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Numerical simulation of the effect of time-to-loading on peri-implant bone
Medical Engineering & Physics 32 (2010) 7–13
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Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Numerical simulation of the effect of time-to-loading on peri-implant bone Kıvanc¸ Akc¸a a,∗ , Atılım Eser b , Senay Canay a a b
Department of Prosthodontics, Faculty of Dentistry, Hacettepe University, 06100 Sıhhiye, Ankara, Turkey Mechanical Engineering Department, Faculty of Engineering, Middle East Technical University, Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 20 February 2009 Received in revised form 7 September 2009 Accepted 1 October 2009 Keywords: Biomechanics Immediate loading Early loading Conventional loading Finite element analyses
a b s t r a c t Purpose: To evaluate the effect of time-to-loading on trabecular bone around single-tooth dental implants using numerical solutions based on computer models. Materials and methods: A global model with a coarse mesh carrying a Straumann dental implant (043.033S; Institut Straumann, Basel, Switzerland) was created. A region of interest in trabecular bone was defined to study a localized part of the global model with a refined mesh. Time-to-loading submodels to simulate 2 h, 4 days, 1, 4, 6 and 12 wks of trabecular bone-healing status were designed and created. Bone types were considered in the simulation by different elastic bone properties. A 100-N oblique static load was applied. Maximum and minimum principal stresses were calculated and visualized. Results: Bone types with higher elastic moduli experienced higher stress levels. Changes in the quality and quantity of bone at the bone-implant interface did not affect the overall stress distribution. Peri-implant bone with a higher elastic modulus preserved the stress increase at the implant–bone interface. Discussion: Reduced bone contact may not have a prevailing effect over bone quality and quantity on stress generation at the peri-implant bone. Conclusion: Time-to-loading of single-tooth implants may not differ in terms of load distributions in neighboring peri-implant bone. © 2009 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Oft-cited scientific papers [1,2] showing direct bone apposition on a titanium surface are accepted as milestones that initiated substantial changes in prosthetic treatment principles. In this regard, intraosseous anchorage [1] and functional ankylosis [2] were the outcome used to describe bone regeneration upon a titanium implant. Initially, a load-free healing period and a machined titanium surface were the dictated prerequisites that were widely accepted to achieve osseointegration [3]. However, multiple scientific endeavors have led to clarification of the biomechanical aspects of the many different surgical and prosthetic approaches. Consequently, consensus reports from independent foundations have been published to present the scientifically acceptable protocols in implant dentistry [4–6]. From a prosthetic point of view, eliminating or shortening the edentulous state of patients has been a topic of interest over the years. Accordingly, the expressions and the definitions of immediate- and early-loading were made depending on published evidence [7]. The biological concepts behind the immediately- and early-loaded dental implants are quite different from each other.
∗ Corresponding author at: C¸etin Emec¸ Bulvarı, 6.cadde 54/3 06450 Övec¸ler, Ankara, Turkey. Tel.: +90 532 2838758. E-mail address: [email protected] (K. Akc¸a).
The concept of transmucosal healing [8] and the clinical use of a rough implant surface [9] were overlooked in the early developmental years of dental implantology. However, extension of an implant into the oral cavity following surgical placement and the requirement of a rough surface are now accepted as mediators for mechanico-biological stimulation. Single-tooth replacements in anterior and posterior sites without excessive tissue deficiencies utilize dental implants as predictable treatment. However, scientific documentation so far is inconclusive concerning the time-to-loading schedule for singletooth implants [10]. In this regard, clinical studies are inconclusive about the immediate loading of single-tooth implants [11,12,10]. A decision on the loading protocol for single-tooth implants is crucial because load participation is extremely limited. This is even more complicated with site-specific mechanical potential of bone and macro/micro-properties of implant design. The bone–implant interface at immediate- and early-loading is naturally different than that of an osseointegrated implant subjected to conventional loading. Cortical bone quality and quantity is a key to success in the maintenance of biological bone contact with the implant. However, trabecular bone becomes more important during the healing period where the immediate- and early-loading protocols are concerned because of its high physiological remodeling capacity. Thus, understanding the load transfer on peri-implant trabecular bone during initial bone remodeling is crucial. For this purpose, animal studies [13,14] have focused on tra-
1350-4533/$ – see front matter © 2009 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2009.10.001
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becular bone rather than cortical bone. Due to demanding scientific procedures in animal studies, numerical simulations [15,16] have been applied, despite concerns on the information gathered from simulations. Conceptually, two common methods are employed in simulative approaches. One depends on mathematical theories of bone adaptation to predict changes in bone [17]. The other claims a creation of realistic numerical models to virtualize the actual as closely as possible [18]. Due to the efficacy of the latter approach, the actual behavior of bone–implant interface was evaluated using refined numerical models [19]. Additionally, implementation of actual data into finite elements models for highly accurate simulations has been considered, and even a methodology in creation of finite element models based on computer reconstructions from cross-sectional images made by a micro-CT scanner was defined elsewhere [20]. Various approaches such as integration of animal study outcomes into computational simulations [21] or referral to histologic data [22] have been applied to ensure more realistic solutions. Detailed numerical modeling supplemented with biologically verified data may be better at approximating the bone–implant relationship when compared with computer models solely based on assumptions. The purpose of this study, therefore, was to evaluate the stress distribution in the neighboring trabecular bone at various times-to-loading of single-tooth implants within the models created using experimental biological data.
