Mechanical weakening of devitalized teeth: three-dimensional Finite Element Analysis and prediction of tooth fracture.

doi:10.1111/iej.12381

Mechanical weakening of devitalized teeth: three-dimensional Finite Element Analysis and prediction of tooth fracture

K. Zelic1, A. Vukicevic2, G. Jovicic2, S. Aleksandrovic2, N. Filipovic2,3 & M. Djuric1 1

Laboratory for Anthropology, Institute of Anatomy, School of Medicine, University of Belgrade, Belgrade; 2Faculty of Engineering, University of Kragujevac, Kragujevac; and 3Bioengineering Research and Development Center Kragujevac, Kragujevac, Serbia

Abstract Zelic K, Vukicevic A, Jovicic G, Aleksandrovic S, Filipovic N, Djuric M. Mechanical weakening of devitalized teeth: three-dimensional Finite Element Analysis and prediction of tooth fracture. International Endodontic Journal.

Aim To determine to which extent cavity preparation and each step of dentine removal in the process of root canal treatment (access cavity preparation and root canal enlargement) both individually and jointly contribute to the weakening of the tooth. Methods Numerical analysis using finite element method (FEM) of separate and combined influence of two-surface Class II preparation and root canal treatment was undertaken to evaluate the decrease in tooth strength. The influence of the two stages in root canal treatment, access cavity preparation and root canal enlargement, was also analysed separately and jointly. After each of these phases, the crown was restored with composite resin, and the FEA was performed only on restored teeth. To estimate the influence of all these procedures on tooth fracture resistance numerically, a Failure Index based on the maximum principal stress criterion (MPCS) was applied. Compressive and tensile stresses were analysed separately and corresponding Failure Indices were calculated. Results A two-surface resin composite restoration weakened the tooth by 23.25%. Nevertheless, the

Failure Indices showed that this tooth was not likely to fracture even under high occlusal stress (710N). However, after access cavity preparation, the Failure Indices reached the point where, under high occlusal force that may occur in the posterior area, a tooth fracture occurred. The enlargement of root canals had an additional, but relatively small impact on tooth weakening, making the tooth even more susceptible to fracture. The combined influence of both cavity preparation and root canal enlargement led to weakening of 62.6% under a load of 710N, ultimately causing tooth fracture. Conclusion The combined finite element method and the maximum principal stress analysis gave insight into the fracture mechanisms of teeth with two-surface composite restorations followed by root canal preparation. Removal of tooth tissue, despite its subsequent restoration with dental materials, weakened the tooth by changing the stress intensity and distribution through tooth structures. Access cavity preparation had the greatest influence on tooth strength whilst canal enlargement did not contribute to this process substantially. Keywords: devitalized teeth, finite element method, fracture resistance. Received 21 June 2013; accepted 17 September 2014

Introduction Correspondence: Marija Djuric, Laboratory for Anthropology, Institute of Anatomy, School of Medicine, University of Belgrade, 4/2 Dr Subotica, 11000 Belgrade, Serbia (Tel/Fax: +381 11 2686 172; e-mail: [email protected]).

© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd

There are various factors which may affect tooth fracture resistance; however, the influence of each particular factor remains unclear. Some authors support

International Endodontic Journal

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FEA predicition of tooth fracture Zelic et al.

the concept that dentine becomes more fragile after devitalization, which subsequently influences the overall tooth strength (Marshall et al. 1995, Kishen 2006, Zelic et al. 2014). Although there are many hypotheses about dentine changes, the one most discussed is based on the loss of moisture, which can affect the mechanical properties of dentine (Sedgley & Messer 1992, Papa et al. 1994, Kishen 2006, Kishen & Vedantam 2007). However, it is still unclear which structural changes in dentine make a devitalized tooth more susceptible to fracture. Additionally, the removal of tooth tissue during root canal treatment influences the mechanical behaviour of devitalized teeth even though the tooth is restored with dental materials (Soares et al. 2008, Wu et al. 2010). From a biomechanical aspect, it would be interesting to determine the relative contribution of cavity preparation and each step of dentine removal during the root canal treatment to the overall weakening of teeth. In this context, it should be determined whether tooth fragility is related mostly to the amount of coronal tissues removed during the preparation of the intracoronal cavity (Ross 1980, Reeh et al. 1989), access cavity preparation (Assif & Gorfil 1994) or widening of the root canal (Hurmuzlu et al. 2003). In answering these questions, investigators initially used destructive experimental methods in which the teeth were loaded until fracture (Reeh et al. 1989, Sedgley & Messer 1992). However, the destructive nature of the experimental method usually provides only information if the tooth is damaged, but gives no information regarding the stress level required to induce fracture and stress and strain distribution through tooth structures. Recent studies have applied biomechanical analysis based on the finite element method (FEM) (Cheng et al. 2009, Chen et al. 2012). FEM can reveal the stress distribution and high-stress concentration points in different tooth tissues as well as in the dental materials used in the treatment. It could also clarify the mechanical impact of dental procedures on tooth weakening (Soares et al. 2008). Many reported FEM analyses have been based on simplified models (Asmussen & Peutzfeldt 2008) or models of average teeth dimensions taken from the literature (Ren et al. 2010). Nevertheless, as the accuracy of the FEM analysis depends on precise data, the most reliable data are those obtained from CT or micro-CT scans of real teeth (Romeed & Dunne 2013), which are then used to create the FEM model

