Abstract
Objectives
Inlay-retained fixed partial dentures are conservative prosthetic restorations. Their failure resistance is influenced by the stress distribution that depends on the material properties as well as the loading conditions. Finite element analysis provides the ability to estimate the loading capacity by simulating the stress distribution in all-ceramic dental restorations. The null-hypothesis of this study was that tooth mobility or tooth bearing condition significantly influences the stress distribution and therefore the failure resistance of all-ceramic inlay-retained fixed dental prostheses. Therefore, the stress distribution under different loading and bearing conditions of the teeth was analyzed using the finite element method.
Methods
Three different bearing conditions, one fixed and two flexible were chosen to simulate tooth mobility. The flexible models were constrained with spring elements to a virtual center of rotation. In addition, loading conditions were varied.
Results
The influence of tooth mobility on the stress distribution depended on the degree of modeled tooth mobility, as well as the loading conditions. The maximum first principal stresses differed significantly in magnitude and location depending on the modeled bearing condition and the simulated load case. The maximum difference between fixed and flexible model was more than 100%.
Significance
Tooth mobility and occlusal loading conditions have to be considered in finite element analyses as the simulated stress distribution is strongly influenced by these factors.
1
Introduction
Inlay-retained fixed dental prostheses (FDP) are a treatment option for indirect restorations . All-ceramic inlay-retained fixed dental prostheses offer excellent esthetics and are less invasive compared to complete-crown-retained fixed dental prostheses . Their structure is more fragile than that of conventional fixed dental prostheses, thus the mechanical reliability must be evaluated very carefully. Furthermore, their failure resistance is dependent on various factors that are all not yet clear. Some of these factors are already identified, such as the material of coping and veneering and the connector dimensions . Other possible factors influencing the reliability of all-ceramic FDPs are the degree of tooth mobility and varying load conditions. These factors are still not sufficiently examined. Therefore one aim of the presented study was therefore to focus the numerical analysis on the influence of these aspects on the resulting stress distributions, which are responsible for the failure of the FDPs.
Moreover, the motivation of this work was a planned integration of structural analysis into a computer-aided design/computer-aided manufacturing (CAD/CAM) software. CAD/CAM for dental restorations is a commonly used method of production . However, as of now no FEM-simulations are integrated within those software packages. An implementation of such simulation tools will allow the dentist or the dental technician to check the design of a dental restoration before integration. The geometry data of crowns and gingiva can be imported from optical scanners. However, no geometry data of the roots is available in this case. Due to this limitations, and because the design process in combination with the structural analyses might be iterative, the model for tooth mobility should be simple.
In order to estimate the clinical long term reliability of all-ceramic dental restorations, it is necessary to calculate the stress distribution resulting from different loading conditions. Finite element analysis is a widespread method to investigate stress distributions numerically . In the literature, two-dimensional and three-dimensional models of dental restorations can be found. There are only a few published works on inlay-retained dental prostheses that consider three-dimensional stress distributions in finite element analysis . Therefore, work on conventional fixed partial dentures was also considered. In these studies, the restoration’s geometric data was designed using computer software or determined by section data from optical scans , computer tomography or X-ray . The data of the root geometry was either found by section data , computer tomography or was designed .
Teeth are integrated in a complex apparatus, the periodontium, which is the most deformable part during short term loading . The periodontal ligament is the main reason for the ability of the teeth to move slightly under loading . The results and precision of numerical simulation of the initial tooth mobility is highly dependent on the chosen constitutive mechanical material properties of the periodontal ligament . In published work, the periodontal ligament and sometimes the surrounding bone material were modeled as one material based on the properties of epoxy (of in vitro test design) or other elastic materials . Some authors modeled the surroundings with different values for bone, roots of dentin and periodontal ligament, all as a linear elastic material . An additional way of modeling the boundary of the root was with rotational axes . Another approach for modeling the surroundings of the root is to represent the tooth mobility with linear and non-linear springs that are oriented around the root in horizontal or normal directions to the surface . In the case of the application of a single force (uncontrolled tipping), the location of the center of rotation is coincident with the center of resistance according to Natali . The center of resistance lies between gingival third of the root and cemento-enamel junction for single rooted teeth and for multi-rooted teeth at the furcation .
Most of the reviewed studies concentrate on perpendicular loading relative to the occlusion plane . The stress distribution of conventional fixed-partial denture under perpendicular loading revealed tensile stress peaks on the basal surface . In studies where different boundary conditions were modeled in order to consider tooth mobility, it was found that tooth mobility, in fact, had an influence. The stresses grew with the increasing resilience of the tooth . In comparison to fully constrained teeth, the maximum first principal stresses increased . Although publications can be found with non-perpendicular loadings , their focus was not on the effect of tooth mobility.
This current study focused on the general effect of tooth mobility on the stress level and distribution within a FDP. Additionally, it evaluated the effect of load angulations. The null-hypothesis of this work was that tooth mobility, especially in combination with different load angulations, has an important influence on stress distribution.
