Design optimization of a radial functionally graded dental implant Paul I. Ichim,1 Xiaozhi Hu,2 Jennifer J. Bazen,2 Wei Yi2 1 2
School of Dentistry, University of Western Australia, Perth, Western Australia, Australia School of Mechanical and Chemical Engineering, University of Western Australia, Perth, Western Australia, Australia
Received 28 March 2014; revised 27 August 2014; accepted 18 November 2014 Published online 00 Month 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/jbm.b.33345 Abstract: In this work, we use FEA to test the hypothesis that a low-modulus coating of a cylindrical zirconia dental implant would reduce the stresses in the peri-implant bone and we use design optimization and the rule of mixture to estimate the elastic modulus and the porosity of the coating that provides optimal stress shielding. We show that a low-modulus coating of a dental implant significantly reduces the maximum stresses in the peri-implant bone without affecting the average stresses thus creating a potentially favorable biomechanical environment. Our results suggest that a resilient coating is capable of reducing the maximum compressive and tensile
stresses in the peri-implant bone by up to 50% and the average stresses in the peri-implant bone by up to 15%. We further show that a transitional gradient between the high-modulus core and the low-modulus coating is not necessary and for a considered zirconia/HA composite the optimal thickness of the coating is 100 m with its optimal elastic at the lowest value conC 2015 Wiley Periodicals, Inc. J Biomed Mater Res sidered of 45 GPa. V Part B: Appl Biomater 00B: 000–000, 2015.
Key Words: dental/craniofacial material, dental/endosteal implant, implant design, implant interface, stress shielding
How to cite this article: Ichim PI, Hu X, Bazen JJ, Yi W. 2015. Design optimization of a radial functionally graded dental implant. J Biomed Mater Res Part B 2015:00B:000–000.
INTRODUCTION
Dental implants have undoubtedly been one of the most significant scientific breakthroughs in dentistry over the past 30 years.1At its very basic level, a dental implant is a prosthetic piece, which allows for an artificial crown to be anchored to the bone of the jaws. Implants are surgically placed in the alveolar bone and can have different designs such as blade, cylinder or conical with or without screw threads. When replacing a single tooth, dental implants have obvious biological and functional advantages when compared to conventional restorative options, such as fixed or removable partial dentures, and since the early 1970s, osseointegrated dental implants have been offered as an alternative.2 Over the past two decades dental implants have quickly become the treatment of choice for replacing missing teeth. A decade ago3 has identified [mt]90 implants available to clinicians and since then the number and variety has only increased. There is overwhelming evidence that screwshaped endosseous osseointegrated dental implants have superior clinical outcomes in comparison to other types of dental implants, such as subperiosteal implants, transosseous implants, needle implants, blade implants, etc, which are rarely employed clinically nowadays. Root-shaped or screwshaped implants are currently available in different materials, shapes, sizes, lengths, and with different surface characteristics or coatings. However, it is suggested that there is not
enough evidence from trials to demonstrate superior clinical performance of any particular type amongst various rootformed osseointegrated dental implants.4 The constant improvement in materials and surgical techniques is reflected in the clinical outcomes and existing literature data shows that current survival of oral implants after 10 years varies between 82 and 94%.5 It is rather difficult to define when an implant is “successful” considering the complexity of the factors at play. A number of criteria have been proposed, developed and improved over time and it appears that osseointegration is the major, if not the exclusive, reason for a successful long-term dental treatment.6 Osseointegration as a term stems from Bra˚nemark’s work and nowadays it is described as a “direct structural and functional connection between ordered living bone and the surface of a load-carrying implant.”2,7 The implant surface is critical for osseointegration and will condition how much of the implant surface directly contacts bone, how rapidly this bone accrual occurs, and the mechanical nature of the bone/implant connection is influenced by the nature of the implant surface itself.8 Apart from surface quality, factors such as surgical trauma, occlusal overload, peri-implantitis, microgap, biologic width, and implant crest module are contributing to the osseointegration and long-term clinical success.9
Correspondence to: P. Ichim; e-mail: [email protected] Contract grant sponsor: Australian Research Council’s Discovery Project Grant; contract grant number: DP110105296 Contract grant sponsor: China Scholarship Council (CSC)
C 2015 WILEY PERIODICALS, INC. V
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Occlusal overload is considered a major cause of failure and research shows that overloading produces marginal bone loss and deosseointegration of successfully integrated implants.10,11 It has been postulated that the lack of mechanoreception along the ankylosed interface between the implant and the bone as well as the geometry of the crestal bone can be used to explain the damaging effects of overloading. Consequently, a significant volume of research has been directed toward identifying which implant design or design features yield lower stresses in the surrounding bone.12–15 Additionally, it was suggested that implants, which contain micromechanical parts designed to partially absorb the masticatory load will show less peri-implant bone loss.16 Functionally, graded materials have received significant attention in the recent years as potential candidates for the next generation of dental implants improvement.17 In the case of dental implant, functionally graded materials (FGM) are usually considered to comprise of a mixture of titanium and bioactive hydroxyapatite (HA)/collagen and there are several models presented in literature.18,19 FGM implants are usually graded in axial direction that is, the elastic modulus of the material decreases from the cervical to the apical region of the implant. This gradient can be distributed through the whole implant volume18 or only through its coating.17 Axial grading configurations have been tested using finite element analysis17,18,20 showing a reduction of stresses in peri-implantar bone as well as improved biocompatibility.19 The gradient can also be distributed radially with the elastic modulus decreasing from the centre to the periphery of the implant along its cross-sectional radius and such an effect can be obtained by coating the implant with a thick, strong porous layer. The ingression of bone inside the porosity will generate a more resilient hybrid layer which may contribute to stress buffering as it has the potential to have the same stiffness of the bone tissue at the implant–bone interface. This introduces the concept of isoelastic-dental implants.21 Such an implant can be manufactured using HA in combination with a stronger material (such as zirconia or other ceramic) to provide mechanical resistance as bending strength of a porous HA scaffold is close to zero. A HA-rich scaffold-like coating on a strong HA-containing substrate can be introduced during ceramic composite processing. Our group has recently developed a HA-coating deposition method and the trials have yielded promising results using HA and zirconia to develop a system with graded porosity and material composition.22–24 In this work, we use FEA to test the hypothesis that a low-modulus coating of the implant would reduce the stresses in the peri-implant bone and we use design optimization and the rule of mixture to estimate the elastic modulus and the porosity of the coating that provides optimal stress shielding of the peri-implantar bone.