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(Soares et al. 2008, Chen et al. 2012). However, although this is rarely seen in published articles, the most reliable FEM studies include experimental confirmation of the results obtained (Soares et al. 2008). In that case, the scanned teeth are subjected to in vitro mechanical testing, with the same conditions as those proposed in the FEM analysis. So far, the investigation of the influence of dental restorations on tooth fracture resistance has been limited to Class I (Wu et al. 2010) and Class II mesiooccluso-distal (MOD) preparations (Reeh et al. 1989, Lin et al. 2001, Asmussen & Peutzfeldt 2008). However, although two-surface restorations are common, their impact on tooth resistance has not been reported. The aim of this study was to apply numerical FEM analysis and experimental validation of the influence of two-surface Class II cavity preparation, and two steps of major dentine removal in the process of root canal treatment, access cavity preparation and root canal enlargement on tooth strength. After each of these steps (cavity preparation, access cavity preparation and root canal enlargement), the tooth crown was restored and FEA was performed only on restored teeth models. To estimate the influence on tooth fracture resistance, Failure Indices based on maximum principal stress criterion (MPSC) were determined.

Material and methods The schematic illustration of the procedures performed sequentially is presented in Fig. 1.

Tooth preparation Two intact maxillary second premolars extracted for orthodontic purposes (Fig. 1a) from the same patient (35 years of age) were used (approved by the Ethics Committee of the School of Dentistry, University of Belgrade). Dental radiographs of the teeth confirmed the similarity of the root canal morphology between them. One tooth remained intact whilst the other one underwent root canal treatment ex vivo. A mesio-occlusal (MO) Class II preparation was performed followed by an endodontic access cavity preparation and root canal enlargement. Working length (WL) was set at 0.5 mm coronal to the apical foramen. Original root canal diameter at this point corresponded to diameter of a size 10 file which was able to reach the working length without preparation. The step-back technique was used for canal


Zelic et al. FEA predicition of tooth fracture

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Figure 1 Schematic overview of the study design.

instrumentation. The apical region was enlarged to a size 30 hand K-file at full WL. To prepare the coronal third of the canal, size 6 Gates Glidden drills were used to obtain good visibility of the canal orifices. Irrigation with 1.0% NaOCl was used throughout the preparation. The canal was filled with cold Gutta-percha and endodontic sealer with the lateral compaction technique. In Fig. 2, a comparison of the enlarged canal and the initial canal shape is shown. The tooth was restored with composite resin (3M ESPE Filtek Z250, St. Paul, MN, USA).

Imaging Both intact and treated teeth were scanned using computed tomography (Siemens Somatom Sensation


16, Munich, Germany) operating at 120 kV, 100 mAs, orthogonally to the long axis of the teeth, with slice thickness of 0.75 mm (1024 9 1024 pixels per scan) (Fig 1b).

Experimental estimation of critical force After image acquisition, the two teeth were submitted to the fracture test. As previously suggested (Soares et al. 2008), the teeth were embedded in auto-polymerizing acrylic resin (Technovit 4000, Kulzer, Wehrheim, Germany), and the periodontal ligament (PDL) was imitated by covering the root of the tooth with a 0.2 mm thick layer of polyurethane impression material (Impregum F, 3M ESPE, St Paul, MN, USA) (Fig. 1c). To prevent overheating, the tooth


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magnitude was 1 N, and the accuracy of the compressive strain was approximately 0.001 mm.

was submerged in water for 5 min during resin polymerization. The compression test was performed on a mechanic testing machine (ZWICK ROELL Z 100; Ulm, Germany). Compressive loading was applied using a steel bar with a round tip placed in the centre of the tooth, with contacts only on the buccal and lingual cusps, thereby producing a force parallel to the long axis of the tooth (Fig. 1d,e and f). The test speed was 5 mm min1. The accuracy of measuring force

Development of the finite element models Image segmentation and reconstruction After image acquisition, the segmentation and generation of a surface mesh from CT volume data were performed in Mimics 10.01 (Materialise, Leuven, Belgium) by image thresholding. For each kind of material, a separate STL surface mesh was generated (Fig. 1g). Mesh refinement and generation of virtual models Meshes retrieved from Mimics are not suitable for performing FEA, so additional refinement and assembly of different parts of the model were achieved in Gemagic Studio 10 (Geomagic GmbH, Stuttgart, Germany). Specific points were selected and saved as separate STL files to prepare the model for boundary conditions and loads. In model 1 (intact tooth), four distinct parts were modelled: enamel, dentine, pulp chamber, periodontal ligament (Fig. 3). The thin root cementum was

Figure 2 A schematic view of the canal enlargement.

