Abstract
Objectives
To evaluate via finite element analysis the effect of different ferrule heights on stress distribution within each part of a maxillary first premolar (MFP) restored with adhesively luted glass fiber-reinforced resin (GFRR) posts and a ceramic crown.
Methods
The solid models consisted of MFP, periodontal ligament and the corresponding alveolar bone process. Four models were created representing different degrees of coronal tissue loss (0 mm, 1 mm, 2 mm and 3 mm of ferrule height). First set of computing runs was performed for in vivo FE-model validation purposes. In the second part, a 200-N force was applied on the buccal cusp directed at 45° to the longitudinal axis of the tooth. Principal stresses values and distribution were recorded within root, abutment, posts, crown and related adhesive interfaces.
Results
All FE-models showed similar stress distribution within roots, with highest stress present in the chamfer area. In composite abutments higher stress was observed when no ferrule was present compared to ferruled FE-models. Stress distribution within crown and GFRR posts did not differ among the models. Stress values at the adhesive interfaces decreased with increasing ferrule height.
Significance
The stress state at abutment-crown and post-root interfaces was very close to their strength, when ferrule was not present. Similarly, higher ferrule produced more favorable stress distribution at post-abutment and abutment-root interfaces. Endodontically treated teeth with higher ferrule exhibit lower stress at adhesive interfaces that may be expected to lower the probability of clinical failure.
1
Introduction
Endodontically treated teeth are generally considered weaker and more susceptible to fracture than vital teeth . The main change in the biomechanical behavior is attributed to the considerable loss of tooth structure . Preservation of sound radicular and coronal tooth tissue and especially presence of ferrule are important factors for enhancing the performance of structurally compromised endodontically treated teeth . Ferrule is provided by parallel walls of dentin extending coronal to the shoulder of the preparation , which after being encircled by a crown produces a protective effect, called ferrule effect, by reducing stresses within a tooth .
This topic has been studied over the past years and still represents an interesting field of research. Most of the laboratory studies agree on the beneficial effect of ferrule on the fracture resistance of compromised teeth . In addition, the presence of ferrule could reduce the incidence of non-restorable root fractures . Regarding the height of ferrule that is necessary to provide the protective effect, various results were reported. While 1-mm was found enough to significantly increase the number of fatigue cycles prior to failure , no difference in fracture resistance between teeth with 1-mm ferrule and those with no ferrule was found . Additionally, during chewing simulation teeth with 1-mm ferrule exhibited worse performance compared with 2-mm high dentin walls . The minimum heights of ferrule required to significantly improve fracture resistance were 2 mm and 3 mm .
Existing clinical trials could not confirm that ferrule was a factor that significantly influenced the survival of endodontically treated teeth . When all coronal walls were missing, similar failure risk was found in teeth with complete absence of ferrule and those with 2 mm ferrule . Nevertheless, when adequate 2-mm ferrule was included in the preparation design successful treatment outcome was recorded over 2- and 7 year observation period, irrespective of the post type.
The impact of ferrule on stress distribution within the restored tooth under stress has been assessed by several finite element analysis (FEA) studies . It was proved that cervical region of the tooth is indeed exposed to the highest stress and that presence of ferrule reduced the stress level . Analyzing von Mises stresses within the central incisor with 0-mm, 1-mm and 2-mm ferrule it was observed that stress decreased with increased ferrule height, regardless of the post material . However, the differences in stress values were small . Another study, investigating metal cast post-and-core restored tooth, suggested that ferrule height should be determined individually based on the bucco-lingual cervical diameter of the root .
Therefore, the aim of this study was to evaluate via finite element analysis the effect of different ferrule heights on stress distribution within each part of a maxillary first premolar (MFP) restored with adhesively luted glass fiber-reinforced resin (GFRR) posts and a ceramic crown. The null hypothesis was that different ferrule heights do not affect the stress distribution within the tooth.