MATERIALS AND METHOD
For the purpose of this study, cylindrical implant models with a straight crest module were manually created in a
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commercial CAD software (Rhinoceros 3D for Windows, Robert McNeel&Associates). Cylindrical implant design was chosen to reduce the gradient of stresses at the interface, which would have resulted from a tapered design. The abutment was modelled as contiguous with the implant fixture and its attachment features (e.g., internal screw, hex) were not modelled. All cylindrical implant models consisted of a core covered by two 100 lm concentric layers of coating. This particular setting was chosen to reflect our manufacturing procedure in which a strong zirconia core is layered with a porous zirconia-HA coating.22 The coating layer thickness was chosen to accommodate a pore size which has been shown to facilitate bone formation during osseointegration of scaffolding structures.25 Also included in the analysis was a generic threaded implant design (screw-shaped) to allow for a more comprehensive referencing of the peri-implantar stresses generated by the optimized implant. Four implant sizes were considered to account some of the most common implants dimensions, 3.25, 4, 5, and 6 mm. For all sizes considered the length of the implant was 10 mm with a 7 mm height abutment. For the screwshaped implant design, the thread features [Figure 1(B)] were identical for all diameters considered. All implant models were embedded in simulated alveolar bone which consisted of a 2 mm thick cortical layer enclosing the cancellous bone. A minimum of 2.5 mm thickness of cancellous bone was maintained around the implant. Eleven regions of interest (sensors) have been further defined in the bone volume around the implant as concentric 1 mm height and 0.5 mm width layers to gather the numerical readings from simulations. The junctional margin of the cervical bone (S11) was further rounded slightly to avoid numerical-induced stress concentrations [Figure 1(A)]. The geometrical models were then exported to a commercial FEA package (SolidWorks, Dassault Systems) and meshed with 0.4 mm high-order solid elements. The sensors were meshed with 0.2 mm high-order elements [Figure 1(B)]. All the contacts between the implant and the bone were considered as bonded, a situation which can approximate full osseointegration of the implant.26 All the materials in this study have been assumed as isotropic and uniform and although it has been shown that biological structures such as bone are not isotropic, this is a common assumption in numerical modelling of oral structures.27–29 The cortical bone was considered to have an elastic modulus of 13.7 GPa and the cancellous bone of 7.9 GPa. The core of the cylindrical implant was considered to be made out of zirconia-HA composite with an elastic modulus of 110 GPa. The threaded implant was taken as manufactured of titanium alloy with an elastic modulus of 110 GPa. The Poisson’s ratio for all materials was considered as 0.3. All the models have been restrained on base supporting bone and loaded with a force of 100 N applied vertically and at 15 , 30 , and 45 in bucco-lingual direction on the top of the abutment. We have chosen these four loadcases to encompass the range of directions under which the implant receives occlusal loading.
DESIGN OPTIMIZATION OF DENTAL IMPLANT
ORIGINAL RESEARCH REPORT
FIGURE 1. Axial cross-section of the layered geometry used for this study (A) showing the sensors numbered from 1(apical) to 11(cervical) and the cortical and cancellous bone. Inset shows the coating layers and the rounded cervical margin of S11. B: shows the meshed threaded model and the specifications of the thread. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
To calculate the optimal elastic modulus of the coating layers we have used successive linear elastic analyses using the optimization algorithm built in a commercial CAD package (Solidworks, Dassault Syste`mes SolidWorks Corp) and which is based on design of experiments method, Rechtschafner design. Because the screw-shaped designs were used only for referencing, they were not subjected to optimization analyses; instead we only mapped the resulting stresses in each of the 10 sensors for each loadcase and diameter. The optimization process consisted of 27 analyses for each loadcase and for each implant diameter. The variables of the optimization procedure were the elastic moduli of the two coating layers and its goal was to minimize the stresses in the surrounding bone as calculated in the sensor areas. Because each layer was calculated separately we could identify if the solution indicated a gradient of the modulus across the thickness of the coating layer, from the high modulus core to the soft cancellous bone. The variables, that is, elastic modulus of the coating layers ranged from 45 to 110 GPa with a step of 20 GPa. The initial 45 GPa elastic modulus was calculated using the rule of mixtures and considering that the resulting hybrid bone/coating can be regarded as particulate composite material. During the coating process, the pores are introduced using PMMA spherical microspheres and the maximum random close packing ratio of spherical particles is 0.63.30 Under the ideal and simplified assumption that all the pores will be fully colonized by cancellous bone, we used direct rule of mixture to estimate the upper bound of the resulting coating with maximum porosity as Efinal 5
VboneEbone 1 (1 2 Vbone)Eimplant where Vbone 5 0.63 and Eimplant 5 110 GPa. Rule of mixtures has been used previously by other authors to estimate the material boundaries for implant optimization studies.17,18 The goal of the optimization was set as reduction of compressive and tensile stresses in sensor S10, weighted equally 50:50 in their priority. S10 was located 1 mm below the crest module of the implant. We have chosen the cervical area of the bone as the site for our numerical readings as it was shown in a number of previous analysis that it concentrates the highest stresses and a consistent gradient develops from the cervical to the apical area. The very top S11 was not used to avoid referring to a site where errors could occur due to numerical artefacts caused by the sharp junction between three materials. After the optimization process was finalized, the magnitude of principal stresses (their maximum and average values) were recorded and contrasted at every sensor site for every loadcase and dimension. This approach allowed us to compare both absolute values as well as the efficiency of the optimized design to minimise stress. We have opted for principal stresses so that we can differentiate between compression and tension as comparative in vivo data suggested that the bone has different resorption thresholds in tension and compression.31
RESULTS
The optimization results for the elastic modulus of the coatings are given in Table I. It can be seen that the results are
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TABLE I. Results of the Optimization Starting from an Initial Elastic Modulus of 110 GPa for Both External and Internal Layers Implant Diameter 3.25 mm 4 mm 5 mm 6 mm
Layer (GPa)
Vertical Loading
15 Loading
30 Loading
45 Loading
External layer modulus Internal layer modulus External layer modulus Internal layer modulus External layer modulus Internal layer modulus External layer modulus Internal layer modulus
45 110 45 110 45 110 45 110
45 110 45 110 45 110 45 110
45 110 45 110 45 110 45 110
45 110 45 110 45 110 45 110