Figure 3 Presentation of different materials in each tooth model.

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neglected. A periodontal ligament (PDL) was modelled as a 250-lm-thick shell surrounding the root, finishing 2 mm apical to the cemento-enamel junction. The bone was not modelled, but the external nodes on the PDL were strangulated. Two postoperative models (models 2 and 3) were made using data obtained from the scans of the contralateral (treated) tooth. Model 2 included MO Class II cavity preparation restored with composite resin (Fig. 3). In model 3 MO Class II restoration and access cavity to the pulp chamber was modelled, but there was no root canal enlargement (Fig. 3). The cavity was restored with composite resin. The root canals were filled with cold Gutta-percha up to 1 mm from the canal orifices (Fig. 3). Model 4 was based on scans of the treated tooth and included MO Class II cavity, an access cavity and root canal enlargement (Fig. 2). The cavity preparation was filled with a composite resin, and the root canals were filled with cold Gutta-percha up to 1 mm short of the orifices. The endodontic sealer was neglected in the FEA modelling (Fig. 3.).

et al. 2008) (Fig. 1k). All the analyses performed were static linear, and all materials in the simulation were assumed to be homogenous, isotropic and linear. The number of nodes and elements for each model as well as the applied forces are shown in Table 2. Shrinkage stress measurements The volumetric change of the restoration during polymerization shrinkage was simulated in models 2, 3 and 4 as the analogy of thermal expansion in a heat transfer analysis (Chuang et al. 2011.) Load conditions To compare stress distribution between the four tooth models, an experimentally determined critical break-

3D meshing and materials For every part of the tooth, defined with a single STL file, a 3D volume discretization was carried out using TetGen meshing software (Hang Si, WIAS, Berlin, Germany). At this stage, a high-quality four-nodal tetrahedral elements (TET4) mesh was retrieved (Fig. 1h). After splitting the tetrahedral elements into eight-nodal hexahedral (Fig. 1j), the material properties were assigned in accordance with Table 1. Boundary conditions Boundary conditions were applied to the nodes on the outer surface of the PDL (dark blue section on Fig. 1i and Fig. 4), restricting displacements in all three directions. Finite element analysis Following the previous steps, FEA analysis was performed using PAK software (Filipovic 2008, Kojic

Table 1 Mechanical properties of dental structures and restorative materials

Figure 4 Schematic view of boundary conditions (dark blue section correspond to the nodes strangulated in all three directions) and loads magnitude and direction.

Table 2 Number of nodes, elements and applied forces for each model Tooth model

Number of nodes

Number of elements

Applied force [N]

1 2 3 4

141907 157651 129061 136299

124768 139284 112828 119492

1025, 710 710 710 710

Material

Young’s modulus [Mpa] (Ref.)

Poisson’s ratio (Ref.)

Pulp Dentin Enamel PDL Composite resin Gutta-pecha

6.8 (Shen et al. 2009) 18.6 9 103 (Magne 2010) 84.10 9 103 (Magne 2010) 0.68 (Ruse 2008) 16.6 9 103 (Soares et al. 2008) 70 (Ruse 2008)

0.45 (Shen et al. 2009) 0.31 (Magne 2010) 0.3 (Magne 2010) 0.45 (Magne 2010) 0.24 (Soares et al. 2008) 0.40 (Magne 2010)



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ing force obtained for the treated tooth (model 4) was applied to each model. Furthermore, to verify the validity of the FEA simulation, model 1 was also loaded with the critical breaking force obtained for the intact tooth (model 1). The load was applied on the buccal and lingual cups (red colour (Fig. 1i and Fig. 4) simultaneously, to gain the resulting force parallel to long axis of the tooth. In models 2, 3 and 4 the previously calculated residual stress (polymerization stress) was included. Maximum principal stress criterion After performing the FEA, a numerical estimation of the fracture risk for each tooth model was acquired by calculating a Failure Index based on the maximum principal stress criterion (MPSC). As tensile stress is expressed in positive values and compressive is expressed in negative values, the maximum principal stress r1 represents the peak of tensile stress, whilst the minimum principal stress r3 represents the peak of compressive stress. MPSC assumes that a material fails when the maximum principal stress in the material exceeds its tensile strength rTS or minimum principal stress is lower than compressive strength rCS of the material. The safe region for the material is assumed to be rCS < r3 < r1 < rTS. The failure index is calculated according to the equation FI = rPS/rSM, where rPS is the principal stress generated in the material and rPS is tensile or compressive strength of the material. If rPS > 0 than for the rSM, the tensile strength value of the material is accepted (rSM = rTS), and if rPS is negative (as mentioned before, negative values of generated stress correspond to compressive stress), the value for compressive strength is accepted (rSM = rCS). A failure initiates when the Failure Index FI = 1. Calculations for Failure Indices FI (r1) and FI (r3) correspond to stress distributions r1 and r3 respectively. For material strength (rSM), the following was adopted: for dentine rTS = 105.5 MPa (Sano et al. 1994, Nalla et al. 2004), rCS = 297 MPa (Craig & Payton 1958); for enamel rTS = 24.7 MPa (Carvalho et al. 2000), rCS = 384 MPa (Haines 1968); for composite resin rTS = 77 MPa and rCS = 294 MPa (Chuang et al. 2011). Additionally, the stress analysis included the distribution of the most commonly used effective Von Mises stress. Weakening of each tooth model is estimated using the following formula:

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Weakening½% ¼ 100 ½FailureIndexðiÞ FailureIndexð1Þ =FailureIndexð1Þ; Failure Index (1) is the maximum value of Failure Index achieved for the model 1 (intact tooth) and Failure Index (i) is the maximum value of Failure Index achieved of considered model respectively.

Results The results of the compression test are given in Fig. 5. The graph shows the compressive displacement (strain) dependence on compressive force for the two specimens. The critical breaking force for the intact tooth (model 1) was 1025 N at a compressive strain of 0.9 mm, whilst for the treated tooth (model 2) the breaking force was 710 N at a compressive strain of 1.02 mm. Both teeth fractured in the buccal cervical region. This graph also shows the compressive force dependence on the compressive displacement (strain) generated by the FE simulation for model 1 (representing an intact tooth) and model 4 (representing a treated tooth). The results obtained in the experiment and FE simulation showed a good correlation (Fig. 5). The discrepancy between the results throughout the experiment was mostly lower than 5%, being higher (8.2%) only on one point of the experiment. In the beginning of the experiment, the discrepancy was 1.6% whilst at the fracture point, the ideal matching of the results was achieved. Figure 6 shows the distribution of principal stress of the polymerization shrinkage process in models 2, 3 and 4. A sharp transition is noticeable between

Figure 5 Diagram of compressive displacement (strain) dependencies on compressive force in experiment (intact and treated tooth) and in FE simulations which correspond to these teeth (model 1 and model 4).



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Figure 6 Distribution of principal and Von Mises stress generated in the simulation of resin composite shrinkage and corresponding Failure Indices.

tooth tissue and composite filling (Fig. 6a,b and c). The compressive stress is present within the composite material as a consequence of polymerization shrinkage (Fig. 6g,h,i). On the other hand, as composite material is bonded to enamel and dentine, tensile stress is generated in the part of these tissues which are in contact with the filling (Fig. 6d,e,f). Tensile stress reached 2.35 MPa in model 4, whilst maximum compressive stress was 9.4 MPa in the same model (Fig. 6f,i). Other models expressed lower values of principal stresses (Fig. 6d,e,g,h). Maximum value of Failure Index was FI = 0.25, that is calculated for the tensile stress in the enamel of model 4, as this tissue has relatively low tensile strength. Calculated Failure Indices were much lower for dentine and composite resin. Based on the results of the experiment, all teeth in the FEA simulation were loaded axially with a force


of 710 N. The intact tooth was also loaded with 1025 N to verify the results from the FEA simulation. In model 2, 3 and 4, the previously calculated residual stress (polymerization stress) was included. Figures 7 and 8 illustrate the principal stress distribution under occlusal loading and FI of each model. Figure 7 reveals the distribution of the principal tensile stresses (b, f) and corresponding Failure Indices (a, e) as well as the principal compressive stress (d, h) and analogous Failure Indices (c, g) for the loading of 710 N and 1025 N, respectively, in model 1. Tensile stress was generated in the approximal enamel, whilst compressive stress was obvious on the occlusal surface (where the load is applied) and in dentine at the buccal cervical area. Under the load of 710 N, a small critical zone appeared in enamel at the approximal surfaces where tensile stress exceeded the tensile strength of enamel - FI (r1) = 1.239 (Fig. 7a).


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Figure 7 Distribution of principal stresses and Failure Indices in model 1 under loads of 710 and 1025N.

Therefore, crack development in enamel is possible under these conditions. However, maximum values of compressive stress in the buccal cervical region did not exceed the compressive strength of dentine (FI (r3) = 0,787) (Fig. 7c). Therefore, failure in dentine is not likely to occur. When model 1 was loaded with 1025 N, the compressive stress in dentine exceeded the failure risk point FI (r3) = 1.11 (Fig. 7g), which concurs with the experimental results. Von Mises stress values in model 1 are shown on (Fig. 10a,e). Figure 8 shows the distribution of the principal stress r1 and r3 as well as the corresponding Failure Indices on models 2, 3 and 4 under the load of 710 N. Tensile stress is generated in the buccal enamel and, in all these models, it exceeded the tensile strength of enamel. However, the zone of high risk for failure increased and was the largest in model 4. The simulation revealed the presence of compressive stress on the occlusal surface in each model and within the composite filling in models 3 (Fig. 8h) and 4 (Fig. 8i). However, the extreme values were found in the cervical buccal region in all models. In model 2, the Failure Index for compressive stress was very close to 1 (FI = 0.97), which indicates greater risk for failure (Fig. 8j). In models 3 and 4, the extreme values for compressive stress exceeded the compressive strength of dentine (Fig. 8k,l), which indicates that failure will occur in the cervical buccal region. Based on this