Fig. 1. A global model with a coarse mesh was used to facilitate the effect of the local details at the defined area.
cortical layer and included 0.9 mm wide peri-implant bone with a length of one thread in symmetrical configuration (Fig. 2).
2. Materials and methods In this biomechanical study, the effect of time-to-loading on stress generation in peri-implant trabecular bone was evaluated on models created numerically. Early-loading of a dental implant at 4 days and 1, 4 and 6 wks was simulated. Models of 2 h and 12 wks after implant placement were created for simulation of immediate- and conventional-loading, respectively. In the simulations of immediate-, early- and conventional-loading conditions, bone quality and quantity were designed and modeled according to the histologic, histometric and morphometric findings around a rough surfaced a dental implant that were presented previously [23,24]. 2.1. Numerical models to simulate time-to-loading Submodeling with a global model was applied in the creation and analysis of early-, immediately- and conventionally-loaded single-tooth implant scenarios. A submodeling technique was utilized to study localized parts of a model with a refined mesh based on the solution from a global model with a coarse mesh. In the modeling, the node-based technique was applied. The displacements were derived from the global analyses and used for the submodel analyses. Accordingly, the global model was comprised of a Straumann Dental Implant (043.033S; Institut Straumann, Basel, Switzerland) with a solid abutment (048.541; Institut Straumann) embedded vertically in the center of a rectangular prism, representing trabecular bone with 1 mm cortical bone (Fig. 1). The submodel for localized details rested in trabecular bone below the
2.2. Peri-implant bone modeling Six submodels with refined mesh representing 2 h, 4 days, 1, 4, 6 and 12 wks of bone healing were modeled. In peri-implant bone, two regions of interest (ROI) were defined referring to implant surface; adjacent (a-ROI) and near (n-ROI). a-ROI was defined to simulate different states of bone–implant interface with a width of 0.25 mm adjacent to implant surface. The remaining area resting in 0.9 mm wide peri-implant bone was assumed to be neighboring constant bone support (n-ROI) (Fig. 3). Trabecular architecture was considered in the modeling of periimplant bone. For n-ROIs, elements were randomly selected once in the 2 h model and kept unchanged for the others. For a-ROIs, the element selection process was fundamentally based on histomorphometric data presented previously [24]. Trabecular bone around the tip of thread displayed with nondecalcified ground sections were traced and copied manually for the selected time intervals. Each drawing was separately coupled with a print of 2-D mesh to establish each submodel and the outlines of trabecular bone were transferred. Accordingly the elements were selected that remained in the outline drawing of trabecular bone. To represent marrow spaces, the elements not selected for trabecular architecture were not set in any material. Bone apposition was simulated in a-ROIs, as the neighboring elements were either in contact or bonded to the implant surface based on the information given with the boneto-implant contact data [24].
Fig. 2. A defined area to study a localized part of the global model, and submodel, with a refined mesh.
K. Akc¸a et al. / Medical Engineering & Physics 32 (2010) 7–13
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Fig. 3. Virtual landmark in peri-implant bone to distinguish the elements to simulate the bone-healing process.
Woven, parallel-fibered, lamellar and mature bone types in bone formation during healing were addressed in ROIs according to the histologic definitions provided earlier [23]. The relationship between elasticity and density of bone [25] and the density changes during healing of peri-implant bone [26] constituted the basis for numerical simulation of bone types. Mature bone was considered for the elements at the n-ROIs. For the a-ROIs, bone types consecutively differed for 4 days, 1, 4 and 6 wks model in accordance with the formation of woven, parallel-fibered lamellar and mature bone types [23]. 2.3. Preprocessing, analyses and postprocessing
Fig. 4. Models with element definitions and descriptions are shown.