2
Materials and methods
2.1
Finite elements models generation
The solid models consisted of a maxillary first premolar (MFP), the periodontal ligament (PDL) and the corresponding alveolar bone process. The average anatomical dimensions of the alveolar bone and periodontal ligament (PDL) were generated according to the literature data . The external shape of the premolar was obtained by laser-based 3D digitizing (Cyberware, Inc., Monterey, California, USA) of a plaster cast (Thanaka manufacturer, Japan). The scanned profiles were assembled in a 3D wire frame structure using a 3D CAD (Autocad 12, Autodesk Inc.) and exported into a 3D parametric solid modeler (Pro-Engineering 16.0 Parametric Technologies, USA). Arrangement of dentin and enamel internal volumes and morphologies were modeled according to literature data . The solid models of premolar and surrounding alveolar bone are presented in Fig. 1 a .
The 3D parametric solid modeler software was used to generate four solid-models representing different degrees of coronal tissue loss. The solid-models were represented in a consistent manner, with the ferrule height as the unique geometry variable. Solid-model 0 simulated a premolar restored with a crown in absence of dentin ferrule. Solid-models 1, 2 and 3 simulated teeth with ferrule heights of 1 mm, 2 mm and 3 mm, respectively. Roots of solid-models 0, 1, 2 and 3 are presented in Fig. 1 b. Buccal and palatal glass fiber-reinforced resin (GFRR) post space preparations were modeled in the root canals. GFRR posts had the following dimensions: length 12 mm, coronal diameter 1.5 mm, apical diameter 1.2 mm. Part of the post that was inserted within the root was 9 mm of length, while the remaining 3 mm were incorporated within the abutment. An abutment was modeled according to the dimensions of the MFP prepared for the full crown coverage. The ceramic crown was modeled to fit the abutment.
The four solid-models were imported to the Finite Elements Analysis (FEA) software ANSYS rel. 9.0 (Ansys Inc. Houston). The solid-models were meshed with eight nodes brick with 3 degrees of freedom per node, the crown structure was meshed with 4 nodes tetrahedral elements, finally resulting in four 3D FE models made up of 31,240 elements and 35,841 nodes ( Fig. 2 a ). Accuracy of the model was checked by convergence tests . Cement and adhesive interfaces were simulated by layers of solid brick elements: abutment-root and the abutment-post interfaces, average thickness of 10 μm ; root-post interface, average thickness of 50 μm ; abutment-crown interface, average thickness of 50 μm ( Fig. 2 b).
Enamel and spongy bone were considered as isotropic linear elastic materials . Cortical bone was considered as an orthotropic elastic material according to the mechanical characterization reported by Schwartz-Dabney and Dechow . Dentin was considered as an orthotropic linear material . Although the elastic moduli of the dentin are similar along its plane of symmetry, it could be safely considered as an isotropic material without a significant influence on the outcome. Management of cortical bone and dentin orthotropicity was previously described by Aversa et al. . Crowns elements were coupled to the isotropic mechanical properties (IMP) of zirconia. Abutment elements were coupled to the IMP of a dental composite material (Gradia Core, GC Corp. Tokyo, Japan). Post elements were considered as elastic orthotropic material and coupled to the mechanical properties of unidirectional GFRR. Abutment-root and abutment-posts interfaces volumetric elements were coupled to the IMP of a dental adhesive material . Root-post interface elements were coupled to the IMP of a composite cement (Gradia Core, GC Corp. Tokyo, Japan). Abutment-crown interface elements were coupled to the IMP of a glass-ionomer cement (GC Fuji PLUS, GC Corp. Tokyo, Japan). The mechanical properties of the tissues and the materials simulated in the present study (Young’s modulus [E], shear modulus [G] and Poisson’s ratio [ν]) are reported in Table 1 .
