Finite element analysis of weakened roots restored with composite resin and posts

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1 Dental Materials Journal 2009; 28(6): Finite element analysis of weakened roots restored with composite resin and posts Carla Santina de Miranda COELHO 1, João Carlos Gabrielli BIFFI 2, Gisele Rodrigues da SILVA 3, Anthony ABRAHÃO 4, Roberto Elias CAMPOS 3 and Carlos José SOARES 3 1 Department of Endodontics, School of Dentistry, Catholic University of Brasilia, Q.S.07 lot-01 EPCT, , Distrito Federal, Brazil 2 Department of Endodontics, School of Dentistry, Federal University of Uberlândia, Pará B24, , Minas Gerais, Brazil 3 Department of Operative Dentistry, School of Dentistry, Federal University of Uberlândia, Pará B24, , Minas Gerais, Brazil 4 Faculty of Mechanical Engineering, Federal University of Uberlândia, João Naves de Ávila, 2160, Bloco 1M, , Minas Gerais, Brazil Corresponding author, Carlos José SOARES; carlosjsoares@umuarama.ufu.br Finite element analysis (FEA) was used to investigate the influence of different post systems on the stress distribution of weakened teeth under oblique-load application. A maxillary central incisor root obtained from a sound tooth was weakened by partial removal of dentin inside the root canal. Seven two-dimensional numerical models, one from the sound tooth and six from the weakened root restored with composite resin and post systems were created as follows ST: sound tooth; CPC: cast CuAl post and core; SSP: stainless steel post + composite core; GP: fiberglass + composite core; CP: carbon fiber + composite core; ZP: zirconium dioxide post + composite core; TP: titanium post + composite core. The numerical models were considered to be restored with a leucite-reinforced all-ceramic crown and received a 45º occlusal load (10 N) on the lingual surface. All the materials and structures were considered linear elastic, homogeneous, and isotropic, with the exception of fiberglass and carbon fiber posts which assumed orthotropic behavior. The numerical models were plotted and meshed with isoparametric elements, and the results were analyzed using von Mises and Sy stress criteria. When compared with the sound tooth, FEA revealed differences in stress distribution when post systems were used. Among the restored teeth, the use of CPC, SSP, ZP, and TP resulted in higher stress concentration in the post itself when compared to GP and CP. Therefore, results from the FEA images suggested that the use of non-metallic post systems could result in improved mechanical behavior for the weakened restored teeth. Keywords: Weakened roots, Posts, Finite element analysis Received Mar 10, 2008: Accepted May 19, 2009 INTRODUCTION The restoration of endodontically treated teeth is a complex procedure as it involves teeth that are weakened due to a significant loss of tooth structure. To add confusion to complexity, there remains a lack of consensus on two key issues that confront the different techniques that have been established for endodontic treatment: do they provide an efficient rehabilitation of the tooth and do they maximize the preservation and protection of the remaining tooth structure 1-7). The loss of more than half of the coronal tooth structure, caused by caries, fracture or extensive cavity preparation, mandates the use of posts 8) as they provide restorations with enhanced retention and stability. However, posts do not seem to reinforce and protect the remaining tooth structure 9,10). It is noteworthy that a few factors influence the mechanical behavior of endodontically treated teeth, namely the characteristics of the interface between post and dentin and the rigidity and stiffness of the post material. Therefore, use of inappropriate posts such as a post material that is more rigid than dentin may increase the fracture risk of the remaining tooth structure 11-13). Prior to inserting a root post, various factors related to the tooth need to be examined and analyzed, such as occlusion, position in the arch, amount of remaining tooth tissue, canal configuration and diameter 3-4,6,14,15). In the same way, variables related to the post should be carefully considered before choosing a restorative technique, such as the length 16,17), diameter 17,18), shape 7,13,17,19), surface configuration 20), and material 5,13,17,20-24) of the post. Nonetheless, it must be put into perspective that even a painstakingly selected system may reproduce the stress distribution that occurs in vital teeth, which means increasing the risk of biomechanical failure in endodontically treated teeth 5,10,13,17,25,26). The restoration of an endodontically treated tooth becomes more complicated if the canal is excessively weakened 3,4,27). The stress tends to concentrate in specific areas, which may increase the risk of fracture 10). To predict the probability of failure of endodontically treated teeth, in vitro