consistently identical for all the diameters and loadcases considered. The optimization solution indicates that only the external layer requires a low modulus and the optimal value is the initial one of 45 GPa. By contrast the internal layer retains its initial E of 180 GPa. These polarized results show that the solution does not indicate a benefit of gradient of the elastic moduli of the coating. Furthermore, there is no difference in the solution between the implant diameters considered. When the optimization trends are analyzed separately, the elastic modulus of the external coating layer shows a significant and nonlinear relationship with the stresses generated in the peri-implant bone. Figure 2 shows the relationship between the value of the E of the external coating and the maximum principal stresses in the peri-implantar bone for the 5 mm implant with the E of internal layer set at 110 GPa (optimal result). The figure shows that the correlation pattern is mirrored in compression and in tension and the stress reduction effect is reduced once the E of the external coating exceeds 100 GPa. This trend was consistent amongst all the cases considered. By contrast, the variation in the elastic modulus of the internal coating layer shows a rather opposite effect with an inverse and nonlinear relationship with the stresses generated in the peri-implant bone. Figure 3 shows the relationship between the value of the E of the internal coating and the maximum principal stresses in the peri-implantar bone for the 5 mm implant with the E of external layer set at 45
GPa (optimal result). By comparing to Figure 2, the modest effect that the variation of the elasticity of the internal layer has on the stress reduction can also be seen. Table II shows the change in maximum principal stresses (tension and compression) between the optimized, nonoptimized and threaded designs at S10. The threaded design has consistently induced the highest stresses in the peri-implantar bone for both compression and tension. It can also be seen that the optimized design induces a consistent reduction of the maximum tensile and compressive stresses of 60% across all the loadcases compared to the nonoptimized design. The only exception from this consistency is the case of vertical loading when a very small or no reduction is recorded. Table III shows the change in average principal stresses (tension and compression) between the optimized, nonoptimized, and threaded designs at S10. Unlike the maximum stresses, these results have been calculated by averaging all the compressive or tensile nodal values for the whole volume of the sensor. The reduction in average tensile and compressive stresses is lesser than for the maximum ones but it preserves the pattern with a very small, if any reduction recorded for the tensile stresses under vertical loading. Again, the threaded design shows the highest average stresses in the peri-implantar bone. A detailed comparative mapping of the principal and average stresses shows a remarkably consistent pattern in
FIGURE 2. Trend lines illustrating the influence of the elastic modulus of the external layer on the maximum principal stresses in the periimplant bone measured at S10 (10 mm from the apex) as a function of the direction of loading for 5 mm implants. The elastic modulus of the internal coating was 110 GPa. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
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DESIGN OPTIMIZATION OF DENTAL IMPLANT
ORIGINAL RESEARCH REPORT
FIGURE 3. Trend lines illustrating the influence of the elastic modulus of the internal layerand on the maximum principal stresses in the periimplant bone measured at S10 as a function of the direction of loading for 5 mm implants. The elastic modulus of the external coating was 45 GPa. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
all cases considered with a reduction in the calculated tensile and compressive stresses in the bone surrounding the optimized implants. The results indicate that magnitude of this stress reduction is greater for maximum and less so for the average calculated principal stresses. Figures 4 and 5 show such a comparative mapping of the maximum principal compressive and tensile stresses as calculated for each sensor for the 5 mm implant under 0 and 45 loading, respectively, for the threaded, nonoptimized and optimized cases. It can be seen that the periimplantar bone surrounding the optimized implant design experiences far less stress (both compressive and tensile) as compared with the ones generated by a high-modulus nonoptimized or a threaded design. By contrast, this reduction affects the average stresses developed in the peri-implantar bone to a lesser extent. Our results further suggest that the stress reduction of the maximum stresses in the bone increases with the direction of loading with the least reduction for vertical loading and with a slight tendency to affect more compressive stresses than the tensile ones.
An interesting observation is that the top cervical millimetre of peri-implantar bone constantly experienced the most intense stresses for all loadcases and implant diameters and designs both in tension and compression (Figures 4 and 5). Figure 6 comparatively illustrates the cross-section of the tensile plots for the 5 mm diameter implants under 45 loading for the nonoptimized, optimized, and threaded designs. It can be observed that the low modulus external layer of the optimized design is experiencing lower stressed [Figure 6(B), arrow inset] as compared with a similar design implant manufactured entirely from high-modulus material [Figure 6(A)]. Additionally, it shows an increase in the stress around the threads of the implant for the screw design, as compared with the smooth surface one [Figure 6(C)]. This pattern was consistent amongst all cases considered. DISCUSSION
In this work, we use FEA to test the hypothesis that a lowmodulus coating of a cylindrical zirconia dental implant would reduce the stresses in the peri-implant bone and we
TABLE II. Maximum Calculated Principal Stresses in MPa at S10 (1 mm Below the Crest Module) for the Nonoptimized (N/O), Optimized (O), and Screw-Shaped Implant Designs 15
Vertical Implant diameter
Maximum stress
3.25 mm Compression (MPa) Tension (MPa) 4 mm Compression (MPa) Tension (MPa) 5 mm Compression (MPa) Tension (MPa) 6 mm Compression (MPa) Tension (MPa)
N/O
O
Screw Shaped
N/O
O
30 Screw Shaped
N/O
O
45 Screw Shaped
N/O
O
Screw Shaped
26.81 23.85 217.06 229.08 212.53 266.65 249.51 226.63 2111.52 265.89 228.54 2147.47 1.05 1.05 24.65 22.03
3.9 15.46 7.08 10.70 217.19 210.03
0.78 0.74 23.14 21.80
2.67 9.06 26.54 210.71
5.06 16.08 22.04 26.07 220.81 217.58
12.32 29.97
41.6 233.7
0.55 0.54 22.25 21.28
1.87 25.32
4.73 27.00
2.67 8.4 12.26 24.03 214.54 211.28
6.92 26.51
21.38 18.75 222.98 214.61
1.34
2.50
0.43
0.43
1.56
27.17 36.56 20.07 32.27 228.88 216.81
3.7
7.01
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4.28
62.85 54.66 24.48 54.46 238.12 230.34
10.49
33.15 26.78 222.99 213.02
10.93
93.5 72.22 63.67 243.86
10.61 28.45
32.59 229.64
6.65
16.41
5
TABLE III. Average Calculated Principal Stresses in MPa at S10 (1 mm Below the Crest Module) for the Nonoptimized (N/O), Optimized (O) Implant Design and Threaded Designs 15
Vertical
30
45
Implant Diameter
Average Stress (MPa)
N/O
O
Screw Shaped
N/O
O
Screw Shaped
N/O
O
Thread
N/O
O
Screw Shaped
3.25 mm
Compression Tension Compression Tension Compression Tension Compression Tension
21.98 0.00 21.33 0.32 20.92 0.22 20.66 0.15
21.71 0.00 20.97 0.31 20.81 0.23 20.57 0.16