Modeling and analysis/visualization procedures were carried out using MSC.Marc.Mentat 2003 (MSC.Software Corporation, Los Angeles, CA) and Abaqus 6.5.1-Abaqus/Viewer (Simulia, Providence, RI), respectively. Initially, the global model with a coarse mesh was created using 3-D 2nd order tetrahedral elements (Abaqus Element Library: element type C3D10) with 10 nodes. The element quality was verified for free of distortion using Abaqus standard element quality criteria. The numbers of elements and nodes were 25,165 and 41,886, respectively. Then the wireframe and solid geometry of a submodel was created and a 2-D finite
element mesh generation was performed. The refined mesh was manually edited to designate trabeculae in peri-implant bone and the separation between a-ROI and n-ROI. Editing further proceeded for each a-ROI to define the bone types in simulations of 2 h, 4 days, 1, 4 and 6 wks of the bone state after surgery (Fig. 4). Material properties were provided in accordance with the elements selected for woven, parallel-fibered, lamellar and mature bone sets as well as for commercially pure titanium for the elements that replaced the implant (Table 1). Either contact or bond rela-
Table 1 Material properties utilized in the analyses. Young’s modulus (GPa) Bone type Cortical Mature Trabecular Woven Parallel-fibered Lamellar Mature Implant (commercially pure titanium)
Poisson’s ratio
Reference
22.5
0.3
[31]
2.11 3.8 6.6 13.4
0.3 0.3 0.3 0.3
[32] [33] [34] [31]
0.369
[35]
114
10
K. Akc¸a et al. / Medical Engineering & Physics 32 (2010) 7–13 Table 2 Number of nodes and elements used in submodels. Nodes Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
85,698 65,368 77,865 95,684 10,6487 115,848
C3D15 29,581 10,568 12,659 36,849 42,789 45,879
C4D20
Total elements
15,684 15,684 15,684 15,684 15,684 15,684
45,265 26,252 28,343 52,533 58,473 61,563
from the region of interest, according to Saint Venant’s Principle [27], to minimize the effect on the results at the implant bone interface. To enhance the presentation of the results, maximum and minimum principal stresses developed at the elements in the a-ROIs were recorded separately to calculate the mean for each bone type at mid-planar section. The highest values were also noted (Fig. 6). The stresses were further visualized to describe the load distribution in peri-implant bone. 3. Results Maximum principal stresses that primarily denote the tensile stress state were remarkably higher on the side of load application (tension side), whereas minimum principal stresses that delineate the compressive stress state appeared dominant on the opposite side (compression side). Maximum and minimum principal stresses developed in a-ROIs under 100 N of oblique loading are presented at Table 3. To facilitate the interpretation of the results, tension and compression sides are separately evaluated in accordance with maximum and minimum principal stress values, respectively. On the tension side (Table 3), stresses generated at mature bone were similar at 2 h, 4 days and 1 wk models. With the establishment of a bond relation at 4, 6 and 12 wks model, stresses slightly increased but remained close to each other. Mature and lamellar bone received remarkably higher stresses than parallel-fibered and woven bone. On the compression side (Table 3), a discernable increase in stress at mature bone between the 2 h and 4 days models was folTable 3 Maximum and minimum principal stress, both means and highest values, at all time-to-loading models for each bone type. Fig. 5. The completed 3-D numerical models of peri-implant bone with different bone quality and quantity.
Maximum principal stress Mature
tionships were proposed between the elements in a-ROIs and the implant surface, based on the peri-implant healing progress (Fig. 4). Then 3-D finite element (FE) model conversions were performed by 360◦ axial rotation of the planar models. The 3-D submodels were visualized and verified for analyses (Fig. 5). 3-D 2nd order triangular prism and brick elements (Abaqus Element Library: element type C3D15 and C3D20) were used in the submodels. An element quality check applied to the global model was also performed for all submodels, and no distorted element was found. The numbers of elements and nodes for the models are given in Table 2. All materials were assumed to be homogenous, isotropic and linearly elastic. A static load of 100 N was applied on top of the abutment surface with an inclination of 20◦ , and submodel analyses were run separately. The boundary conditions for the global model were established by fixing all of the outer faces of the rectangular prism that represented the bone in all degrees of freedom in x, y and z directions. Submodels used the displacements from the global analysis as a boundary load seed. The boundary conditions were set far enough
Mean Tension side Model 1 0.80 Model 2 1.10 Model 3 1.17 Model 4 1.82 Model 5 1.81 Model 6 2.00
Lamellar
Parallel-fibered
Woven
Highest
Mean
Highest
Mean
Highest
Mean
Highest
3.45 3.52 3.38 4.37 4.09 5.39
– – – – 1.18 –
– – – – 6.04 –
– – – 0.08 0.47 –
– – – 0.44 1.97 –
– – 0.00 0.15 0.55 –
– – 0.08 1.33 1.69 –
Minimum principal stress Mature
Lamellar
Parallel-fibered Woven
Mean Highest Mean Highest Mean Highest Mean Highest Compression side Model 1 1.97 Model 2 2.61 Model 3 2.69 Model 4 2.77 Model 5 2.73 Model 6 2.92
8.30 8.62 8.46 6.89 6.49 5.84
– – – – 1.02 –
– – – – 3.21 –
– – – 0.60 0.74 –
– – – 2.71 1.79 –
– – 0.37 0.30 0.96 –
– – 1.55 1.28 2.34 –
K. Akc¸a et al. / Medical Engineering & Physics 32 (2010) 7–13
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Fig. 6. Mid-planar section of the model displays the numbered elements for each bone type.
lowed by a small but continuous increase within the others. Stresses that developed at lamellar, parallel-fibered and woven bone were significantly lower than those observed at mature bone. Numerically fixed contour plots of all models are presented at Fig. 7 to visualize maximum and minimum principal stress distributions on the tension and compression side, respectively. On
the tension side, similar stress distribution at n-ROIs were noted for the 2 h, 4 days and 1 wk models, and changes in bone quantity and quality at a-ROIs did not affect the stresses. For the 4, 6 and 12 wks models, stress distributions differed remarkably. Stress concentration was evident around the n-ROI and a-ROI interface. On the compression side, for the 2 h, 4 days and 1 wk models,
Fig. 7. Maximum and minimum principal stress counter plots at tension and compression sides, respectively.
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stress distributions resembled each other closely, and significant stress concentration was localized near the tip and inferior surface of the implant thread. For the 4, 6 and 12 wks models, stresses were distributed more evenly at a-ROIs, but gradually increased with the time-to-loading period. At 12 wks, stress distribution at peri-implant bone was almost homogenous.