fracture resistance tests are widely used to assess the performance of teeth restored with different post systems. However, the variations in fracture modes, unrealistically high values of fracture resistance, and methodologies which do not closely simulate clinical situations rendered the results unreliable 10,17,28). This was so chiefly because the tests were performed with static loads 29,30) and without periodontal ligament simulation 31). As a result of advances and expansion in computational technology, the mechanical behavior of structures can be adequately analyzed by means of Finite Elements Analysis (FEA) 12,13,32-34). This numerical analysis tool allows the simulation of clinical situations and may be used to analyze and solve complex

2 672 Dent Mater J 2009; 28(6): problems in the biomechanical area. It adopts approximation methods known since the beginning of the past century, such as the Ritz method established in FE models are based on a simplified geometry and a finite number of elements. Materials used for the manufacturing of prostheses are considered linear elastic, homogeneous, and isotropic, with known mechanical and elastic properties. It is important that these physical properties be correctly represented, because FEA results depend on the size, placement, and type of external loads which induce the stress, and which may eventually lead to deformation and fracture. However, while the FEA method can identify regions of stress concentrations that present a higher probability of failure, it cannot accurately predict the fracture path and its progress through materials 5). Notwithstanding this shortcoming, FEA has been successfully employed to compare the stress distributions in the dentin and cement layer of an endodontically treated maxillary incisor 5), investigate the influence of tooth preparation design on stress distribution in maxillary central incisors restored by means of alumina porcelain veneers when under functional loading 11), analyze cusp movements in premolars restored with adhesive resin-based composites 33), and evaluate the mechanical behavior of teeth restored with different post systems 12,13,17,18,20,35-37). The selection of a post system is one that is plagued with many controversies. This is because of the variability of materials currently available, deficiencies of the mechanical tests currently used, and the lack of consensus on the type of material which will improve the mechanical behavior of the weakened tooth toward that of intact tooth 17). While some authors recommended posts with high modulus of elasticity 17), others advocated posts with modulus of elasticity close to that of dentin 5,12,13). Therefore, the aim of this study was to analyze, by means of FEA, the stress distributions in weakened roots which were restored with composite resin core and different types of post systems in comparison to that in sound tooth. The hypothesis to be tested in this study was that the post system influences the stress distribution in weakened roots. MATERIALS AND METHODS Post space preparation One intact maxillary human incisor was used to create the model. The crown was cut horizontally at 2 mm coronal to the cementoenamel junction, leaving a tooth length of 15 mm. The root canal was manually instrumented to a working length of 14 mm (1 mm above the apical foramen) with K-files (Dentsply- Maillefer, Ballaigues, Switzerland) up to a #50 master apical file. Using the lateral condensation technique, the root canal was filled with gutta-percha (Dentsply- Herpo, Petrópolis, RJ, Brazil) and an endodontic cement (Sealer 26, Dentsply). After which, the root canal space was prepared using #05 bur (Dentsply Maillefer) to remove 10 mm of the filling material, measured using a plastic stop. To simulate a weakened tooth, the root canal was overprepared using a diamond rotary cutting instrument (#4137, KG Sorensen, Barueri, São Paulo, Brazil). Root canal space preparation was limited to a 9- mm vertical extension, providing a standardized canal space 10 mm in length and 3.5 mm in diameter. The height of the ferrule was limited to 2.5 mm and was prepared using a diamond rotary cutting instrument (#3215, KG Sorensen, Barueri, São Paulo, Brazil). The residual dentin wall in the ferrule region was standardized at 1.0 mm in thickness, checked with a digital caliper (Sylvac-Nucleon, São Paulo, Brazil). Fig. 1 Geometrical delimitation and meshing of numerical models, where: 1 - Sound tooth; 2 - Restored tooth; Cab - Cancellous bone; Cob - Cortical bone; PL - Periodontal ligament; D Dentin; DP -Dental pulp; GP - Gutta-percha; CR - Composite resin; P Post; E Enamel; C - Allceramic crown. Fig. 2 Meshing of models, where: 1 - Sound tooth; 2 - Restored tooth; Cab - Cancellous bone; Cob - Cortical bone; PL - Periodontal ligament; D Dentin; DP - Dental pulp; GP- Gutta-percha; CR - Composite resin; P Post; E Enamel; C - Allceramic crown.