22.38 0.51 21.55 2.67 21.06 0.22 20.75 0.16
23.27 1.79 21.99 1.01 21.30 0.64 20.91 0.44
22.36 1.49 21.81 0.96 21.17 0.61 20.81 0.43
23.95 2.01 22.42 1.06 21.42 0.69 21 0.43
25.38 4.07 23.21 2.33 22.09 1.50 21.46 1.04
24.70 3.65 22.94 2.18 21.89 1.41 21.33 0.99
26.4 4.58 23.88 2.51 22.22 1.65 21.57 1.05
27.09 6.05 24.20 3.49 22.73 2.27 21.90 1.57
25.32 4.73 23.63 3.11 22.49 2.10 21.74 1.48
28.4 6.83 25.07 3.79 22.87 2.5 22.03 1.61
4 mm 5 mm 6 mm
FIGURE 4. Comparative mapping of the maximum and average principal stresses calculated for a 5 mm diameter implant under vertical loading. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
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DESIGN OPTIMIZATION OF DENTAL IMPLANT
ORIGINAL RESEARCH REPORT
FIGURE 5. Comparative mapping of the maximum and average principal stresses calculated for the optimized and nonoptimized design of the 5 mm diameter implant under a 45 loading. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
use design optimization and the rule of mixture to estimate the elastic modulus and the porosity of the coating that provides best stress shielding. Design optimization of dental implants is not new and a number of efforts have been made in this direction. However, they were concerned more with an axial grading of the material from cervical to apical, be it the whole body of the implant18 or just the coating.17 In this work, we have taken a different approach and we have tried first to establish if the gradient is needed and then to determine the elastic modulus of the coating. Another difference between our work and previously published ones is that we have employed principal stresses (compression and tension) and not von Mises. We have opted for principal stresses as we are interpreting our results in the light of proposed thresholds for bone resorption31 and whilst von Mises is a relatable quantity, it only gives an indication of an overall
distortion of the body and cannot differentiate between tension and compression. The screw-shaped design has consistently shown the highest maximum stresses when compared to a nonthreaded and this can be explained by the presence of the threads whose geometry facilitate stress concentration. By contrast the differences between the average stresses induced by threaded and nonthreaded designs are rather small. Our results show that a thick, low modulus coating is capable of reducing the maximum compressive and tensile stresses in the peri-implant bone by up to 50% over the body of the fixture. The coating also reduces the average stresses in the peri-implant bone, but to a lesser degree of about 15%. The calculated optimal thickness of the coating was consistently 100 lm, which is only half of the considered total thickness of the optimization domain and it is not
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FIGURE 6. Comparative tensile stresses cross-sectional plots in the nonoptimized (A), optimized (B) and screw-shape design (C) for a 5 mm diameter implant loaded at 45 . Deformation scale 3100. Insets show close-ups of the interfacial areas; note the reduced stress recorded in the optimized low-modulus layer (B, arrows). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
influenced by the diameter of the implant. Previous works have reported stress reduction with a thicker coating of 150 lm17 but this discrepancy can be explained by difference in the direction of grading and numerical method. The results suggest that the optimal elastic modulus is 45 GPa, which is also the lowest boundary as considered by us for the optimization problem. This translates in a porosity fraction of 0.63 which is the maximum random close packing fraction of spherical particles.30 The implant pore size considered in this work is 100 lm because of its need to physically fit within the optimization layers and furthermore, such a porous structure can be manufactured using the method developed by our team.22–24 This involves a low-density-slip coating-deposition and coating-substrate cosintering process to deposit micro-porous HA/tri-calcium phosphate based coatings on zirconia substrate presintered at 900 C. The final coatingsubstrate cosintering is carried out at higher temperature, for example, 1300 C. In this way, thick scaffold-like HA-coatings with multiscale open pores can be achieved and the method is more versatile because the polymer and gelatine required for freeze-drying allow more freedom in pore structure design and formation. The density of the pores eventually dictates the elastic modulus of the resulting coating as it gives the total volume fraction available for bone ingrowth which in turn is the lowest of the elastic moduli considered in the rule of mixtures. As our optimization shows that a lower modulus of the external coating results in an increased buffering capacity then it is reasonable to assume suggest that pore size and porosity of the coating will influence the tensile and compressive stresses in the peri-implant bone in addition to the thickness of the coating. Indeed, experimental measurements of porous HA-based scaffolds indicate that increasing the concentration of porogen compromised the mechanical properties and a larger porogen particle size led to increased tensile strength but a reduction in Young’s modulus.32
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Additional to pore dentistry and size, their bone infill content will also come into play in determining the final elastic modulus of the coating. As a limitation of this study, we based it on the ideal assumption that all the pores of the coating will be colonized and fully filled with bone. These are conditions that are unlikely to be met in vivo and experimental human data shows that the average percentage of contact between bone and implant ranges from 25.1 to 83%. As such, a partial colonization of the pores will further lower the elastic modulus of the coating. Another limitation of our modeling in this study is the thickness of the cortical bone, which is generally
School of Dentistry, University of Western Australia, Perth, Western Australia, Australia School of Mechanical and Chemical Engineering, University of Western Australia, Perth, Western Australia, Australia
Received 28 March 2014; revised 27 August 2014; accepted 18 November 2014 Published online 00 Month 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/jbm.b.33345 Abstract: In this work, we use FEA to test the hypothesis that a low-modulus coating of a cylindrical zirconia dental implant would reduce the stresses in the peri-implant bone and we use design optimization and the rule of mixture to estimate the elastic modulus and the porosity of the coating that provides optimal stress shielding. We show that a low-modulus coating of a dental implant significantly reduces the maximum stresses in the peri-implant bone without affecting the average stresses thus creating a potentially favorable biomechanical environment. Our results suggest that a resilient coating is capable of reducing the maximum compressive and tensile
stresses in the peri-implant bone by up to 50% and the average stresses in the peri-implant bone by up to 15%. We further show that a transitional gradient between the high-modulus core and the low-modulus coating is not necessary and for a considered zirconia/HA composite the optimal thickness of the coating is 100 m with its optimal elastic at the lowest value conC 2015 Wiley Periodicals, Inc. J Biomed Mater Res sidered of 45 GPa. V Part B: Appl Biomater 00B: 000–000, 2015.