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analysis, the greatest risk for failure was recorded in model 4. Figure 9 gives Von Mises (Fig. 9a,b,c), tensile (Fig 9d,e,f) and compressive stress distribution (Fig. 9g,h,i) in dentine connected to the composite restoration. It is evident that tensile stress is dominant in the dentine-filling interface being the highest in model 4. Figure 9 also shows the stress generated in dentine wall of root canal. The stress intensity in this dentine area is low and has not changed significantly after root canal enlargement. The Von Mises stress distribution in all models and extreme stress values are presented in Fig. 10. The largest values of the Von Mises stress equivalents indicate locations with the highest risk of fracture. Table 3 shows the peak tensile, compressive and effective (Von Mises) stress in enamel and dentine as well as the corresponding Failure Indices in all models. Displacement achieved in the FE analysis is also shown. Weakening is expressed in percentage for all models. The greatest influence on tooth weakening was associated with the access cavity preparation.

Discussion In this study, a general framework for numerical FEM analysis and experimental validation of the influence of dental restorations and root canal procedures on tooth fracture resistance were proposed (Fig. 1). The



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Figure 8 Distribution of principal stresses and Failure Indices in models 2, 3 and 4 under load of 710N.

FEA models were developed based on CT data of real teeth, and the experimental validation of the FEA results was performed on an intact tooth (model 1) and on the mechanically weakest tooth (model 4). By performing numerical FEM analysis with plausible input information, a clear insight into the influence of


the geometry of each tooth element on stress distribution was achieved. As a result, possible inaccuracies, which could arise from the use of simplified models in FEA and experimentally unverified results, were avoided. To avoid complicated FEA models, the bone surrounding the tooth was not modelled as the


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Figure 9 Distribution of Von Mises and principal stresses in dentine connected to the composite restoration and in root canal

wall.

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(e) Figure 10 Distribution of Von Mises stress in all models under corresponding loads.

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Table 3 Maximum effective stress, maximum displacement, maximum tensile and compressive principal stress, maximum Failure Index in dentin and enamel and estimated weakening of each model of tooth under the load of 710N and 1025N on model 1 Model Max Von Mises stress [Mpa] Displacement in model [mm] Max tensile stress in enamel [Mpa] Failure Index in enamel [] Max compressive stress in dentin [Mpa] Failure Index in dentin [] Weakeninga[%] a

1 126.32 0.649 30.63 1.239 232.1 0.787 0

b

187.15 0.913b 48.43b 1.853b 325.9b 1.11b

2

3

4

155.33 0.781 36.1 1.454 281.8 0.97 23.25

176.1 0.864 49.2 1.97 351.3 1.2 52.5

180.6 0.890 52.27 2.12 375.8 1.28 62.6

Weakening [%] = 100 9 [FailureIndex (i)- FailureIndex (1)]/FailureIndex (1) values correspond to the load of 1025 N applied on model 1.

b

analysis of the stress development, and distribution in bone was not the aim of this study. However, the external nodes of periodontal ligament were strangulated so as to mimic the mechanism of tooth fixation in alveolar bone. Furthermore, in the FEA models, root cementum was neglected as it was reported that its presence in FEA models affects only the stress intensity generated in the apical part of the root and the bone surrounding the root apex (Ren et al. 2010). The results of the present study revealed that stress distribution in this area is not affected by the widening of root canals. Thus, the differences in the results that could be the consequence of the lack of root cementum in the FEA models are insignificant. Finally, modelling of the endodontic sealer was also neglected. However, the mechanical properties for the root filing (cold Gutta-percha with endodontic sealer) were taken from the literature (Ruse 2008, Soares et al. 2008, Chen et al. 2012). The FE simulation results corresponded very well to the experimental results with ideal matching at the fracture point. Furthermore, the FE simulation revealed that the region most at risk for fracture was the buccal cervical area. This result corresponded to the fracture test results given that both teeth fractured in this area. The question posed in this study was ‘what are the individual and combined impacts on tooth weakening of two-surface Class II preparation and two procedures that are performed sequentially during root canal treatment: access cavity preparation and root canal enlargement’. To answer this question, each of these procedures (models 2, 3 and 4) were analysed, and the stress behaviour after each stage was compared with the stress behaviour of an intact tooth (model 1). However, in contrast to the clinical