3 Dent Mater J 2009; 28(6): Post and core restoration The weakened root was restored with an adhesive system (Adper Single Bond 2, 3M-ESPE) and a composite resin (Shade A2B, Filtek Supreme, 3M ESPE, St Paul, MN, USA) 27,38,39). The composite was polymerized using a light-transmitting polymerization post (Luminex; Dentatus). After curing, one #3 fiberglass post (Ângelus, Londrina, PR, Brazil) of 1.5 mm diameter was cemented with a dual-cure resin cement (RelyX Arc, 3M ESPE) according to manufacturer s instructions. A composite core was made in four increments, whereby each increment was polymerized for 40 seconds. The coronal preparation was realized using a high-speed diamond rotary cutting instrument (#2135, KG Sorensen), resulting in 4.0 mm height and 3.5 mm diameter at the cervical area. Impression was taken with a polyether material (Impregum, 3M ESPE), and a leucite-reinforced all-ceramic crown (IPS Empress, Ivoclar Vivadent, Schaan, Liechtenstein) with occlusal thickness of 1.5 mm was obtained following manufacturer s instructions. The all-ceramic crown was adhesively cemented using Adper Single Bond 2 (3M ESPE) and a dual-cure resin cement (RelyX Arc, 3M ESPE) according to manufacturer s instructions. Finite element mesh generation The restored tooth was longitudinally sectioned in the vestibular-lingual direction and ground flat with silicon carbide abrasive paper (#600, Norton, Campinas, Brazil). Using a digital camera (EOS Rebel, Canon, Japan), the images of both the sound tooth and the flared canal restored with a post system were captured. These captured digital images were then virtually inserted into an image of the alveolus of the anterior maxillary alveolar process obtained from the human anatomy laboratory. The completed images of both the sound and restored teeth (Fig. 1) were imported into a computer software (AutoCad 12, Autodesk Inc., Neuchatel, Switzerland, 1992) to generate seven twodimensional numerical models with the same geometry: sound tooth (ST); cast CuAl post and core (CPC); stainless steel post (SSP); fiberglass post (GP); carbon fiber post (CP); zirconium dioxide post (ZP); and titanium post (TP). These CAD models were exported as IGES files to ANSYS software (ANSYS 9.0, ANSYS Inc., Houston, USA). Areas corresponding to each structure were Table 1 Elastic properties of isotropic materials Structure/material Elastic modulus (GPa) Poisson ratio Enamel Ko et al. 35) Dentin Ko et al. 35) Pulp Rubin et al. 41) Reference Ligament Holmes et al. 18) Cortical bone Ko et al. 35) Cancellous bone Ko et al. 35) Gutta-percha Ko et al. 35) Luting agent Zarone et al. 42) Composite resin Huysmans and Van der Varst 36) Cast CuAl alloy Zirconium post Christel et al. 43) Titanium post Clelland et al. 40) Stainless steel post Lanza et al. 5) Leucite-reinforced ceramic Fischer et al. 44) Information from manufacturer (Leben ST, Sao Paulo, Brazil) Table 2 Elastic properties of orthotropic materials Property Carbon fiber post Fiberglass post Reference E x (GPa) E y (GPa) E z (GPa) V xy V xz V yz G xy G xz G yz Lanza et al. 5)

4 674 Dent Mater J 2009; 28(6): plotted and meshed (Fig. 2) with isoparametric elements of four nodes (PLANE 182) in accordance with the mechanical properties 5,18,35,36,40-44) of the tooth structures and dental materials used (Table 1). All structures and materials used in the models were considered linear elastic, homogeneous, and isotropic (Table 1), except for the fiberglass and carbon fiber posts which were considered orthotropic (Table 2). To simulate adhesion between the structures, all interfaces (ceramic-resin cement, resin cement-composite core, composite core-post, post-resin cement, and resin cement-dentin) were considered as completely bonded interfaces. Stress analysis using FEA Mesh convergence test was carried out, and it was determined that the ideal element size was 0.1 mm. Null displacement was defined for each model simulating the maxilla bone, whereby nodes at the top of the maxilla in each model were fixed and that the movement was restricted in the posterior and superior directions. A compressive load of 10 N was applied on the palatal side in the incisal third at a 45º angle to the radicular axis, in the vestibular direction 13,18,37). Stress distribution analysis was qualitatively performed using the von Mises and Sy stress criteria. To analyze the stress concentration areas, each tooth was divided into seven regions (Fig. 3), where 1: facial surface of post; 2: lingual surface of post; 3: apical portion of post; 4: facial surface of cervical and middle third dentin; 5: lingual surface of cervical and middle third dentin; 6: facial surface of apical third dentin; 7: lingual surface of apical third dentin. RESULTS According to FEA analysis, all groups (Fig. 3) showed different stress distributions with respect to the use and type of post. In terms of comparison between the Fig. 3 von Mises (MPa) stress distributions in maxillary central incisor after 10-N loading. Model 1 - Sound tooth; Model 2 - Cast CuAl post and core; Model 3 - Stainless steel post; Model 4 - Titanium post; Model 5 - Zirconium dioxide post; Model 6 - Carbon fiber post; Model 7 - Fiberglass post. Stress regions analyzed: 1 - facial surface of post; 2 - lingual surface of post; 3- apical portion of post; 4 - facial surface of cervical and middle third dentin; 5 - lingual surface of cervical and middle third dentin; 6 - facial surface of apical third dentin; 7 - lingual surface of apical third dentin.