2
Materials and methods
In this study, a finite element analysis was performed to calculate the stress distribution of an all-ceramic, fully anatomical, three-unit, inlay-retained dental prosthesis. The designed inlay-retained dental prosthesis was located between the retainer teeth 45 and 47, which had been optically scanned for the design (etkon es1-Scanner, today: Straumann, Basel, Switzerland). Based on the design data of the inlay-retained dental prosthesis, a 3D-model for the finite element analysis was built (etkon visual, today: Straumann, Basel, Switzerland).
The data of the inlay-retained prosthesis and the retainer teeth were imported in STL-format into the software 3matic (Materialise, Leuven, Belgium). Existing artifacts and defects were fixed in 3matic and holes were virtually closed. Since the aim was to check the general effect of tooth mobility, the inlay-retained dental prostheses were modeled fully as anatomic zirconia to avoid any influence of veneering material or from the design.
The commercial software package ANSYS 12.0 (Ansys Inc., Canonsburg, PA, USA) was used for the finite element analysis. The STL data was imported, and a curvature-based mesh was created. The finite element model was generated by 170,000 ten-node tetrahedral solid elements. The material parameters were Young’s modulus 205 GPa for zirconia and 18 GPa for dentin and the Poisson’s ratios 0.31 for zirconia and 0.27 for dentin .
To investigate the influence of the tooth mobility on the resulting stresses, three bearing conditions were analyzed. The reference model (Model F) was fully constrained at the bottom of the scanned abutment teeth. As a comparison, two additional models were created that were constrained with spring elements to represent tooth mobility (Model R and RT). The roots of the abutment teeth were each replaced by a master node located at the center of rotation proposed by Natali . This master node was rigidly connected to the bottom of the geometry and the springs were connected to the master node guiding the movement of the whole geometry ( Fig. 1 a ). For each degree of freedom one spring element was used. Three translational spring elements with allowed tension and compression were applied in X , Y and Z -directions and three rotational spring elements were added with allowed rotation around respective axes. Assuming small deflections for the presented studies only linear material properties were used. The spring rate values for rotational and translational springs are shown in Table 1 .
| Model | Rotational spring rate | Translational spring rate |
|---|---|---|
| F | – | – |
| R | 100 Nm/rad | 10 9 N/m |
| RT | 100 Nm/rad | 10 6 N/m |
Three load cases were simulated for each bearing condition. The loads were applied to three contact points on the occlusal surface in the center of the pontic ( Fig. 1 a). A total load of 600 N was applied and remained constant in each of the following load cases. The three different investigated load cases were achieved by varying the loading direction 0°, 30° or 60° from posterior.
The finite element analysis type was linear and quasi-static. In post processing, the stress concentration zones were analyzed. For ceramic materials, tensile stresses affect strength much more than compressive stresses . Therefore, the distribution of first principal stress was evaluated.
2
Materials and methods
In this study, a finite element analysis was performed to calculate the stress distribution of an all-ceramic, fully anatomical, three-unit, inlay-retained dental prosthesis. The designed inlay-retained dental prosthesis was located between the retainer teeth 45 and 47, which had been optically scanned for the design (etkon es1-Scanner, today: Straumann, Basel, Switzerland). Based on the design data of the inlay-retained dental prosthesis, a 3D-model for the finite element analysis was built (etkon visual, today: Straumann, Basel, Switzerland).
The data of the inlay-retained prosthesis and the retainer teeth were imported in STL-format into the software 3matic (Materialise, Leuven, Belgium). Existing artifacts and defects were fixed in 3matic and holes were virtually closed. Since the aim was to check the general effect of tooth mobility, the inlay-retained dental prostheses were modeled fully as anatomic zirconia to avoid any influence of veneering material or from the design.
The commercial software package ANSYS 12.0 (Ansys Inc., Canonsburg, PA, USA) was used for the finite element analysis. The STL data was imported, and a curvature-based mesh was created. The finite element model was generated by 170,000 ten-node tetrahedral solid elements. The material parameters were Young’s modulus 205 GPa for zirconia and 18 GPa for dentin and the Poisson’s ratios 0.31 for zirconia and 0.27 for dentin .
To investigate the influence of the tooth mobility on the resulting stresses, three bearing conditions were analyzed. The reference model (Model F) was fully constrained at the bottom of the scanned abutment teeth. As a comparison, two additional models were created that were constrained with spring elements to represent tooth mobility (Model R and RT). The roots of the abutment teeth were each replaced by a master node located at the center of rotation proposed by Natali . This master node was rigidly connected to the bottom of the geometry and the springs were connected to the master node guiding the movement of the whole geometry ( Fig. 1 a ). For each degree of freedom one spring element was used. Three translational spring elements with allowed tension and compression were applied in X , Y and Z -directions and three rotational spring elements were added with allowed rotation around respective axes. Assuming small deflections for the presented studies only linear material properties were used. The spring rate values for rotational and translational springs are shown in Table 1 .