4. Discussion In the last two decades various loading protocols have emerged in dental implantology. Accordingly, the understanding of biological response of bone to enhanced implant surface specifications is accepted as one of the critical factors to effectively model the process. The effect of time-to-loading on load distribution at different bone types around a dental implant with a rough surface was evaluated using numerical models in this study. Submodeling with a global model technique was utilized to determine the effect of local details at defined region of interests. Stress levels at mature bone in a-ROIs on the tension and compression sides showed different rates of progression along the time-to-loading schedule. Notable stress increases were observed at the 4 wks and 4 days models for the tension and compression sides, respectively. The state of boneto-implant relation, contact or bond mainly affects the stress levels on tension side, while the bone quantity might have been decisive on compression side. However, an unexpected decrease in the highest stress values specifically at 4 wks of time-to-loading may suggest that osseointegration may also be important for the compression side. Also, visualization of stress distribution displayed a higher stress concentration at the tip of the thread at 2 h, 4 days and 1 wk models that dissipated following the establishment of bone-to-implant bonding at the 4 wks model. Similarity in stress distributions at n-ROIs for all models was probably due to the proposed constant state of bone quality and quantity at n-ROIs. Interestingly, at 4 days time-to-loading, when bone-to-implant contact is reduced, there are similar stress levels and distributions on both the tension and compression sides in comparison to the 2 h and 4 wks loadings. Therefore, a decrease in the amount of bone at close proximity to the implant in the very early period (4 days) following implant placement may not have a prevailing effect on stress generation at peri-implant bone. The reason behind selecting the node-based technique is that the average stiffness in the region of the submodel does not significantly differ from the average stiffness of the global model. Finite element analysis utilized for osseointegrated dental implants may be too coarse to produce satisfactory results at neighboring bone. To analyze a separate finely meshed region of interest, a submodel was created as part of an entire finite element model to produce more accurate results. The boundaries of the submodel were critically evaluated from an engineering point of view [28]. In addition, there are some studies to enlighten the application procedures of this modeling technique into biological problems [29,30]. However, the necessary information is missing in the field of dental implants. When the shared 2 mm optimum distance between an implant and a tooth root is considered, the 0.9 mm of peri-implant bone in the current study is a reasonable boundary condition for accurate calculations in submodeling. Additionally, similar stiffness properties in submodels and global models may justify the set boundary condition. Evaluation of the displacement pattern would have given more information to explain the relation between stress generation and reduced bone-to-implant contact. The submodeling is also known as the cut-boundary displacement method. In other words, analysis results calculated on the cut boundary of the coarse model are specified as boundary conditions for the submodel. Evaluation of displacement outcomes, therefore, may not be reliable to expand
the outcomes to evaluate the effect of contact loss on peri-implant bone biomechanics. However, another numerical simulation performed with a similar approach to the current study presented increased displacement values for the model with the smaller elastic modulus [19]. Spontaneous changes in the mechanical properties of bone may be another important factor to be considered. Biomechanical consequences of peri-implant bone morphology, particularly at different time-to-loading circumstances, are not well known. In the present study, changes in bone quality and quantity at a-ROIs were simulated to enable comprehension of load distribution around single-tooth implants subjected to various times-to-loading. For this purpose, different elastic properties were considered to represent the mechanical properties of different bone types, as was performed previously [19]. Higher stress levels recorded at bone types with higher elastic moduli on both the tension and compression sides in the current study were consistent with the presented outcomes [19]. Eventually, stress distribution became more homogenized at the 12 wks model, in which bone type at aROI was designed to be mature. Therefore, it can be concluded that stress levels slightly increase as the bone quality and quantity does at the peri-implant trabecular bone. From another point of view, increased stress levels but a more homogenized load distribution at 12 wks may be accepted as normative based on successful longterm clinical outcomes of conventional-loading of dental implants. Decreased but concentrated stresses particularly for 4 and 6 wks models may not accepted as a risk factor for bone–implant interface when promising clinical outcomes of early loaded dental implants are contemplated. However similar stress distribution at earlier time intervals (2 h, 4 days and 1 wk) in which bone-to-implant contact remains contact, may be questioned for increased failures for immediately loaded implants. The perplexing nature of bone architecture and its dynamic capabilities related to mechano-biological properties of bone are not easily incorporated into simulations. The resulting information, therefore, is limited to the scope of the employed modeling approaches, since proof of concept is always demanding. The models created in this study, for example, cannot accurately predict the mechanical competence of trabecular bone based on calculations made using a microstructural finite element approach [20]. Nevertheless, representation of trabecular bone architecture even at a hypothetical level in the current study is similar to an approach applied in another study [22], and is likely to result in more realistic outcomes, as demonstrated recently [36]. In addition to considerations at the structural level for mechanical competence, there are biological factors that play a delicate role in osseointegration. In one model, a proliferation of adherent cells was studied to use in biology and medicine for simulations of cell–substrate interaction [37]. Two studies in which three types of cells and two growth factors were involved in simulation [22,38] concluded that some features of biological factors may be reproduced. Integration of the current outcomes from the consecutively produced models may not be promising, because the numerical solutions are based on verified mathematical theories of bone adaptation [17,39]. Implementation of time-dependent bone modeling/remodeling theories into dental implant biological history is scarce [15,40] and not biologically validated yet.