5 Dent Mater J 2009; 28(6): sound tooth model and the restored tooth models, differences in stress distribution were observed. Stress concentrations in the facial and lingual cervical regions, especially in middle third dentin, were higher in the sound tooth than in the restored teeth. However, with the intact tooth model, stress was more homogenously distributed around the crown and in the internal and external root surfaces. In terms of comparison among the restored tooth models, the use of cast CuAl post and core, stainless steel, zirconium dioxide, and titanium post systems resulted in similar stress concentration in the post and which was higher when compared to the fiberglass and carbon fiber post systems. Moreover, the use of cast CuAl post and core, stainless steel, zirconium dioxide, and titanium post systems also induced a higher stress concentration in the facial surface of the posts than in the lingual surface of the posts. At this juncture, it must be pointed out that among the aforementioned post systems, the titanium post yielded comparatively lower stress concentration in the facial and lingual surfaces of the post. As for all the metallic post systems tested, stress concentration was observed at the apex of the post. Between the fiberglass and carbon fiber posts, no differences in stress distribution were found in the post-and-core restoration and in root dentin. When compared to the rest of the restored teeth, the use of fiberglass and carbon fiber posts resulted in higher stress concentration at the facial surface of cervical and middle third dentin regions. Images of stress distribution in Sy direction (Fig. 4), irrespective of the post system used, showed compressive stress concentration in the root and in the facial surface of post, as well as tensile stress concentration in the lingual surfaces of both root dentin and the post. Fig. 4 Stress distribution in Sy direction in maxillary central incisor, where negative values in MPa represent compressive stress and positive values indicate tensile stress. Model 1 - Sound tooth; Model 2 - Cast CuAl post and core; Model 3 - Stainless steel post; Model 4 - Titanium post; Model 5 - Zirconium dioxide post; Model 6 - Carbon fiber post; Model 7 - Fiberglass post. Stress regions analyzed: 1 - facial surface of post; 2 - lingual surface of post; 3- apical portion of post; 4 - facial surface of cervical and middle third dentin; 5 - lingual surface of cervical and middle third dentin; 6 - facial surface of apical third dentin; 7 - lingual surface of apical third dentin.

6 676 Dent Mater J 2009; 28(6): DISCUSSION When a structure is subjected to a load, stress is induced in the structure which may lead to deformation of the latter. By means of FEA, the stress generated can be accurately analyzed by evaluating the stress concentration areas. In addition, FEA allows the investigation of a single variable in a complex structure. This means that FEA is less expensive and time-consuming as no time needs to be wasted on standardization issues nor the need to prepare multiple specimens both of which are typically required for mechanical tests. By virtue of these advantageous capabilities, this method has been used to investigate the mechanical behavior of endodontically treated teeth subjected to different techniques and restorative materials 5,11-13,17,20,32,33,35). Similarly, in this study, FEA was used to investigate the influence of post systems on stress distribution in weakened roots. Results from the FEA images revealed different stress distribution patterns in each tooth model, and hence the hypothesis tested in this study was affirmatively accepted. At this juncture, a few limitations need to be acknowledged and addressed regarding the present study. First, the structures and materials used in this study were considered to be linear elastic, homogeneous, and isotropic. This meant that the computational simulation was not absolutely faithful of the real-life model which represents the structures, materials and dental tissues in vivo. Only the fiberglass and carbon fiber posts were considered orthotropic, because they exhibit different mechanical properties in the X and Y directions and that their mechanical behavior differs in relation to the direction of the main maximum stresses (Sx and Sy). Secondly, the elastic modulus and Poisson s ratio values applied for the structures and materials in this study were used as thus determined from a wide range of published studies 5,18,35,36,40-44). The third limitation was the way in which the load was applied in this study. The applied loading pattern simulated a protrusion movement, as opposed to the intermittent loading of teeth in clinical conditions which may then result in a fatigue process. Moreover, another limitation stemmed from the use of twodimensional numerical models, such that stress distribution in the Z direction could not be assessed. On the latter limitation, it must be pointed out that it was addressed by generating the numerical models with meticulous attention in that the anatomical structures namely the periodontal ligament, cortical bone, cancellous bone, and the cement layer around the post were simulated in their real proportions. In terms of load application, it was applied at an angle of 45, which is