Abstract
Objectives
A validated numerical model for stress/strain predictions is essential in understanding the biomechanical behavior of implant-supported dental prostheses. The digital image correlation (DIC) method for full-field strain measurement was compared with finite element analysis (FEA) in assessing bone strain induced by implants.
Methods
An epoxy resin model simulating the lower arch was made for the experimental test with acrylic resin replicas of the first premolar and second molar and threaded implants replacing the second premolar and first molar. Splinted (G1/G3) and non-splinted (G2/G4) metal-ceramic screw-retained crowns were fabricated and loaded with (G1/G2) or without (G3/G4) the second molar that provided proximal contact. A single-camera, two-dimensional DIC system was used to record deformation of the resin model surface under a load of 250 N. Three-dimensional finite element (FE) models were constructed for the physical models using computer-aided design (CAD) software. Surface strains were used for comparison between the two methods, while internal strains at the implant/resin block interface were calculated using FEA.
Results
Both methods found similar strain distributions over the simulant bone block surface, which indicated possible benefits of having splinted crowns and proximal contact in reducing bone strains. Internal strains predicted by FEA at the implant–resin interface were 8 times higher than those on the surface of the model, and they confirmed the results deduced from the surface strains. FEA gave higher strain values than experiments, probably due to incorrect material properties being used.
Significance
DIC is a useful tool for validating FE models used for the biomechanical analysis of dental prosthesis.
1
Introduction
Understanding how functional loads are transferred to the bone–implant interface will help determine the best prosthetic solution for rehabilitating partially edentulous patients. The transfer of functional loads and the accompanying stresses in an implant supported prosthesis depends on the physical properties and geometric configuration of each component . Continual induction of such stresses affects the bone remodeling process around implants, thus playing an important role in implant survival .
Several techniques have been employed to evaluate the biomechanical behavior of an implant-supported prosthesis, for example, photoelasticity , strain gages and two- or three-dimensional finite element analysis (FEA) . However, no single experimental technique meets all the requirements for completely displaying the extensive physiological interactions involved, while numerical techniques require validation by experiments . Understanding the strengths and shortcomings of each technique is therefore crucial in judging the significance of the biomechanical performance of dental prostheses reported in the literature .
FEA is a numerical method of analysis for stresses and deformations in structures of any given geometry . Physiologic loading involving multiple muscle groups with varying recruitment levels is very difficult to replicate in vitro and has ethical and technical limitations for in vivo testing . Finite element modeling is not limited by some of the complexities of experimental loading scenarios. Among its many applications, it has been used to study the load transfer from a dental implant, and the implant-supported prosthesis, to the supporting tissues by calculating, rather than measuring, tissue stresses and strains . The structure is broken down into many small simple blocks or elements whose mechanical relationships can be described with a set of equations. Solution of these equations allows researchers to predict the stress distribution in the entire structure, including the areas of the implants in contact with the bone that cannot be measured easily. However, the quality of the FE predictions depends strongly on the accuracy of the material data and boundary conditions assumed.
A common strategy is to develop a simple model for the system of interest which can be validated using in vitro or in vivo studies. Once validated, the model is then refined to more accurately represent the system, both anatomically and physiologically , so that it can provide more meaningful or clinically relevant results. Some studies have aimed to validate finite element models by comparing their results with in vitro or in vivo experimental testing using strain gages . Agreement was generally good when considering the overall distribution of the strains induced under the applied load, and the results did not suggest inconsistency in the predicted/measured strains between the FE method and the SG method . However, a linear regression analysis comparing the numerical and experimental strains found only moderate correlation between the two methods ( r 2 = 0.57) . The exclusion of strain comparisons in regions that required greater modeling assumptions improved the correlation ( r 2 = 0.70) . A similar study also found significant differences between the simulated and the experimental results . More validation work is therefore required to improve the accuracy of finite element models for biomechanical analysis.
Digital image correlation (DIC) is an optical method that has been developed to measure the flow of fluid and the surface strain distribution in materials testing . Recent studies have used the DIC method to analyze the biomechanics of an implant-supported prosthesis . Unlike other strain-measuring methods, for example, strain gages that are restricted to measuring where the gage is located, the DIC method provides a full-field strain measurement of the surface of the model under study. It therefore allows a better comparison with the finite element method (FEM), which can provide 2- or even 3-D stress distributions.