5. Conclusion Taking the limitations of the current study into consideration, bone type and the relation status to implant (bonded or contacted) are important factors on both stress level and stress distribution at neighboring trabecular bone around single-tooth implants. Changes in trabecular bone at bone-to-implant proximity, partic-
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Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Numerical simulation of the effect of time-to-loading on peri-implant bone Kıvanc¸ Akc¸a a,∗ , Atılım Eser b , Senay Canay a a b
Department of Prosthodontics, Faculty of Dentistry, Hacettepe University, 06100 Sıhhiye, Ankara, Turkey Mechanical Engineering Department, Faculty of Engineering, Middle East Technical University, Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 20 February 2009 Received in revised form 7 September 2009 Accepted 1 October 2009 Keywords: Biomechanics Immediate loading Early loading Conventional loading Finite element analyses
a b s t r a c t Purpose: To evaluate the effect of time-to-loading on trabecular bone around single-tooth dental implants using numerical solutions based on computer models. Materials and methods: A global model with a coarse mesh carrying a Straumann dental implant (043.033S; Institut Straumann, Basel, Switzerland) was created. A region of interest in trabecular bone was defined to study a localized part of the global model with a refined mesh. Time-to-loading submodels to simulate 2 h, 4 days, 1, 4, 6 and 12 wks of trabecular bone-healing status were designed and created. Bone types were considered in the simulation by different elastic bone properties. A 100-N oblique static load was applied. Maximum and minimum principal stresses were calculated and visualized. Results: Bone types with higher elastic moduli experienced higher stress levels. Changes in the quality and quantity of bone at the bone-implant interface did not affect the overall stress distribution. Peri-implant bone with a higher elastic modulus preserved the stress increase at the implant–bone interface. Discussion: Reduced bone contact may not have a prevailing effect over bone quality and quantity on stress generation at the peri-implant bone. Conclusion: Time-to-loading of single-tooth implants may not differ in terms of load distributions in neighboring peri-implant bone. © 2009 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Oft-cited scientific papers [1,2] showing direct bone apposition on a titanium surface are accepted as milestones that initiated substantial changes in prosthetic treatment principles. In this regard, intraosseous anchorage [1] and functional ankylosis [2] were the outcome used to describe bone regeneration upon a titanium implant. Initially, a load-free healing period and a machined titanium surface were the dictated prerequisites that were widely accepted to achieve osseointegration [3]. However, multiple scientific endeavors have led to clarification of the biomechanical aspects of the many different surgical and prosthetic approaches. Consequently, consensus reports from independent foundations have been published to present the scientifically acceptable protocols in implant dentistry [4–6]. From a prosthetic point of view, eliminating or shortening the edentulous state of patients has been a topic of interest over the years. Accordingly, the expressions and the definitions of immediate- and early-loading were made depending on published evidence [7]. The biological concepts behind the immediately- and early-loaded dental implants are quite different from each other.
∗ Corresponding author at: C¸etin Emec¸ Bulvarı, 6.cadde 54/3 06450 Övec¸ler, Ankara, Turkey. Tel.: +90 532 2838758. E-mail address: [email protected] (K. Akc¸a).
The concept of transmucosal healing [8] and the clinical use of a rough implant surface [9] were overlooked in the early developmental years of dental implantology. However, extension of an implant into the oral cavity following surgical placement and the requirement of a rough surface are now accepted as mediators for mechanico-biological stimulation. Single-tooth replacements in anterior and posterior sites without excessive tissue deficiencies utilize dental implants as predictable treatment. However, scientific documentation so far is inconclusive concerning the time-to-loading schedule for singletooth implants [10]. In this regard, clinical studies are inconclusive about the immediate loading of single-tooth implants [11,12,10]. A decision on the loading protocol for single-tooth implants is crucial because load participation is extremely limited. This is even more complicated with site-specific mechanical potential of bone and macro/micro-properties of implant design. The bone–implant interface at immediate- and early-loading is naturally different than that of an osseointegrated implant subjected to conventional loading. Cortical bone quality and quantity is a key to success in the maintenance of biological bone contact with the implant. However, trabecular bone becomes more important during the healing period where the immediate- and early-loading protocols are concerned because of its high physiological remodeling capacity. Thus, understanding the load transfer on peri-implant trabecular bone during initial bone remodeling is crucial. For this purpose, animal studies [13,14] have focused on tra-
1350-4533/$ – see front matter © 2009 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2009.10.001
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becular bone rather than cortical bone. Due to demanding scientific procedures in animal studies, numerical simulations [15,16] have been applied, despite concerns on the information gathered from simulations. Conceptually, two common methods are employed in simulative approaches. One depends on mathematical theories of bone adaptation to predict changes in bone [17]. The other claims a creation of realistic numerical models to virtualize the actual as closely as possible [18]. Due to the efficacy of the latter approach, the actual behavior of bone–implant interface was evaluated using refined numerical models [19]. Additionally, implementation of actual data into finite elements models for highly accurate simulations has been considered, and even a methodology in creation of finite element models based on computer reconstructions from cross-sectional images made by a micro-CT scanner was defined elsewhere [20]. Various approaches such as integration of animal study outcomes into computational simulations [21] or referral to histologic data [22] have been applied to ensure more realistic solutions. Detailed numerical modeling supplemented with biologically verified data may be better at approximating the bone–implant relationship when compared with computer models solely based on assumptions. The purpose of this study, therefore, was to evaluate the stress distribution in the neighboring trabecular bone at various times-to-loading of single-tooth implants within the models created using experimental biological data.