| Material | Direction of maximum stiffness | E1 | E2 | E3 | G12 | G31 | G23 | ν 12 | ν 31 | ν 23 |
|---|---|---|---|---|---|---|---|---|---|---|
| Cortical bone on facial side | 39.9° with respect to the occlusal plane | 11.2 | 14.8 | 18.3 | 4.5 | 4.7 | 5.7 | 0.21 | 0.25 | 0.42 |
| Cortical bone on buccal side | 4.4° with respect to the occlusal plane | 12.1 | 17.7 | 19.5 | 4.9 | 4.9 | 5.1 | 0.16 | 0.31 | 0.53 |
| Dentin | Normal to dentin tubules | 25 | 23.2 | 8.6 | 9.4 | 0.45 | 0.29 | |||
| Glass fibers reinforced resin post | Parallel to glass fibers | 37 | 9.5 | 9.5 | 0.27 | 0.34 | 0.27 | 3.1 | 3.5 | 3.1 |
| Enamel | Isotropic | 84.1 | 0.33 | |||||||
| Cancellous bone | Isotropic | 0.91 | 0.30 | |||||||
| Resin cement/Core build-up (Gradia core, GC Corp.) | Isotropic | 13 | 0.22 | |||||||
| Adhesive material | Isotropic | 1 | 0.24 | |||||||
| Glass-ionomer cement (GC Fuji PLUS, GC Corp.) | Isotropic | 5.1 | 0.27 | |||||||
| Zirconia | Isotropic | 205 | 0.30 |
PDL was considered a non-linear vischo-hyper-elastic material . The method used to account for the strain-rate dependency of stress required the definition of five visco-elastic materials models based on five different stress–strain curves performed at different straining rates . In the present study, “elastic modulus vs. time” curve was evaluated for each stress–strain curve. Then, data were uploaded in the FEA software. A macro was set up in order to enable a time dependent analysis that computed the strain rate of a given element at each sub-step time. The strain value and the corresponding strain rate were interpolated between the “nearest” visco-elastic material FE-models table to evaluate the corresponding stress value. The full explanation of the method, as well as the adopted phenomenological data (stress–strain curves images), has been previously described by the Authors . PDL stiffness in the direction normal to fibers’ main axis depending by PDL shear modulus (G) was evaluated through the procedure reported by Maceri et al. .
2.2
FE-model validation, boundary conditions and applied loads
A healthy volunteer with healthy conditions of MFP tissues, MFP periodontal tissues and MFP dimensions comparable with those of the MFP FE-model was selected for the in vivo FE-model validation. The involvement of a human subject in the study received the ethical approval by an Institutional Review Board (IRB) of the University of Siena (ClinicalTrials.gov number CT01532947). The rights of the enrolled participants have been protected by the IRB of the University of Siena, Italy, and written informed consent was provided by the participant. A linear strain-gauge self-compensated in temperature (C-980204, Micro-oup, Inc. Raleigh, North Carolina, USA) was bonded (Histoacryl, Braun, Italy) on the buccal aspect of the MFP ( Fig. 3 a ). Strain-gauge was connected to a digital strain measuring hardware (Omicron-T, Battipaglia, Italy) interfaced to a personal computer equipped with a software providing data visualization and storage. The strain state was recorded as a function of time.
During the experiments, the MFP was subjected to five loading tests. A force of 5 N was applied 45° with respect to the MFP main axis, in a palatal to buccal versus on the palatal aspect of the buccal cusp by a linear dynamometer (MD1000, Pesola, Italy). The force was kept constant for 10 s. The strain state was reported as the mean of 5 loading tests. A preliminary FEA test showed that 3rd principal strain prevailed on the buccal aspect of the MFP and 3rd principal strain direction was parallel to MFP main axis. Accordingly, the strain-gauge was bonded with its main-axis parallel to the MFP. The strain-gauge signals were recorded in the compressive modalities.
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The FE-models were constrained along the x , y and z axis at the top surface of the maxillary bone.