Key Words: dental/craniofacial material, dental/endosteal implant, implant design, implant interface, stress shielding
How to cite this article: Ichim PI, Hu X, Bazen JJ, Yi W. 2015. Design optimization of a radial functionally graded dental implant. J Biomed Mater Res Part B 2015:00B:000–000.
INTRODUCTION
Dental implants have undoubtedly been one of the most significant scientific breakthroughs in dentistry over the past 30 years.1At its very basic level, a dental implant is a prosthetic piece, which allows for an artificial crown to be anchored to the bone of the jaws. Implants are surgically placed in the alveolar bone and can have different designs such as blade, cylinder or conical with or without screw threads. When replacing a single tooth, dental implants have obvious biological and functional advantages when compared to conventional restorative options, such as fixed or removable partial dentures, and since the early 1970s, osseointegrated dental implants have been offered as an alternative.2 Over the past two decades dental implants have quickly become the treatment of choice for replacing missing teeth. A decade ago3 has identified [mt]90 implants available to clinicians and since then the number and variety has only increased. There is overwhelming evidence that screwshaped endosseous osseointegrated dental implants have superior clinical outcomes in comparison to other types of dental implants, such as subperiosteal implants, transosseous implants, needle implants, blade implants, etc, which are rarely employed clinically nowadays. Root-shaped or screwshaped implants are currently available in different materials, shapes, sizes, lengths, and with different surface characteristics or coatings. However, it is suggested that there is not
enough evidence from trials to demonstrate superior clinical performance of any particular type amongst various rootformed osseointegrated dental implants.4 The constant improvement in materials and surgical techniques is reflected in the clinical outcomes and existing literature data shows that current survival of oral implants after 10 years varies between 82 and 94%.5 It is rather difficult to define when an implant is “successful” considering the complexity of the factors at play. A number of criteria have been proposed, developed and improved over time and it appears that osseointegration is the major, if not the exclusive, reason for a successful long-term dental treatment.6 Osseointegration as a term stems from Bra˚nemark’s work and nowadays it is described as a “direct structural and functional connection between ordered living bone and the surface of a load-carrying implant.”2,7 The implant surface is critical for osseointegration and will condition how much of the implant surface directly contacts bone, how rapidly this bone accrual occurs, and the mechanical nature of the bone/implant connection is influenced by the nature of the implant surface itself.8 Apart from surface quality, factors such as surgical trauma, occlusal overload, peri-implantitis, microgap, biologic width, and implant crest module are contributing to the osseointegration and long-term clinical success.9
Correspondence to: P. Ichim; e-mail: [email protected] Contract grant sponsor: Australian Research Council’s Discovery Project Grant; contract grant number: DP110105296 Contract grant sponsor: China Scholarship Council (CSC)
C 2015 WILEY PERIODICALS, INC. V
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Occlusal overload is considered a major cause of failure and research shows that overloading produces marginal bone loss and deosseointegration of successfully integrated implants.10,11 It has been postulated that the lack of mechanoreception along the ankylosed interface between the implant and the bone as well as the geometry of the crestal bone can be used to explain the damaging effects of overloading. Consequently, a significant volume of research has been directed toward identifying which implant design or design features yield lower stresses in the surrounding bone.12–15 Additionally, it was suggested that implants, which contain micromechanical parts designed to partially absorb the masticatory load will show less peri-implant bone loss.16 Functionally, graded materials have received significant attention in the recent years as potential candidates for the next generation of dental implants improvement.17 In the case of dental implant, functionally graded materials (FGM) are usually considered to comprise of a mixture of titanium and bioactive hydroxyapatite (HA)/collagen and there are several models presented in literature.18,19 FGM implants are usually graded in axial direction that is, the elastic modulus of the material decreases from the cervical to the apical region of the implant. This gradient can be distributed through the whole implant volume18 or only through its coating.17 Axial grading configurations have been tested using finite element analysis17,18,20 showing a reduction of stresses in peri-implantar bone as well as improved biocompatibility.19 The gradient can also be distributed radially with the elastic modulus decreasing from the centre to the periphery of the implant along its cross-sectional radius and such an effect can be obtained by coating the implant with a thick, strong porous layer. The ingression of bone inside the porosity will generate a more resilient hybrid layer which may contribute to stress buffering as it has the potential to have the same stiffness of the bone tissue at the implant–bone interface. This introduces the concept of isoelastic-dental implants.21 Such an implant can be manufactured using HA in combination with a stronger material (such as zirconia or other ceramic) to provide mechanical resistance as bending strength of a porous HA scaffold is close to zero. A HA-rich scaffold-like coating on a strong HA-containing substrate can be introduced during ceramic composite processing. Our group has recently developed a HA-coating deposition method and the trials have yielded promising results using HA and zirconia to develop a system with graded porosity and material composition.22–24 In this work, we use FEA to test the hypothesis that a low-modulus coating of the implant would reduce the stresses in the peri-implant bone and we use design optimization and the rule of mixture to estimate the elastic modulus and the porosity of the coating that provides optimal stress shielding of the peri-implantar bone.