Fig. 1. A global model with a coarse mesh was used to facilitate the effect of the local details at the defined area.
cortical layer and included 0.9 mm wide peri-implant bone with a length of one thread in symmetrical configuration (Fig. 2).
2. Materials and methods In this biomechanical study, the effect of time-to-loading on stress generation in peri-implant trabecular bone was evaluated on models created numerically. Early-loading of a dental implant at 4 days and 1, 4 and 6 wks was simulated. Models of 2 h and 12 wks after implant placement were created for simulation of immediate- and conventional-loading, respectively. In the simulations of immediate-, early- and conventional-loading conditions, bone quality and quantity were designed and modeled according to the histologic, histometric and morphometric findings around a rough surfaced a dental implant that were presented previously [23,24]. 2.1. Numerical models to simulate time-to-loading Submodeling with a global model was applied in the creation and analysis of early-, immediately- and conventionally-loaded single-tooth implant scenarios. A submodeling technique was utilized to study localized parts of a model with a refined mesh based on the solution from a global model with a coarse mesh. In the modeling, the node-based technique was applied. The displacements were derived from the global analyses and used for the submodel analyses. Accordingly, the global model was comprised of a Straumann Dental Implant (043.033S; Institut Straumann, Basel, Switzerland) with a solid abutment (048.541; Institut Straumann) embedded vertically in the center of a rectangular prism, representing trabecular bone with 1 mm cortical bone (Fig. 1). The submodel for localized details rested in trabecular bone below the
2.2. Peri-implant bone modeling Six submodels with refined mesh representing 2 h, 4 days, 1, 4, 6 and 12 wks of bone healing were modeled. In peri-implant bone, two regions of interest (ROI) were defined referring to implant surface; adjacent (a-ROI) and near (n-ROI). a-ROI was defined to simulate different states of bone–implant interface with a width of 0.25 mm adjacent to implant surface. The remaining area resting in 0.9 mm wide peri-implant bone was assumed to be neighboring constant bone support (n-ROI) (Fig. 3). Trabecular architecture was considered in the modeling of periimplant bone. For n-ROIs, elements were randomly selected once in the 2 h model and kept unchanged for the others. For a-ROIs, the element selection process was fundamentally based on histomorphometric data presented previously [24]. Trabecular bone around the tip of thread displayed with nondecalcified ground sections were traced and copied manually for the selected time intervals. Each drawing was separately coupled with a print of 2-D mesh to establish each submodel and the outlines of trabecular bone were transferred. Accordingly the elements were selected that remained in the outline drawing of trabecular bone. To represent marrow spaces, the elements not selected for trabecular architecture were not set in any material. Bone apposition was simulated in a-ROIs, as the neighboring elements were either in contact or bonded to the implant surface based on the information given with the boneto-implant contact data [24].
Fig. 2. A defined area to study a localized part of the global model, and submodel, with a refined mesh.
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Fig. 3. Virtual landmark in peri-implant bone to distinguish the elements to simulate the bone-healing process.
Woven, parallel-fibered, lamellar and mature bone types in bone formation during healing were addressed in ROIs according to the histologic definitions provided earlier [23]. The relationship between elasticity and density of bone [25] and the density changes during healing of peri-implant bone [26] constituted the basis for numerical simulation of bone types. Mature bone was considered for the elements at the n-ROIs. For the a-ROIs, bone types consecutively differed for 4 days, 1, 4 and 6 wks model in accordance with the formation of woven, parallel-fibered lamellar and mature bone types [23]. 2.3. Preprocessing, analyses and postprocessing
Fig. 4. Models with element definitions and descriptions are shown.