procedure, after each these phases of tissue removal, the tooth crown was restored. This approach was undertaken as the removal of tooth tissue weakens the tooth considerably, but after the restoration of the crown, a part of the lost strength is recovered (Assif & Gorfil 1994, Soares et al. 2008). Consequently, the results of the current study are more clinically relevant. To estimate the influence on tooth fracture resistance numerically, a Failure Index based on maximum principal stress criterion (MPSC) was applied. In the proposed formula of MPSC, the tensile and compressive strength of dentine, enamel and composite resin were used. Considering that these parameters differ between these materials, the same stress intensity induces different Failure Indices in different tissues. Thus, stress distribution through the interfaces between different materials becomes more visible. As dentine is a dominant material in the structure of teeth (Rasmussen et al. 1976, Giannini et al. 2004, Nalla et al. 2004), the fracture of a tooth under high occlusal load is based on failure of dentine. Yet, this study also provides information on enamel and composite failure. The shrinkage of the filling during the polymerization process had to be taken into account as resin composite was the material used for tooth restoration. The shrinkage was simulated on FE models as the analogy of thermal expansion as previously suggested (Chuang et al. 2011). Tensile stress in the enamel surrounding the composite filling reached 2.35 MPa in model 4, whilst in other models the stress intensity was lower. It has been reported that the level of residual stress is highly influenced by the amount of the residual dental tissue and the shape of the cavity (Fleming et al. 2007, Lee et al. 2007). In this study,


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the cavity preparation corresponded to a two-surface Class II preparation which was not analysed in the previous studies. Still, the results are in the same range of values as the results from studies analysing the shrinkage stress in Class I and Class II MOD preparations (Asmussen & Peutzfeldt 2008, Chuang et al. 2011). Findings of this study are also in agreement with the study of Barink et al. (2003) who analysed the shrinkage in the cusp replacement procedure. In all these studies, the generated stress was below the maximum stress that dental tissues can bear, and therefore, enamel failure cannot occur. Nevertheless, the findings of the present study are in line with Chuang et al. (2006, 2011) who showed that microcracks in the surrounding enamel can be caused by the shrinkage of the composite filling. This finding is clinically significant. Thus, there are many studies focused on finding the treatment protocols that reduce polymerization stress (Dauvillier et al. 2000, Moraes et al. 2011). Following polymerization shrinkage, the stress analysis in this study showed distribution of the principal and effective (Von Mises) stresses in all models under the load of 710 N. As the intact tooth fractured under the force of 1025 N, the model 1 (intact tooth) was additionally loaded with 1025 N. In all analysed models, high compressive stress was generated in the buccal cervical area. Tensile stress exceeded enamel tensile strength in approximal enamel in model 1 and in buccal enamel in all other models. It was previously reported that a tooth with cavity preparation is reinforced by composite resin and that it shows similar stress distribution to the healthy tooth (Assif & Gorfil 1994, Soares et al. 2008). However, the stress distribution in tooth with two-surface Class II type restoration was found to be somewhat different from that of the intact tooth, with stress reaching a much higher level (Fig. 8a,g). Failure Index revealed that tensile stress in buccal cervical part of enamel already exceeded enamel tensile strength, and cracks could occur. On the other hand, although subjected to relatively high compression stress, dentine in the buccal cervical area remained in the safe zone. The Failure Index and formula used to calculate the tooth weakening showed that the fracture resistance was reduced by 23.25%. Still, the tooth was not weakened enough to fracture during a load of 710 N (Fig. 8d,j). It was previously reported that maximum biting forces can reach 700 N in the posterior area (van Eijden 1991, Ichim et al. 2007).

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Therefore, it can be expected that a premolar restored with a two-surface Class II composite filling would rarely fracture even under the highest occlusal stress. However, enamel fractures, especially on the buccal surface, are possible. After the access cavity preparation (model 3), the distribution of stress changed considerably. In Fig. 8h, the compression stress is noticeable within the composite material. As in this model the pulp chamber was filled with composite resin, stress was conducted through the filling to the buccal dentine wall resulting in compressive stress accumulation in the bottom of this wall (Fig. 8h). Furthermore, the level of the tensile stress in buccal enamel was increased, and the area of extreme stress was larger. Taking that into account, the fracture was likely to occur in the buccal cervical area. With the preparation of the access cavity, the tooth was further weakened by 29.25% and reached the point of failure under a load of 710 N (Fig. 8k). Contrary to Reeh et al. (1989) who did not find great influence of access cavity preparation, other studies suggest that this phase significantly weakens the tooth with MOD cavity (Assif & Gorfil 1994, Soares et al. 2008) due to increased cusp deflection, which is a result of dentine wall thinning (Soares et al. 2008). However, this deflection is questionable in the two-surface cavity. It was previously reported that adhesive restorations were able to better transmit stress from the filling to dentine (Trope et al. 1986, Magne & Belser 2003). Furthermore, the stress concentration in the inner dentine can lead to a catastrophic failure (Magne & Belser 2003). It was assumed that changed conduction of stress was the main factor contributing to increased tooth fragility. After the enlargement of the root canals (model 4), the stress distribution remained similar to model 3, but with larger high-stress zones in the buccal dentine wall. Also, failure is possible in occlusal and approximal enamel. This study suggests that the enlargement of root canals had relatively little additional influence on tooth fragility (10.1%), compared to the influence of access cavity preparation (29.25%) (Table 3). In the literature, there are opposite opinions about the influence of the root canal preparation on tooth resistance to fracture. Some authors (Lam et al. 2005, Chen et al. 2012) claim that the tooth is not further weakened by root canal enlargement, but others (Hurmuzlu et al. 2003) reported a negative correlation between root diameter and the ability of the tooth to resist lateral forces. However, the present study demonstrated that the major impact on tooth



