Abstract
Objective
To investigate the influence of implant design factors in terms of bone integrity and implant stability.
Materials and methods
A 3D parametric CAD model was developed. Then, once domain settings and boundary conditions were defined, a 3D FEM model was created. To simulate the physical interaction at the bone–implant interface, identity pairs were introduced. After generating different design scenarios with a DOE approach, the most significant design factors were obtained.
Results
This study showed that the geometry of the screw thread highly influenced the implant stability. In particular the degree of bone damage became minimal when adopting 0.40 mm for the thread width and 0.05 mm for the thickness.
Significance
Thread width and thickness play a crucial role to reduce induced stresses and damage in bone. Considering these preliminary results, future improvements should focus on investigating also two-factor and higher interactions to better understand the implant loading mechanism.
1
Introduction
The main dental implant function is to support the prosthesis after osseointegration with the jaw bone to rehabilitate missing teeth and to maintain clinical success over time . Dental implantology, however, involves some different surgical steps by various techniques but it is based on osseointegration of the titanium implant . This is a biological process and it needs a healing period at least of 3–4 months. Dental titanium implants also consist of different shapes, simple or complex geometries, various length and diameters and they can be inserted in different positions but they have the same objective to remain incorporated in the patient’s bone by physiological bone regeneration actions .
It was reported that osseointegration is affected by many factors, including the implant design, the implant surface treatment, the bone quality, the surgical technique and the postoperative care . Among these factors, the thread design of an implant plays a relevant role and it is one of the dominant factors. In particular, the total contact area between the implant and bone has a significant role in the osseointegration strength of implant–bone interfaces . In addition, the design of the implant threads directly affects the stress distribution and the marginal bone restoration .
Over the years, many experimental and clinical reports revealed that the first thread contacting bone is the site of maximal stress, and thus of initial micro-fracture. Eventually immature osseointegration occurs at this site. There are various commercial dental titanium implants introduced on the market but their designs differ in terms of thread shape.
Recent studies have focused on the influence and sensitivity of the implant features: thread-pitch, -depth, -width, -helix angle, among others. Understanding these factors and applying them appropriately in the science of dental implants can help reduce the potential implant failure. A comprehensive overview of the effects of implant geometrical features on osteo-integration was reported . A valid and valuable support in clinical and in vivo / vitro investigations is provided by numerical FEA simulations. When analyzing the sensitivity to different design settings, FEA modeling has a valid application. Many studies, mainly based on FEM approaches, have been conducted to study the influence of different design implants. A valid contribution was done in , where by using a parametric FEM model the sensitivity of thread-pitch and thread-width was studied. A very interesting research was conducted , concluding that the most favorable configuration, in terms of implant stability, was the single-threaded one, followed by the double threaded. The triple threaded was found to be the less stable. Mechanical fixation by implant threads is a major contributor to the initial stability of the titanium implant .
One critical aspect to consider is how to “quantify” the stability of a dental implant. Chia-Chin et al. used the contact area to measure the stability. They found that the higher the contact area, the less the bone damage. A more quantitative approach was suggested , where the implant failure was associated with the maximum normal stress criterion. Experimental tests were also conducted to measure the ultimate bone strength. In agreement with a large number of studies the Von Mises stress field was used as an indicator of the average stress level at the bone–implant region, providing a global measure of the load transfer mechanism.
Very often FEA models have been generated under some key assumptions. Overall, 2D axial-symmetric models have been widely adopted since they allow fast and accurate results to be reached and may be performed quite easily via parametric analyses. Franciosa et al. used a 2D axial-symmetric model to point out the differences between different commercial designs, accounting for both perfect and imperfect osseointegration. Despite the advantages of 2D axial-symmetric models, they are not able to correctly capture some phenomena that may arise at the bone–implant interface. In fact, the loading mechanism can be strongly affected by the screw-helix angle and also by out-of-plane stress components .