Modeling and analysis/visualization procedures were carried out using MSC.Marc.Mentat 2003 (MSC.Software Corporation, Los Angeles, CA) and Abaqus 6.5.1-Abaqus/Viewer (Simulia, Providence, RI), respectively. Initially, the global model with a coarse mesh was created using 3-D 2nd order tetrahedral elements (Abaqus Element Library: element type C3D10) with 10 nodes. The element quality was verified for free of distortion using Abaqus standard element quality criteria. The numbers of elements and nodes were 25,165 and 41,886, respectively. Then the wireframe and solid geometry of a submodel was created and a 2-D finite
element mesh generation was performed. The refined mesh was manually edited to designate trabeculae in peri-implant bone and the separation between a-ROI and n-ROI. Editing further proceeded for each a-ROI to define the bone types in simulations of 2 h, 4 days, 1, 4 and 6 wks of the bone state after surgery (Fig. 4). Material properties were provided in accordance with the elements selected for woven, parallel-fibered, lamellar and mature bone sets as well as for commercially pure titanium for the elements that replaced the implant (Table 1). Either contact or bond rela-
Table 1 Material properties utilized in the analyses. Young’s modulus (GPa) Bone type Cortical Mature Trabecular Woven Parallel-fibered Lamellar Mature Implant (commercially pure titanium)
Poisson’s ratio
Reference
22.5
0.3
[31]
2.11 3.8 6.6 13.4
0.3 0.3 0.3 0.3
[32] [33] [34] [31]
0.369
[35]
114
10
K. Akc¸a et al. / Medical Engineering & Physics 32 (2010) 7–13 Table 2 Number of nodes and elements used in submodels. Nodes Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
85,698 65,368 77,865 95,684 10,6487 115,848
C3D15 29,581 10,568 12,659 36,849 42,789 45,879
C4D20
Total elements
15,684 15,684 15,684 15,684 15,684 15,684
45,265 26,252 28,343 52,533 58,473 61,563
from the region of interest, according to Saint Venant’s Principle [27], to minimize the effect on the results at the implant bone interface. To enhance the presentation of the results, maximum and minimum principal stresses developed at the elements in the a-ROIs were recorded separately to calculate the mean for each bone type at mid-planar section. The highest values were also noted (Fig. 6). The stresses were further visualized to describe the load distribution in peri-implant bone. 3. Results Maximum principal stresses that primarily denote the tensile stress state were remarkably higher on the side of load application (tension side), whereas minimum principal stresses that delineate the compressive stress state appeared dominant on the opposite side (compression side). Maximum and minimum principal stresses developed in a-ROIs under 100 N of oblique loading are presented at Table 3. To facilitate the interpretation of the results, tension and compression sides are separately evaluated in accordance with maximum and minimum principal stress values, respectively. On the tension side (Table 3), stresses generated at mature bone were similar at 2 h, 4 days and 1 wk models. With the establishment of a bond relation at 4, 6 and 12 wks model, stresses slightly increased but remained close to each other. Mature and lamellar bone received remarkably higher stresses than parallel-fibered and woven bone. On the compression side (Table 3), a discernable increase in stress at mature bone between the 2 h and 4 days models was folTable 3 Maximum and minimum principal stress, both means and highest values, at all time-to-loading models for each bone type. Fig. 5. The completed 3-D numerical models of peri-implant bone with different bone quality and quantity.
Maximum principal stress Mature
tionships were proposed between the elements in a-ROIs and the implant surface, based on the peri-implant healing progress (Fig. 4). Then 3-D finite element (FE) model conversions were performed by 360◦ axial rotation of the planar models. The 3-D submodels were visualized and verified for analyses (Fig. 5). 3-D 2nd order triangular prism and brick elements (Abaqus Element Library: element type C3D15 and C3D20) were used in the submodels. An element quality check applied to the global model was also performed for all submodels, and no distorted element was found. The numbers of elements and nodes for the models are given in Table 2. All materials were assumed to be homogenous, isotropic and linearly elastic. A static load of 100 N was applied on top of the abutment surface with an inclination of 20◦ , and submodel analyses were run separately. The boundary conditions for the global model were established by fixing all of the outer faces of the rectangular prism that represented the bone in all degrees of freedom in x, y and z directions. Submodels used the displacements from the global analysis as a boundary load seed. The boundary conditions were set far enough
Mean Tension side Model 1 0.80 Model 2 1.10 Model 3 1.17 Model 4 1.82 Model 5 1.81 Model 6 2.00
Lamellar
Parallel-fibered
Woven
Highest
Mean
Highest
Mean
Highest
Mean
Highest
3.45 3.52 3.38 4.37 4.09 5.39
– – – – 1.18 –
– – – – 6.04 –
– – – 0.08 0.47 –
– – – 0.44 1.97 –
– – 0.00 0.15 0.55 –
– – 0.08 1.33 1.69 –
Minimum principal stress Mature
Lamellar
Parallel-fibered Woven
Mean Highest Mean Highest Mean Highest Mean Highest Compression side Model 1 1.97 Model 2 2.61 Model 3 2.69 Model 4 2.77 Model 5 2.73 Model 6 2.92
8.30 8.62 8.46 6.89 6.49 5.84
– – – – 1.02 –
– – – – 3.21 –
– – – 0.60 0.74 –
– – – 2.71 1.79 –
– – 0.37 0.30 0.96 –
– – 1.55 1.28 2.34 –
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Fig. 6. Mid-planar section of the model displays the numbered elements for each bone type.
lowed by a small but continuous increase within the others. Stresses that developed at lamellar, parallel-fibered and woven bone were significantly lower than those observed at mature bone. Numerically fixed contour plots of all models are presented at Fig. 7 to visualize maximum and minimum principal stress distributions on the tension and compression side, respectively. On
the tension side, similar stress distribution at n-ROIs were noted for the 2 h, 4 days and 1 wk models, and changes in bone quantity and quality at a-ROIs did not affect the stresses. For the 4, 6 and 12 wks models, stress distributions differed remarkably. Stress concentration was evident around the n-ROI and a-ROI interface. On the compression side, for the 2 h, 4 days and 1 wk models,
Fig. 7. Maximum and minimum principal stress counter plots at tension and compression sides, respectively.
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stress distributions resembled each other closely, and significant stress concentration was localized near the tip and inferior surface of the implant thread. For the 4, 6 and 12 wks models, stresses were distributed more evenly at a-ROIs, but gradually increased with the time-to-loading period. At 12 wks, stress distribution at peri-implant bone was almost homogenous.