MATERIALS AND METHOD
For the purpose of this study, cylindrical implant models with a straight crest module were manually created in a
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commercial CAD software (Rhinoceros 3D for Windows, Robert McNeel&Associates). Cylindrical implant design was chosen to reduce the gradient of stresses at the interface, which would have resulted from a tapered design. The abutment was modelled as contiguous with the implant fixture and its attachment features (e.g., internal screw, hex) were not modelled. All cylindrical implant models consisted of a core covered by two 100 lm concentric layers of coating. This particular setting was chosen to reflect our manufacturing procedure in which a strong zirconia core is layered with a porous zirconia-HA coating.22 The coating layer thickness was chosen to accommodate a pore size which has been shown to facilitate bone formation during osseointegration of scaffolding structures.25 Also included in the analysis was a generic threaded implant design (screw-shaped) to allow for a more comprehensive referencing of the peri-implantar stresses generated by the optimized implant. Four implant sizes were considered to account some of the most common implants dimensions, 3.25, 4, 5, and 6 mm. For all sizes considered the length of the implant was 10 mm with a 7 mm height abutment. For the screwshaped implant design, the thread features [Figure 1(B)] were identical for all diameters considered. All implant models were embedded in simulated alveolar bone which consisted of a 2 mm thick cortical layer enclosing the cancellous bone. A minimum of 2.5 mm thickness of cancellous bone was maintained around the implant. Eleven regions of interest (sensors) have been further defined in the bone volume around the implant as concentric 1 mm height and 0.5 mm width layers to gather the numerical readings from simulations. The junctional margin of the cervical bone (S11) was further rounded slightly to avoid numerical-induced stress concentrations [Figure 1(A)]. The geometrical models were then exported to a commercial FEA package (SolidWorks, Dassault Systems) and meshed with 0.4 mm high-order solid elements. The sensors were meshed with 0.2 mm high-order elements [Figure 1(B)]. All the contacts between the implant and the bone were considered as bonded, a situation which can approximate full osseointegration of the implant.26 All the materials in this study have been assumed as isotropic and uniform and although it has been shown that biological structures such as bone are not isotropic, this is a common assumption in numerical modelling of oral structures.27–29 The cortical bone was considered to have an elastic modulus of 13.7 GPa and the cancellous bone of 7.9 GPa. The core of the cylindrical implant was considered to be made out of zirconia-HA composite with an elastic modulus of 110 GPa. The threaded implant was taken as manufactured of titanium alloy with an elastic modulus of 110 GPa. The Poisson’s ratio for all materials was considered as 0.3. All the models have been restrained on base supporting bone and loaded with a force of 100 N applied vertically and at 15 , 30 , and 45 in bucco-lingual direction on the top of the abutment. We have chosen these four loadcases to encompass the range of directions under which the implant receives occlusal loading.
DESIGN OPTIMIZATION OF DENTAL IMPLANT
ORIGINAL RESEARCH REPORT
FIGURE 1. Axial cross-section of the layered geometry used for this study (A) showing the sensors numbered from 1(apical) to 11(cervical) and the cortical and cancellous bone. Inset shows the coating layers and the rounded cervical margin of S11. B: shows the meshed threaded model and the specifications of the thread. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
To calculate the optimal elastic modulus of the coating layers we have used successive linear elastic analyses using the optimization algorithm built in a commercial CAD package (Solidworks, Dassault Syste`mes SolidWorks Corp) and which is based on design of experiments method, Rechtschafner design. Because the screw-shaped designs were used only for referencing, they were not subjected to optimization analyses; instead we only mapped the resulting stresses in each of the 10 sensors for each loadcase and diameter. The optimization process consisted of 27 analyses for each loadcase and for each implant diameter. The variables of the optimization procedure were the elastic moduli of the two coating layers and its goal was to minimize the stresses in the surrounding bone as calculated in the sensor areas. Because each layer was calculated separately we could identify if the solution indicated a gradient of the modulus across the thickness of the coating layer, from the high modulus core to the soft cancellous bone. The variables, that is, elastic modulus of the coating layers ranged from 45 to 110 GPa with a step of 20 GPa. The initial 45 GPa elastic modulus was calculated using the rule of mixtures and considering that the resulting hybrid bone/coating can be regarded as particulate composite material. During the coating process, the pores are introduced using PMMA spherical microspheres and the maximum random close packing ratio of spherical particles is 0.63.30 Under the ideal and simplified assumption that all the pores will be fully colonized by cancellous bone, we used direct rule of mixture to estimate the upper bound of the resulting coating with maximum porosity as Efinal 5
VboneEbone 1 (1 2 Vbone)Eimplant where Vbone 5 0.63 and Eimplant 5 110 GPa. Rule of mixtures has been used previously by other authors to estimate the material boundaries for implant optimization studies.17,18 The goal of the optimization was set as reduction of compressive and tensile stresses in sensor S10, weighted equally 50:50 in their priority. S10 was located 1 mm below the crest module of the implant. We have chosen the cervical area of the bone as the site for our numerical readings as it was shown in a number of previous analysis that it concentrates the highest stresses and a consistent gradient develops from the cervical to the apical area. The very top S11 was not used to avoid referring to a site where errors could occur due to numerical artefacts caused by the sharp junction between three materials. After the optimization process was finalized, the magnitude of principal stresses (their maximum and average values) were recorded and contrasted at every sensor site for every loadcase and dimension. This approach allowed us to compare both absolute values as well as the efficiency of the optimized design to minimise stress. We have opted for principal stresses so that we can differentiate between compression and tension as comparative in vivo data suggested that the bone has different resorption thresholds in tension and compression.31
RESULTS
The optimization results for the elastic modulus of the coatings are given in Table I. It can be seen that the results are