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First set of computing runs was performed for model validation purposes:
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horizontal load applied on the buccal cusp and directed at 90° to the longitudinal axis of the MFP in palatal to buccal versus. The horizontal load was gradually increased up to 10 N within an overall interval of 75 s ( Fig. 4 a ). The displacement in the direction of the load was computed and compared to literature experimental data ( Fig. 4 b);
Fig. 4 (a) Applied loading conditions: red arrow – 45° load (200 N) applied in the FEA environment to study stress values and distribution in restored premolars (model 0, 1, 2, 3); dashed black arrow – intrusive force (20 N in a time range of 75.00 s) for PDL FE-model validation; orange arrow – 45° load (5 N) applied in the in vivo test for premolar FE-model validation; black arrow – horizontal force (10 N in a time range of 75.00 s) for PDL FE-model validation. (b) Computed horizontal displacement of the premolar FEM compared to in vivo measured data and (c) computed intrusive displacement of the premolar FEM compared to in vivo measured data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) - •
intrusive load applied on the buccal cusp and directed at 0° to the longitudinal axis of the MFP. The intrusive load was gradually increased up to 20 N within an overall interval of 75 s ( Fig. 4 a). The displacement in the direction of the load was computed and compared to literature experimental data ( Fig. 4 c);
- •
oblique load applied on the buccal cusp and directed at 45° to the longitudinal axis of the MFP in palatal to buccal versus. The oblique load was gradually increased up to 5 N within a time interval of 75 s ( Fig. 4 a). Crown 3rd principal strain state was computed and compared to in vivo measured strain ( Fig. 3 b–d).
Second set of computing runs was performed to simulate a characteristic MFP loading condition. The models were loaded with a 200 N force applied on the buccal cusp and directed at 45° to the longitudinal axis of the tooth in coronal-apical and palatal-buccal directions ( Fig. 4 a).
2.3
Presentation of the results
Principals stress analysis was adopted to visualize the computed stress state. Calculated numerical data were transformed into color graphics to visualize mechanical phenomena in the FE models. Principal stresses values and distribution are presented in the following structures: root, abutment, GFRR post, crown, cement layer at the post-root and the post-abutment interface, cement layer between the abutment and the crown, adhesive layer between the abutment and the root or the out-core abutment and the ferrule.
2
Materials and methods
2.1
Finite elements models generation
The solid models consisted of a maxillary first premolar (MFP), the periodontal ligament (PDL) and the corresponding alveolar bone process. The average anatomical dimensions of the alveolar bone and periodontal ligament (PDL) were generated according to the literature data . The external shape of the premolar was obtained by laser-based 3D digitizing (Cyberware, Inc., Monterey, California, USA) of a plaster cast (Thanaka manufacturer, Japan). The scanned profiles were assembled in a 3D wire frame structure using a 3D CAD (Autocad 12, Autodesk Inc.) and exported into a 3D parametric solid modeler (Pro-Engineering 16.0 Parametric Technologies, USA). Arrangement of dentin and enamel internal volumes and morphologies were modeled according to literature data . The solid models of premolar and surrounding alveolar bone are presented in Fig. 1 a .
The 3D parametric solid modeler software was used to generate four solid-models representing different degrees of coronal tissue loss. The solid-models were represented in a consistent manner, with the ferrule height as the unique geometry variable. Solid-model 0 simulated a premolar restored with a crown in absence of dentin ferrule. Solid-models 1, 2 and 3 simulated teeth with ferrule heights of 1 mm, 2 mm and 3 mm, respectively. Roots of solid-models 0, 1, 2 and 3 are presented in Fig. 1 b. Buccal and palatal glass fiber-reinforced resin (GFRR) post space preparations were modeled in the root canals. GFRR posts had the following dimensions: length 12 mm, coronal diameter 1.5 mm, apical diameter 1.2 mm. Part of the post that was inserted within the root was 9 mm of length, while the remaining 3 mm were incorporated within the abutment. An abutment was modeled according to the dimensions of the MFP prepared for the full crown coverage. The ceramic crown was modeled to fit the abutment.
The four solid-models were imported to the Finite Elements Analysis (FEA) software ANSYS rel. 9.0 (Ansys Inc. Houston). The solid-models were meshed with eight nodes brick with 3 degrees of freedom per node, the crown structure was meshed with 4 nodes tetrahedral elements, finally resulting in four 3D FE models made up of 31,240 elements and 35,841 nodes ( Fig. 2 a ). Accuracy of the model was checked by convergence tests . Cement and adhesive interfaces were simulated by layers of solid brick elements: abutment-root and the abutment-post interfaces, average thickness of 10 μm ; root-post interface, average thickness of 50 μm ; abutment-crown interface, average thickness of 50 μm ( Fig. 2 b).