4. Discussion In the last two decades various loading protocols have emerged in dental implantology. Accordingly, the understanding of biological response of bone to enhanced implant surface specifications is accepted as one of the critical factors to effectively model the process. The effect of time-to-loading on load distribution at different bone types around a dental implant with a rough surface was evaluated using numerical models in this study. Submodeling with a global model technique was utilized to determine the effect of local details at defined region of interests. Stress levels at mature bone in a-ROIs on the tension and compression sides showed different rates of progression along the time-to-loading schedule. Notable stress increases were observed at the 4 wks and 4 days models for the tension and compression sides, respectively. The state of boneto-implant relation, contact or bond mainly affects the stress levels on tension side, while the bone quantity might have been decisive on compression side. However, an unexpected decrease in the highest stress values specifically at 4 wks of time-to-loading may suggest that osseointegration may also be important for the compression side. Also, visualization of stress distribution displayed a higher stress concentration at the tip of the thread at 2 h, 4 days and 1 wk models that dissipated following the establishment of bone-to-implant bonding at the 4 wks model. Similarity in stress distributions at n-ROIs for all models was probably due to the proposed constant state of bone quality and quantity at n-ROIs. Interestingly, at 4 days time-to-loading, when bone-to-implant contact is reduced, there are similar stress levels and distributions on both the tension and compression sides in comparison to the 2 h and 4 wks loadings. Therefore, a decrease in the amount of bone at close proximity to the implant in the very early period (4 days) following implant placement may not have a prevailing effect on stress generation at peri-implant bone. The reason behind selecting the node-based technique is that the average stiffness in the region of the submodel does not significantly differ from the average stiffness of the global model. Finite element analysis utilized for osseointegrated dental implants may be too coarse to produce satisfactory results at neighboring bone. To analyze a separate finely meshed region of interest, a submodel was created as part of an entire finite element model to produce more accurate results. The boundaries of the submodel were critically evaluated from an engineering point of view [28]. In addition, there are some studies to enlighten the application procedures of this modeling technique into biological problems [29,30]. However, the necessary information is missing in the field of dental implants. When the shared 2 mm optimum distance between an implant and a tooth root is considered, the 0.9 mm of peri-implant bone in the current study is a reasonable boundary condition for accurate calculations in submodeling. Additionally, similar stiffness properties in submodels and global models may justify the set boundary condition. Evaluation of the displacement pattern would have given more information to explain the relation between stress generation and reduced bone-to-implant contact. The submodeling is also known as the cut-boundary displacement method. In other words, analysis results calculated on the cut boundary of the coarse model are specified as boundary conditions for the submodel. Evaluation of displacement outcomes, therefore, may not be reliable to expand
the outcomes to evaluate the effect of contact loss on peri-implant bone biomechanics. However, another numerical simulation performed with a similar approach to the current study presented increased displacement values for the model with the smaller elastic modulus [19]. Spontaneous changes in the mechanical properties of bone may be another important factor to be considered. Biomechanical consequences of peri-implant bone morphology, particularly at different time-to-loading circumstances, are not well known. In the present study, changes in bone quality and quantity at a-ROIs were simulated to enable comprehension of load distribution around single-tooth implants subjected to various times-to-loading. For this purpose, different elastic properties were considered to represent the mechanical properties of different bone types, as was performed previously [19]. Higher stress levels recorded at bone types with higher elastic moduli on both the tension and compression sides in the current study were consistent with the presented outcomes [19]. Eventually, stress distribution became more homogenized at the 12 wks model, in which bone type at aROI was designed to be mature. Therefore, it can be concluded that stress levels slightly increase as the bone quality and quantity does at the peri-implant trabecular bone. From another point of view, increased stress levels but a more homogenized load distribution at 12 wks may be accepted as normative based on successful longterm clinical outcomes of conventional-loading of dental implants. Decreased but concentrated stresses particularly for 4 and 6 wks models may not accepted as a risk factor for bone–implant interface when promising clinical outcomes of early loaded dental implants are contemplated. However similar stress distribution at earlier time intervals (2 h, 4 days and 1 wk) in which bone-to-implant contact remains contact, may be questioned for increased failures for immediately loaded implants. The perplexing nature of bone architecture and its dynamic capabilities related to mechano-biological properties of bone are not easily incorporated into simulations. The resulting information, therefore, is limited to the scope of the employed modeling approaches, since proof of concept is always demanding. The models created in this study, for example, cannot accurately predict the mechanical competence of trabecular bone based on calculations made using a microstructural finite element approach [20]. Nevertheless, representation of trabecular bone architecture even at a hypothetical level in the current study is similar to an approach applied in another study [22], and is likely to result in more realistic outcomes, as demonstrated recently [36]. In addition to considerations at the structural level for mechanical competence, there are biological factors that play a delicate role in osseointegration. In one model, a proliferation of adherent cells was studied to use in biology and medicine for simulations of cell–substrate interaction [37]. Two studies in which three types of cells and two growth factors were involved in simulation [22,38] concluded that some features of biological factors may be reproduced. Integration of the current outcomes from the consecutively produced models may not be promising, because the numerical solutions are based on verified mathematical theories of bone adaptation [17,39]. Implementation of time-dependent bone modeling/remodeling theories into dental implant biological history is scarce [15,40] and not biologically validated yet.
5. Conclusion Taking the limitations of the current study into consideration, bone type and the relation status to implant (bonded or contacted) are important factors on both stress level and stress distribution at neighboring trabecular bone around single-tooth implants. Changes in trabecular bone at bone-to-implant proximity, partic-
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