narrow implants and the others. As stated by Ueda and Takayama,⁴⁰  we observed a slight increase in minimal principal stress values with NDIs when compared with wide ones. The compact bony structure of the mandible, high tensile strength value of the Ti-Zr alloy, and the use of a splinted prosthesis might have been influential in the findings of this study. Our data indicated that the use of NDIs (3.3 mm) in the mandible may provide an advantage where available bone width is insufficient.

Almeida et al¹⁵  used 3D FEA to compare a 4-implant concept with a 6-implant concept, which involves the addition of 2 distal short implants in the atrophic maxilla. As a result, they reported that the distal short implants reduced stress transmission to the bone and implants and that the most favorable design was found to be the model supported with 2 distally short implants.

High occlusal stresses mainly originating from the concentrated chewing forces in the posterior regions tend to be more destructive, and they are shown to be the potential causes of short implant failure.⁴¹  However, in this study, short implants diminished the stress transmitted to the bone and the implants in model 4. We believe that the hybrid prosthesis distributed occlusal loads among all implants by splinting the short implants with others. Therefore, if sufficient bone height (6 mm minimum) exists in the posterior mandible, the use of short implants by splinting with the fixed prosthesis may be considered as an alternative treatment despite low success rates reported in the literature.^41–43 

On the other side, studies comparing the cantilever length in different models based on 3D FEA concluded that minimization of the amount of cantilever distance by using tilted implants reduces stress.^36–45  However, circumstances such as long edentulous dental arches and/or anteriorly positioned mental foramina preclude insertion of the tilted implants to the most distal position without damaging nerves, and therefore, the reduction in the amount of cantilever distance cannot be frequently achieved.^36,46  In the case of a long distal cantilever, the use of short implants may contribute to the long-term success of both prosthesis and implants in the atrophic mandible.

Loading of the cantilevered extensions of a fixed prosthesis induces considerable stresses on the implants closest to the site of load application.⁴⁷  White et al⁴⁸  reported that the maximum stress values on the distal implants increased with the increasing cantilever length. In a study comparing tilted implants with axial implants of varying cantilever lengths, the tilted model showed lower values of stress arising from its short cantilever extension, indicating a possible biomechanical advantage in reducing the stress.⁴⁹  As also stated by Almeida et al,¹⁵  Tawil et al,⁴⁶  and Rokni et al,⁵⁰  elimination of the cantilever extension with the help of 2 additional short implants significantly reduced the stress values in this study, and the fourth model offered the most favorable biomechanical condition in comparison with the other models with cantilever extension.

Simulating clinical scenarios have well-known inherent limitations, primarily because of the assumptions concerning forces, boundary and loading conditions, and material properties. The most common drawback of FEA is the need to assume most variables are fixed. To achieve standardization, the bone-implant connection was assumed as 100% in conjunction with the previous studies,^15,51  although histological studies in the literature showed that the level of osseointegration ranged from 30% to 70%.³¹  These findings might be influenced by anatomic variations and the variability of materials. Differences in the implant structure and designs play a decisive role on stress distribution. This study was conducted on a mandibular jaw model with D2 bone density, and different findings might be obtained in a maxillary model with a lower bone density.

Thus, the performance of narrow-diameter and short-length implants in terms of stress distribution and fatigue analysis has to be investigated with further experiments using different jaw models. In addition, in vivo and clinical studies are needed to demonstrate the prognosis of the implant designs in the tilted implant concept with/without short implants.

The following conclusions can be drawn within the limits of this in vitro study:

1. The model including 2 vertical, 2 tilted, and 2 short implants was found to be the most favorable biomechanical design.

2. Increasing the diameter of the implant reduces all stress values transmitted to the bone and implant in the atrophic mandible.

3. Because of the absence of cantilever extension, short implants exhibited the lowest stress values among the most distal implants, whereas all distal implants in the first 3 models had stress values amplified because of the cantilever.

4. The model with an increasing number of implants made a greater contribution to stress reduction than models including wide-diameter implants.

5. The highest stress values in all models were within the physiological limits.

1. All 4 models have a potential use in the clinical practice in atrophic mandibular jaws.

2. Increasing the number or the diameter of the implants may affect implant survival in a positive manner.

3. For the posteriorly atrophic mandible, the use of short implants may be preferred for long-term success, especially when the NDIs need to be inserted.

4. It is likely that the combination of narrow-diameter and short implants in the tilted implant concept will offer promising results in the future.

Abbreviations

3D:

three-dimensional

Co-Cr:

cobalt-chromium

FEA:

finite element analysis

NDIs:

narrow-diameter implants

Ti-Zr:

titanium-zirconium

The 3D FEA was carried out by Ay Tasarım Ltd.

The authors declare no conflict of interest.