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TABLE I. Results of the Optimization Starting from an Initial Elastic Modulus of 110 GPa for Both External and Internal Layers Implant Diameter 3.25 mm 4 mm 5 mm 6 mm
Layer (GPa)
Vertical Loading
15 Loading
30 Loading
45 Loading
External layer modulus Internal layer modulus External layer modulus Internal layer modulus External layer modulus Internal layer modulus External layer modulus Internal layer modulus
45 110 45 110 45 110 45 110
45 110 45 110 45 110 45 110
45 110 45 110 45 110 45 110
45 110 45 110 45 110 45 110
consistently identical for all the diameters and loadcases considered. The optimization solution indicates that only the external layer requires a low modulus and the optimal value is the initial one of 45 GPa. By contrast the internal layer retains its initial E of 180 GPa. These polarized results show that the solution does not indicate a benefit of gradient of the elastic moduli of the coating. Furthermore, there is no difference in the solution between the implant diameters considered. When the optimization trends are analyzed separately, the elastic modulus of the external coating layer shows a significant and nonlinear relationship with the stresses generated in the peri-implant bone. Figure 2 shows the relationship between the value of the E of the external coating and the maximum principal stresses in the peri-implantar bone for the 5 mm implant with the E of internal layer set at 110 GPa (optimal result). The figure shows that the correlation pattern is mirrored in compression and in tension and the stress reduction effect is reduced once the E of the external coating exceeds 100 GPa. This trend was consistent amongst all the cases considered. By contrast, the variation in the elastic modulus of the internal coating layer shows a rather opposite effect with an inverse and nonlinear relationship with the stresses generated in the peri-implant bone. Figure 3 shows the relationship between the value of the E of the internal coating and the maximum principal stresses in the peri-implantar bone for the 5 mm implant with the E of external layer set at 45
GPa (optimal result). By comparing to Figure 2, the modest effect that the variation of the elasticity of the internal layer has on the stress reduction can also be seen. Table II shows the change in maximum principal stresses (tension and compression) between the optimized, nonoptimized and threaded designs at S10. The threaded design has consistently induced the highest stresses in the peri-implantar bone for both compression and tension. It can also be seen that the optimized design induces a consistent reduction of the maximum tensile and compressive stresses of 60% across all the loadcases compared to the nonoptimized design. The only exception from this consistency is the case of vertical loading when a very small or no reduction is recorded. Table III shows the change in average principal stresses (tension and compression) between the optimized, nonoptimized, and threaded designs at S10. Unlike the maximum stresses, these results have been calculated by averaging all the compressive or tensile nodal values for the whole volume of the sensor. The reduction in average tensile and compressive stresses is lesser than for the maximum ones but it preserves the pattern with a very small, if any reduction recorded for the tensile stresses under vertical loading. Again, the threaded design shows the highest average stresses in the peri-implantar bone. A detailed comparative mapping of the principal and average stresses shows a remarkably consistent pattern in
FIGURE 2. Trend lines illustrating the influence of the elastic modulus of the external layer on the maximum principal stresses in the periimplant bone measured at S10 (10 mm from the apex) as a function of the direction of loading for 5 mm implants. The elastic modulus of the internal coating was 110 GPa. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
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DESIGN OPTIMIZATION OF DENTAL IMPLANT
ORIGINAL RESEARCH REPORT
FIGURE 3. Trend lines illustrating the influence of the elastic modulus of the internal layerand on the maximum principal stresses in the periimplant bone measured at S10 as a function of the direction of loading for 5 mm implants. The elastic modulus of the external coating was 45 GPa. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
all cases considered with a reduction in the calculated tensile and compressive stresses in the bone surrounding the optimized implants. The results indicate that magnitude of this stress reduction is greater for maximum and less so for the average calculated principal stresses. Figures 4 and 5 show such a comparative mapping of the maximum principal compressive and tensile stresses as calculated for each sensor for the 5 mm implant under 0 and 45 loading, respectively, for the threaded, nonoptimized and optimized cases. It can be seen that the periimplantar bone surrounding the optimized implant design experiences far less stress (both compressive and tensile) as compared with the ones generated by a high-modulus nonoptimized or a threaded design. By contrast, this reduction affects the average stresses developed in the peri-implantar bone to a lesser extent. Our results further suggest that the stress reduction of the maximum stresses in the bone increases with the direction of loading with the least reduction for vertical loading and with a slight tendency to affect more compressive stresses than the tensile ones.
An interesting observation is that the top cervical millimetre of peri-implantar bone constantly experienced the most intense stresses for all loadcases and implant diameters and designs both in tension and compression (Figures 4 and 5). Figure 6 comparatively illustrates the cross-section of the tensile plots for the 5 mm diameter implants under 45 loading for the nonoptimized, optimized, and threaded designs. It can be observed that the low modulus external layer of the optimized design is experiencing lower stressed [Figure 6(B), arrow inset] as compared with a similar design implant manufactured entirely from high-modulus material [Figure 6(A)]. Additionally, it shows an increase in the stress around the threads of the implant for the screw design, as compared with the smooth surface one [Figure 6(C)]. This pattern was consistent amongst all cases considered. DISCUSSION
In this work, we use FEA to test the hypothesis that a lowmodulus coating of a cylindrical zirconia dental implant would reduce the stresses in the peri-implant bone and we
TABLE II. Maximum Calculated Principal Stresses in MPa at S10 (1 mm Below the Crest Module) for the Nonoptimized (N/O), Optimized (O), and Screw-Shaped Implant Designs 15
Vertical Implant diameter
Maximum stress
3.25 mm Compression (MPa) Tension (MPa) 4 mm Compression (MPa) Tension (MPa) 5 mm Compression (MPa) Tension (MPa) 6 mm Compression (MPa) Tension (MPa)
N/O
O
Screw Shaped
N/O
O
30 Screw Shaped
N/O
O
45 Screw Shaped
N/O
O
Screw Shaped
26.81 23.85 217.06 229.08 212.53 266.65 249.51 226.63 2111.52 265.89 228.54 2147.47 1.05 1.05 24.65 22.03
3.9 15.46 7.08 10.70 217.19 210.03