similar to that occurring in the clinical situation. Compared with molars which typically have tripodism type of contact at the occlusal surface during loading, the incisor teeth have a more symmetric relation of loading on the palatal surface. For this reason, a two-dimensional analysis might be better for anterior teeth 20). Nonetheless, there is a prevalent consensus that a three-dimensional analysis is more valid than a two-dimensional one 5,20,32), although the latter may be adequate to be used for qualitative evaluations of stress distributions, thereby providing important findings and conclusions to be correlated with clinical procedures 20). In this study, a maxillary central incisor was used to create the FE models because of its simple anatomy and its high susceptibility to fracture. As for the flared root canal, it was simulated as proposed by Caputo and Stanlee 6), whereby a residual dentin wall of 1 mm thickness was maintained throughout the root circumference to decrease the risk of root fracture. In the event of a severe loss of tooth structure, inserting a post and core before placing a crown is required to restore the tooth. In this study, the post and core materials were selected on the premise and for the purpose of investigating the influence of different types of post systems on stress distribution and fracture resistance of the tooth-post-core-restoration complex. It should be noted that the placement of an endodontic post creates an unnatural restored structure since it fills the root canal space with a material that has a defined stiffness unlike the pulp. Therefore, it is not possible to exactly recreate the original stress distribution of the intact tooth. Nonetheless, when materials such as fiberglass and carbon fiber posts are used, the stress-strain complex produced is more similar to that produced in an intact tooth because their modulus of elasticity and stiffness values are closer to that of dentin. As a result, the flexural movement of such a restored tooth could enable the restored system to mimic the mechanical behavior of an intact tooth, thereby reducing the stress at the interface 42). In the present study, stress concentration was higher in the dentin of the intact tooth model than in the restored tooth models but the distribution was more homogeneous. As reported in a previous study 14), the use of posts reduced the areas of stress distribution, resulting in stress concentration in the remaining tooth structure and at the dentin-post interface (Fig. 3), hence increasing the risk of fracture. Moreover, due to a transfer of the point of flexion to a more apical area, the inserted post alters tooth flexion by making the coronal portion of the restoration more rigid. However, the extent of these induced stress distribution changes depend on a diverse range of factors: material, rigidity, and geometry of the post; rigidity of the tooth structures; core and crown materials; and load magnitude 19,42). In the present study, the use of fiberglass and carbon fiber posts resulted in greater compressive stress to be generated in the facial root surfaces, and this was probably related to their higher flexural moduli as compared to the metallic posts 32). On the other hand, metallic posts were the most rigid component in the restorative complex. Such rigidity restricted the tooth displacement and reduced the strain level on dentin. Consequently, stress was

7 Dent Mater J 2009; 28(6): distributed to the apical third of root canal and into the post, to the effect that the restoration was rendered less durable by fracture or post-debonding 23,24,29,30). The use of complete crowns had a significant influence on stress distribution in endodontically treated teeth 10,32,42) in that fracture resistance was favorably increased 15,44). Besides, the risk of fracture can be reduced if the metallic post length were twothird of the root length of teeth with normal periodontal support 16). To further increase the fracture resistance of endodontically treated teeth, a remaining coronal axial wall of 2.5 mm was provided for ferrule preparation 19). In the present study, the ceramic crown and composite core presented low stress concentration probably because of the ferrule preparation, which was key to reducing stress in the cervical region 10,19). The FEA results of the current study were in good agreement with previously conducted clinical studies, in that restorations were more durable if the endodontically treated teeth were restored with fiberglass or carbon fiber post systems 23,24). Nonetheless, further in vitro non-destructive studies, such as twoand three-dimensional finite element analyses and strain gage analysis, should be conducted in conjunction with clinical studies. This was to be done for the intent of a more thorough and practical understanding of the mechanical behavior of the different post systems and materials currently available for restoring endodontically treated teeth. CONCLUSIONS Based on the methodology employed in this study and the subsequent data analysis, it was possible to conclude that: 1. Stress distribution was highly influenced by the use of posts and that stress distribution was different between metallic and non-metallic posts. 2. 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