This study compared two methods for strain analysis of implant-supported prostheses, the in vitro DIC method and the mathematical FEA. The aim was to validate the FE models using the measured full-field surface strains and then use them to investigate the biomechanical behavior of the implant-supported prostheses in more detail.
2
Materials and methods
2.1
Digital image correlation (DIC) analysis
The in vitro methodology used in this study was similar to the one used in a previously published work .
A polymethylmethacrylate model (Plexiglas ® , Altuglas International, Philadelphia, USA) was made to represent a bone block with dimensions of 68 mm by 25 mm by 15 mm (length, height and depth, respectively). Socket spaces were prepared for the positioning of teeth and implants, simulating part of a partially edentulous mandible restored with two 3.75 mm by 11 mm threaded implants (Titamax GT, Neodent, Curitiba – PR, Brazil). The implants were embedded into the bone block model in the second premolar and first molar positions with cyanoacrylate adhesive (Super Bonder; Loctite Brasil Ltd., Itapevi – SP, Brazil) applied on their surface to represent complete integration . The model was completed with the placement of acrylic replicas of a first premolar and a second molar (Odontofix, Ribeirão Preto – SP, Brazil) using the same adhesive.
One set of implant-supported, 2-unit, splinted fixed partial denture (FPD) and another set of non-splinted FPD were fabricated by an experienced dental technician using current standards for fabrication. The spruing, investment, burnout, and casting techniques were standardized and frameworks were cast in Ni–Cr–Ti alloy (Tilite Omega, Talladium Inc., USA). The splinted framework was placed in the bone block model for laser welding. The specimens were later placed under an optical comparator microscope (Nikon Corp., Tokyo, Japan) at 15× magnification to ensure acceptable fit. The esthetic veneering was made with IPS d.Sign Porcelain (Dentin Body B4, Ivoclar Vivadent, Schaan, Liechtenstein) with the aid of a silicone putty matrix (Zetalabor, Zhermack, SpA, Italy) to standardize the application. Four groups were analyzed: splinted (G1 and G3) and non-splinted (G2 and G4), with (G1 and G2) and without (G3 and G4) the presence of a second molar that provided proximal contact. Interproximal contacts between the FPDs and the resin teeth were standardized by adjusting them using a double-sided carbon foil (AccuFilm II, Parkell, USA) such that an 8-μm tin foil shim could be dragged between the contacting objects without tearing .
Implant-level pick-up impression posts (Neodent) were screwed onto the implants and bonded together with acrylic resin (Pattern Resin LS, GC America Inc., USA) to allow the correct transfer of the implant position to the epoxy model. A polyvinyl siloxane impression (Silicone Master, Talladium do Brasil, Curitiba, PR, Brazil) was made of the acrylic block along with the implant–teeth complex. Roots of the resin teeth were covered with a 0.3-mm layer of polyether impression material (Impregum F, 3M ESPE, Seefeld, Germany) to simulate the periodontal ligament . The tooth replicas and implants were later positioned in the silicone mold and the resin experimental block was cast into this impression directly on the implants and teeth with a medium-modulus epoxy resin designed to simulate healthy cancellous bone (PL-2, Measurements Group, Raleigh, NC, USA) . The crown of the second molar replica was later removed from the model to investigate the effect of not having the proximal contact it provided on the strains generated in the bone block.
The digital image correlation system (StrainMaster, LaVision Inc., Göettingen, Germany) used to calculate the surface strains included a charged-coupled device (CCD) camera (Imager Intense, LaVision Inc.) used for capturing the images of the deforming body and a specialist software package (DaVis 7.2, LaVision Inc.) for subsequent image analysis. The resolution of the CCD camera was of 1039 × 1395 pixels and the maximum gray-scale count (intensity of gray coloring of a pixel) was 4095. A standard calibration plate provided by LaVision was used to calibrate the system. The surface of the resin model facing the CCD camera was sprayed with a fine layer of black paint to produce irregular-shaped speckles for ease of tracking and analysis by the image correlation system . A vertical non-impact point load of up to 250 N was applied to the crown of the FPD replacing the first molar using a universal testing machine (Materials Testing Solutions Systems, Eden Prairie, MN, USA). The bone block model was supported at 2 points with cylindrical pins, giving a 3-point bending configuration with a span length of 48 mm to simulate that of half the arch ( Fig. 1 ).