fracture resistance cannot be attributed to this phase of root canal treatment. This is further confirmed by the analysis of the stress intensity in root dentine walls (Fig. 9h,i), revealing that the changes in stress distribution and intensity were minor after canal instrumentation. Nevertheless, the joint influence of all three dental procedures led to a weakening of 62.6% under a load of 710 N, ultimately causing tooth fracture (FI = 1.28). The experiment confirmed that the treated tooth fractured in the buccal cervical region when the applied force was 710 N. As the maximum biting force in posterior region can reach 700 N (van Eijden 1991, Ichim et al. 2007), a devitalized premolar with a two-surface Class II composite filling has significantly greater risk of fracturing under occlusal force than an intact tooth or a tooth with only a twosurface Class II restoration. In the current literature, most similar studies (Zelic et al. 2013) expressed stress distribution using Von Mises stress criterion. Thus, in this study, the results of the stress distribution expressed in Von Mises stress equivalents were also presented (Fig. 10) to make the results easily comparable with the results of other studies. However, the findings of the present study suggest that the analysis of the principal stress is more informative regarding the fracture mechanisms in teeth, given that tensile and compressive stresses induce different outcomes on tooth structures. Furthermore, tooth tissues have different properties and different tensile and compressive strengths which are taken into account in the analysis of maximum principal stress.

Conclusion Teeth with two-surface composite restorations that underwent root canal treatment are less resistant to high occlusal load, but the main contribution to their weakening arises from access cavity preparation. Canal enlargement does not contribute to this process substantially. This study represents an effective framework which, if applied in a number of different cases, could be useful for calculating the potential risk for tooth fracture.

Acknowledgements This study was funded by grants from Ministry of Education and Science of the Republic of Serbia 45005, III41007 and ON174028.


References Asmussen E, Peutzfeldt A (2008) Class I and Class II restorations of resin composite: an FE analysis of the influence of modulus of elasticity on stresses generated by occlusal loading. Dental Materials 24, 600–5. Assif D, Gorfil C (1994) Biomechanical considerations in restoring endodontically treated teeth. Journal of Prosthetic Dentistry 71, 565–7. Barink M, Van der Mark PC, Fennis WM, Kuijs RH, Kreulen CM, Verdonschot N (2003) A three-dimensional finite element model of the polymerization process in dental restorations. Biomaterials 24, 1427–35. Carvalho RM, Santiago SL, Fernandes CA, Suh BI, Pashley DH (2000) Effect of prism orientation on tensile strength of enamel. The Journal of Adhesive Dentistry 2, 251–7. Chen G, Fan W, Mishra S, El-Atem A, Schuetz M, Xiao Y (2012) Tooth fracture risk analysis based on a new finite element dental structure models using micro-CT data. Computers in Biology and Medicine 42, 957–63. Cheng R, Zhou XD, Liu Z, Yang H, Gao QH, Hu T (2009) Finite element analysis of the effects of three preparation techniques on stresses within roots having curved canals. International Endodontic Journal 42, 220–6. Chuang S, Chang C, Yaman P, Chang L (2006) Influence of enamel wetness on resin composite restorations using various dentine bonding agents: part I—effects on marginal quality and enamel microcrack formation. Journal of Dentistry 34, 343–51. Chuang S, Chang C, Chen T (2011) Contraction behaviors of dental composite restorations-Finite element investigation with DIC validation. Journal of the Mechanical Behavior of Biomedical Materials 4, 2138–49. Craig RM, Payton FA (1958) Elastic and mechanical properties of human dentin. Journal of Dental Research 37, 710–9. Dauvillier BS, Aarnts MP, Feilzer AJ (2000) Developments in shrinkage control of adhesive restoratives. Journal of Esthetic Dentistry 12, 291–9. van Eijden T (1991) Three-dimensional analyses of human bite-force magnitude and moment. Archives of Oral Biology 36, 535–9. Filipovic N (2008) PAK Software for static and dynamics finite element analysis. Kragujevac, Serbia: University of Kragujevac. Fleming GJ, Khan S, Afzal O, Palin WM, Burke FJ (2007) Investigation of polymerisation shrinkage strain, associated cuspal movement and microleakage of MOD cavities restored incrementally with resin-based composite using an LED light curing unit. Journal of Dentistry 35, 97– 103. Giannini M, Soares C, de Carvalho R (2004) Ultimate tensile strength of tooth structures. Dental Materials 20, 322–9. Haines DJ (1968) Physical properties of human tooth enamel and enamel sheath material under load. Journal of Biomechanics 1, 117–25.