The present work aims to analyze stress distributions generated by different fixtures on the bone tissue surrounding the implants. A DOE (Design of Experiment) approach was considered to understand the influence of the geometric and mechanical effects of thread design (i.e. thread-pitch and thread-thickness) on the stress distribution of the marginal bone.
2
Materials and methods
First of all, a 3D parametric CAD model of a dental implant was developed. Then, a FEA model was created, by defining domain settings and boundary conditions. By adopting a DOE approach, different implant designs were automatically generated and for each of them a FEM solution was obtained. By statistically analyzing numerical results, the dominant implant features were observed and discussed. To quickly analyze different design settings, a parametric CAD model of a dental implant was created within the SolidWorks® 2010 (Dassault Systemes) CAD system.
Although accurate detailed anatomical geometry may be obtained from CT scans, a simplified bone geometry was used. Final numerical results were not affected by this assumption since the main aim of this study was to perform a sensitivity analysis among different implant features (without varying the bone geometry).
Bone structure was modeled using a cylinder block (diameter and length equal to 15 mm and 20 mm, respectively). The cortical bone thickness was assumed constant and equal to 2 mm, as previously suggested . In order to ensure the right correlation between the bone–implant interface, a Boolean operation was performed, by subtracting the implant from the bone structure. Fig. 1 depicts the so-modeled implant/bone geometry.
The implant model was calculated by introducing the following geometric parameters (see Fig. 2 ):
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diameter (“ d _{I }”) and length (“ L _{I }”);
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bone–implant interface length ( L _{t });
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thread-pitch (“ p ”), -width (“ w ”), -tick (“ t ”); and,
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upper ( α _{1 }) and lower ( α _{2 }) thread-angles.
The thread-angle is the angle between a face of a thread and a plane perpendicular to the longitudinal axis of the same implant.
The following hypotheses were formulated:
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the abutment is “rigidly” connected to the implant. Its length is L _{I }− L _{t }. The occlusal load will be applied on the upper surface of the abutment. For some commercial solutions , the abutment is joined to the implant with an internal screw (not modeled here);
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the implant diameter is assumed constant and equal to d _{I }= 4 mm. Commercial solutions provide both cylindrical or conical implants. In the present research a cylindrical shape was used;
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a single threaded implant was developed;
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the mechanical behavior of the bone structure was captured with a linear isotropic law. This assumption approximates a type II bone quality ; and,
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perfect osseointegration was simulated.
The main goal of the present study is studying the sensitivity of some thread features (here called “design factors”) on implant stability. For this purpose we assumed that a qualitative measure of the implant stability could be obtained by evocating the maximum stress criterion: that is, the higher the maximum stress at the bone–implant interface, the higher the bone damage. In the following, such a criterion will be named “Bone Damage Degree” (BDD).
Therefore, the proposed approach may be summarized as follows: (1) generate a set of combinations of design factors by using a statistical DOE approach; (2) calculate the BDD for every combination by solving a FEA model; and, then, (3) analyze design scenarios, looking for the influence of design factors.
Among geometric parameters, five design factors were considered: p , w , t , α _{1 }and α _{2 }. Table 1 reports adopted levels (shortly named “1”, “2”, “3” and “4”).
Level/factor | p (mm) | w (mm) | t (mm) | α _{1 }(°) | α _{2 }(°) |
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1 | 0.90 | 0.35 | 0.05 | 5.00 | 5.00 |
2 | 0.95 | 0.40 | 0.10 | 10.00 | 10.00 |
3 | 1.00 | 0.45 | 0.15 | 20.00 | 20.00 |
4 | 1.10 | 0.50 | 0.20 | 30.00 | 30.00 |
A full factorial design would require a large number of tests (4 ^{5 }= 1024). However, in this array design only 5 of the 1024 degrees of freedom correspond to main effects, and only 10 degrees of freedom are related to the two-factor interactions. The remaining degrees of freedom correspond to three-factor and higher interactions. Therefore, since it is reasonable that only main effects or two-factor interactions are significant, a fractional design array, L _{16 }, was adopted. As on the one hand this array required only 16 tests, on the other hand aliasing effects may arise.