0.78 0.74 23.14 21.80
2.67 9.06 26.54 210.71
5.06 16.08 22.04 26.07 220.81 217.58
12.32 29.97
41.6 233.7
0.55 0.54 22.25 21.28
1.87 25.32
4.73 27.00
2.67 8.4 12.26 24.03 214.54 211.28
6.92 26.51
21.38 18.75 222.98 214.61
1.34
2.50
0.43
0.43
1.56
27.17 36.56 20.07 32.27 228.88 216.81
3.7
7.01
JOURNAL OF BIOMEDICAL MATERIALS RESEARCH B: APPLIED BIOMATERIALS | MONTH 2015 VOL 00B, ISSUE 00
4.28
62.85 54.66 24.48 54.46 238.12 230.34
10.49
33.15 26.78 222.99 213.02
10.93
93.5 72.22 63.67 243.86
10.61 28.45
32.59 229.64
6.65
16.41
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TABLE III. Average Calculated Principal Stresses in MPa at S10 (1 mm Below the Crest Module) for the Nonoptimized (N/O), Optimized (O) Implant Design and Threaded Designs 15
Vertical
30
45
Implant Diameter
Average Stress (MPa)
N/O
O
Screw Shaped
N/O
O
Screw Shaped
N/O
O
Thread
N/O
O
Screw Shaped
3.25 mm
Compression Tension Compression Tension Compression Tension Compression Tension
21.98 0.00 21.33 0.32 20.92 0.22 20.66 0.15
21.71 0.00 20.97 0.31 20.81 0.23 20.57 0.16
22.38 0.51 21.55 2.67 21.06 0.22 20.75 0.16
23.27 1.79 21.99 1.01 21.30 0.64 20.91 0.44
22.36 1.49 21.81 0.96 21.17 0.61 20.81 0.43
23.95 2.01 22.42 1.06 21.42 0.69 21 0.43
25.38 4.07 23.21 2.33 22.09 1.50 21.46 1.04
24.70 3.65 22.94 2.18 21.89 1.41 21.33 0.99
26.4 4.58 23.88 2.51 22.22 1.65 21.57 1.05
27.09 6.05 24.20 3.49 22.73 2.27 21.90 1.57
25.32 4.73 23.63 3.11 22.49 2.10 21.74 1.48
28.4 6.83 25.07 3.79 22.87 2.5 22.03 1.61
4 mm 5 mm 6 mm
FIGURE 4. Comparative mapping of the maximum and average principal stresses calculated for a 5 mm diameter implant under vertical loading. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
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DESIGN OPTIMIZATION OF DENTAL IMPLANT
ORIGINAL RESEARCH REPORT
FIGURE 5. Comparative mapping of the maximum and average principal stresses calculated for the optimized and nonoptimized design of the 5 mm diameter implant under a 45 loading. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
use design optimization and the rule of mixture to estimate the elastic modulus and the porosity of the coating that provides best stress shielding. Design optimization of dental implants is not new and a number of efforts have been made in this direction. However, they were concerned more with an axial grading of the material from cervical to apical, be it the whole body of the implant18 or just the coating.17 In this work, we have taken a different approach and we have tried first to establish if the gradient is needed and then to determine the elastic modulus of the coating. Another difference between our work and previously published ones is that we have employed principal stresses (compression and tension) and not von Mises. We have opted for principal stresses as we are interpreting our results in the light of proposed thresholds for bone resorption31 and whilst von Mises is a relatable quantity, it only gives an indication of an overall
distortion of the body and cannot differentiate between tension and compression. The screw-shaped design has consistently shown the highest maximum stresses when compared to a nonthreaded and this can be explained by the presence of the threads whose geometry facilitate stress concentration. By contrast the differences between the average stresses induced by threaded and nonthreaded designs are rather small. Our results show that a thick, low modulus coating is capable of reducing the maximum compressive and tensile stresses in the peri-implant bone by up to 50% over the body of the fixture. The coating also reduces the average stresses in the peri-implant bone, but to a lesser degree of about 15%. The calculated optimal thickness of the coating was consistently 100 lm, which is only half of the considered total thickness of the optimization domain and it is not
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FIGURE 6. Comparative tensile stresses cross-sectional plots in the nonoptimized (A), optimized (B) and screw-shape design (C) for a 5 mm diameter implant loaded at 45 . Deformation scale 3100. Insets show close-ups of the interfacial areas; note the reduced stress recorded in the optimized low-modulus layer (B, arrows). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
influenced by the diameter of the implant. Previous works have reported stress reduction with a thicker coating of 150 lm17 but this discrepancy can be explained by difference in the direction of grading and numerical method. The results suggest that the optimal elastic modulus is 45 GPa, which is also the lowest boundary as considered by us for the optimization problem. This translates in a porosity fraction of 0.63 which is the maximum random close packing fraction of spherical particles.30 The implant pore size considered in this work is 100 lm because of its need to physically fit within the optimization layers and furthermore, such a porous structure can be manufactured using the method developed by our team.22–24 This involves a low-density-slip coating-deposition and coating-substrate cosintering process to deposit micro-porous HA/tri-calcium phosphate based coatings on zirconia substrate presintered at 900 C. The final coatingsubstrate cosintering is carried out at higher temperature, for example, 1300 C. In this way, thick scaffold-like HA-coatings with multiscale open pores can be achieved and the method is more versatile because the polymer and gelatine required for freeze-drying allow more freedom in pore structure design and formation. The density of the pores eventually dictates the elastic modulus of the resulting coating as it gives the total volume fraction available for bone ingrowth which in turn is the lowest of the elastic moduli considered in the rule of mixtures. As our optimization shows that a lower modulus of the external coating results in an increased buffering capacity then it is reasonable to assume suggest that pore size and porosity of the coating will influence the tensile and compressive stresses in the peri-implant bone in addition to the thickness of the coating. Indeed, experimental measurements of porous HA-based scaffolds indicate that increasing the concentration of porogen compromised the mechanical properties and a larger porogen particle size led to increased tensile strength but a reduction in Young’s modulus.32
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Additional to pore dentistry and size, their bone infill content will also come into play in determining the final elastic modulus of the coating. As a limitation of this study, we based it on the ideal assumption that all the pores of the coating will be colonized and fully filled with bone. These are conditions that are unlikely to be met in vivo and experimental human data shows that the average percentage of contact between bone and implant ranges from 25.1 to 83%. As such, a partial colonization of the pores will further lower the elastic modulus of the coating. Another limitation of our modeling in this study is the thickness of the cortical bone, which is generally