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Hurmuzlu F, Kiremitci A, Serper A, Altundasar E, Siso S (2003) Fracture resistance of endodontically treated premolars restored with ormocer and packable composite. Journal of Endodontics 29, 838–40. Ichim I, Kieser J, Swain M (2007) Functional significance of strain distribution in the human mandible under masticatory load: numerical predictions. Archives of Oral Biology 52, 465–73. Kishen A (2006) Mechanisms and risk factors for fracture predilection in endodontically treated teeth. Endodontic Topics 13, 57–83. Kishen A, Vedantam S (2007) Hydromechanics in dentine: role of dentinal tubules and hydrostatic pressure on mechanical stress-strain distribution. Dental Materials 23, 1296–306. Kojic M, Filipovic N, Stojanovic B, Kojic N (2008) Computer modeling in bioengineering - Theoretical background, Examples and Software, 1st edn. London: Wiley and Sons. Lam P, Palamara J, Messer H (2005) Fracture strength of tooth roots following canal preparation by hand and rotary instrumentation. Journal of Endodontics 31, 529–32. Lee R, Cho H, Son H, Um M, Lee B (2007) Influence of cavity dimension and restoration methods on the cusp deflection of premolars in composite restoration. Dental Materials 23, 288–95. Lin C, Chang C, Ko C (2001) Multifactorial analysis of an MOD restored human premolar using auto-mesh finite element approach. Journal of Oral Rehablitation 28, 576–85. Magne P (2010) Virtual prototyping of adhesively restored, endodontically treated molars. The Journal of Posthetic Dentistry 103, 343–51. Magne P, Belser U (2003) Porcelain versus composite inlays/ onlays: effects of mechanical loads on stress distribution, adhesion, and crown flexure. The International Journal of Periodontics and Restorative Dentistry 23, 543–55. Marshall GJ, Balooch M, Kinney J, Marshall S (1995) Atomic force microscopy of conditioning agents on dentin. Journal of Biomedical Materials Research 29, 1381–7. Moraes RR, Garcia JW, Barros MD et al. (2011) Control of polymerization shrinkage and stress in nanogel-modified monomer and composite materials. Dental Materials 27, 509–19. Nalla R, Kinney J, Marshall S, Ritchie R (2004) On the in vitro Fatigue Behavior of Human Dentin: effect of Mean Stress. Journal of Dental Research 83, 211–5. Papa J, Cain C, Messer H (1994) Moisture content of vital vs endodontically treated teeth. Endodontics and Dental Traumatology 10, 91–3.

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Rasmussen S, Patchin R, Scott D, Heuer A (1976) Fracture properties of human enamel and dentin. Journal of Dental Research 55, 154–64. Reeh E, Messer H, Douglas W (1989) Reduction in tooth stiffness as a result of endodontic and restorative procedures. Journal of Endodontics 15, 512–6. Ren L, Wang W, Takao Y, Chen Z (2010) Effects of cementum-dentine junction and cementum on the mechanical response of tooth supporting structure. Journal of Dentistry 38, 882–91. Romeed S, Dunne SM (2013) Stress analysis of different post-luting systems: a three-dimensional finite element analysis. Australian Dental Journal 58, 82–8. Ross I (1980) Fracture susceptibility of endodontically treated teeth. Journal of Endodontics 6, 560–5. Ruse N (2008) Propagation of erroneous data for the modulus of elasticity of periodontal ligament and gutta percha in FEM/FEA papers: a story of broken links. Dental Materials 24, 1717–9. Sano H, Ciucchi B, Matthews WG, Pashley DH (1994) Tensile properties of mineralized and demineralized human and bovine dentin. Journal of Dental Research 73, 1205–11. Sedgley C, Messer H (1992) Are endodontically treated teeth more brittle? Journal of Endodontics 18, 332–5. Shen L, Huang H, Yu J, Lee S, Lee C, Hsieh S (2009) Effects of periodontal bone loss on the natural frequency of the human canine: a three-dimensional finite element analysis. Journal of Dental Sciences 4, 81–6. Soares P, Santos-Filho P, Queiroz E et al. (2008) Fracture resistance and stress distribution in endodontically treated maxillary premolars restored with composite resin. Journal of Prosthodontics 17, 114–9. Trope M, Langer I, Maltz D, Tronstad L (1986) Resistance to fracture of restored endodontically treated premolars. Dental Traumatology 2, 35–8. Wu Y, Cathro P, Marino V (2010) Fracture resistance and pattern of the upper premolars with obturated canals and restored endodontic occlusal access cavities. Journal of Biomedical Research 24, 474–8. Zelic K, Vukicevic A, Jovicic G, Aleksandrovic S, Filipovic N, Djuric M (2013) Finite element analysis of devitalized teeth. Journal of the Serbian Society for Computational Mechanics 7, 38–44. Zelic K, Milovanovic P, Rakocevic Z et al. (2014) Nano-structural and compositional basis of devitalized tooth fragility. Dental materials 30, 476–86.


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