Table 2 presents the adopted L _{16 }array. Table 3 depicts implant geometry configurations, according to the L _{16 }array and generated within the SolidWorks CAD system, starting from the parametric CAD model.
Treatment ID | p | w | t | α _{1 } | α _{2 } |
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I | 1 | 1 | 1 | 1 | 1 |
II | 1 | 2 | 2 | 2 | 2 |
III | 1 | 3 | 3 | 3 | 3 |
IV | 1 | 4 | 4 | 4 | 4 |
V | 2 | 1 | 2 | 3 | 4 |
VI | 2 | 2 | 1 | 4 | 3 |
VII | 2 | 3 | 4 | 1 | 2 |
VIII | 2 | 4 | 3 | 2 | 1 |
IX | 3 | 1 | 3 | 4 | 2 |
X | 3 | 2 | 4 | 3 | 1 |
XI | 3 | 3 | 1 | 2 | 4 |
XII | 3 | 4 | 2 | 1 | 3 |
XIII | 4 | 1 | 4 | 2 | 3 |
XIV | 4 | 2 | 3 | 1 | 4 |
XV | 4 | 3 | 2 | 4 | 1 |
XVI | 4 | 4 | 1 | 3 | 2 |
FEM simulations were performed within Comsol Multiphysics 3.5a. The same domain settings and boundary conditions were applied for all 16 geometry configurations. As an example, Fig. 3 depicts the FEA model related to the geometry configuration III.
Tetrahedral mesh elements were generated. Fig. 3 shows that the mesh size was strongly reduced (about 0.1 mm) around the implant–bone interface, where the highest stresses are expected. The total number of elements was 148,102, while the number of mesh nodes was 34,174. Linear shape functions were adopted to interpolate node displacements. Therefore, the number of degrees of freedom solved for was 102,522.
Materials were considered linear and isotropic.
Table 4 summarizes the adopted mechanical properties ( E , Young’s modulus; ν , Poisson’s ratio). Implants and abutments were assumed to be made of a titanium alloy (Ti6Al-4V).
E (GPa) | ν | |
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Implant | 120.0 | 0.33 |
Cortical bone | 13.7 | 0.30 |
Trabecular bone | 0.50 | 0.30 |
Boundary conditions are depicted in Fig. 3 b and c. The lower surface of the trabecular bone was fixed. Moreover, a static load (350 N), simulating the occlusal force, was applied at the upper surface of the abutment. This force formed an angle of 12° with respect to the implant axis.
The physical interaction of implant–bone and cortical bone–trabecular bone interfaces was captured by introducing identity pairs (colored surfaces in Fig. 3 b and c). Identity pairs ensure that the displacement fields at interfacial surfaces are identical to each other.
In agreement with the maximum normal stress criterion (also known as the Coulomb criterion), principal stresses were used at the bone–implant interface to define a measure of the implant stability. Experimental tests estimated that local overloading at the cortical bone occurred in compression when the maximum compressive principal stress ( σ _{C }) exceeds 30 MPa (in modulus), and in tension when the maximum tensile principal stress ( σ _{T }) exceeds 60 MPa. Moreover, local overloading at the trabecular bone occurs when σ _{T }and/or σ _{C }(in modulus) exceed 5 MPa.
The maximum stress criterion was implemented as follows: (1) stress distributions were calculated by using the FEA model, (2) the region was identified where the maximum principal normal stress exceeds the ultimate bone strength, and (3) the corresponding volume was calculated: this represents the “Bone Damage Degree” (BDD). The BDD can be implemented and calculated within Comsol Multiphysics by using domain expressions and integration of the coupling variables.
By statistically analyzing simulation data through a Pareto ANOVA , contribution indices were calculated. The contribution index quantifies the influence of each parameter on the bone damage. The highest contribution indices correspond to the most significant parameters. The significance level was assumed equal to 90%.