A region of interest below the applied load was selected between the first and second molars ( Fig. 2 A, region a) for which the induced surface strains were calculated. The direct strains in the horizontal direction ( ε xx , %) were chosen for comparison between the groups and ANOVA with Tukey’s test was applied to check for statistical significance in the differences. The effect of noise must be minimized in order to reveal the difference in strain distribution between the different configurations. As a result, strain values averaged over a horizontal distance of 5 pixels, each being 0.5 mm wide, were calculated for each vertical position along the height of the regions of interest.
The correct performance of the optical strain measurement system was verified by repeating 3 times the same measurement on the model with splinted crowns and the second molar replica present. The 3 measurements were statistically compared (ANOVA and Tukey’s test) to each other with specialist software (JMP 8.1, SAS Institute Inc., NC, USA) to verify repeatability of the results.
2.2
Finite element (FE) modeling and analysis
Three-dimensional FE-models based on the epoxy model used in the experimental analysis (DIC method) were constructed using a computer-aided design (CAD) software (Solidworks, Dassault Systemes, Solidworks Corps, USA) for both splinted and non-splinted FPDs. All models were then transferred to Ansys Workbench 11.0 (Ansys Inc., Canonsburg, PA, USA) for FE simulation. Young’s moduli and Poisson’s ratios of the materials used to construct the 3-D FE models are presented in Table 1 . All materials were assumed to behave linear elastically. The mechanical properties for each material were collected from previously published FE studies . The loading configuration followed that for the DIC analysis, i.e. with a static load of 250 N.
| Material | Young’s modulus (MPa) | Poisson’s ratio |
|---|---|---|
| Dentin | 18,600 | 0.31 |
| Ni–Cr alloy | 218,000 | 0.33 |
| Cortical bone | 13,700 | 0.3 |
| Cancellous bone | 1370 | 0.3 |
| Feldspathic porcelain | 69,000 | 0.3 |
| Titanium | 110,000 | 0.35 |
| Enamel | 84,100 | 0.20 |
| Polyether (Impregum) | 0.35 | 0.13 |
| Epoxy resin (PL-2) | 210 | 0.42 |
| Acrylic resin | 2979 | 0.4 |
The interproximal contacts between the teeth and implants were set as nonlinear frictionless contacts, allowing free sliding and formation of gaps from their relative displacements. To simulate the occlusal load, the upper cylindrical portion of the conical structure was configured with frictionless support to permit only a vertical movement. Frictionless contact was also defined between the ceramic crown and the conical structure, and between the beam and the two supports, which were assumed to be rigid. All other interfaces, for example those between the implants and the epoxy resin, were configured to be perfectly bonded. A geometrically nonlinear, static analysis was carried out.
To ensure consistency and accuracy in the simulations for this study, all the FE models had similar mesh densities, with higher node density in the regions of interest. The 3D models contained a total of 468,590–494,392 quadratic 10-noded tetrahedral elements and 741,500–785,665 nodes. Simple beam theory for 3-point bending was used to calculate the upper bound for the maximum strain at midsection for the model used in this study, i.e. <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='ϵˆ=FLh/8IE’>ϵˆ=FLh/8IEϵˆ=FLh/8IE
ϵ ˆ = F L h / 8 I E
, where <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='ϵˆ’>ϵˆϵˆ
ϵ ˆ
is the maximum strain, F is the force (250 N), L is the span length (50 mm), h is the height (25 mm) of the beam, E is Young’s modulus (210 MPa) and I is the second moment of area at the midsection. For a homogeneous rectangular cross-section, I = bh 3 /12, where b is the width (15 mm) of the beam. Given the reinforcement provided by the model teeth and implants, and the off-center load ( Fig. 1 ), the expected maximum strain at midsection should therefore be lower than 0.95%.
Minimum (most compressive) and maximum (most tensile) principal strains were also calculated with the FE method at the interface between the implant and the resin block for further comparison between the different groups in this study.
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