doi:10.1111/iej.12397
Stress distribution in root filled teeth restored with various post and core techniques: effect of post length and crown height
K. Kainose1, M. Nakajima1, R. Foxton2, N. Wakabayashi3 & J. Tgami1,4 1
Cariology and Operative Dentistry, Oral Restitution Department, Graduate School of Medical and Dental Sciences, Tokyo Medical and Dental University, Tokyo, Japan; 2Division of Conservative Dentistry, King’s College London Dental Institute at Guy’s, King’s and St Thomas’ Hospitals, King’s College London, London, UK; 3Removable Partial Prosthodontics Department, Graduate School of Medical and Dental Sciences, Tokyo Medical and Dental University, Tokyo; and 4Global Center of Excellence (GCOE) Program, International Research Center for Molecular Science in Tooth and Bone Diseases, Tokyo Medical and Dental University, Tokyo, Japan
Abstract Kainose K, Nakajima M, Foxton R, Wakabayashi N, Tgami J. Stress distribution in root filled teeth restored with various post and core techniques: effect of post length and crown height. International Endodontic Journal.
Aim To investigate interfacial stress distribution in restored root filled teeth with various post lengths and crown heights. Methodology Three-dimensional mathematical models of a root filled mandibular premolar tooth were constructed. Parts of the tooth structures were replaced with ceramic crowns having three crown heights incorporating, either a cast post and core or a resin post and cores with fibre post or metallic post with four post lengths. Finite element linear analysis was performed to calculate equivalent and shear stress distribution at the interfaces between the teeth and post and cores under mesiodistal symmetrical boundary conditions and an oblique static load of 400 N.
Introduction Root filled teeth often require post and core build-ups because of extensive loss of tooth tissue resulting from
Correspondence: Masatoshi Nakajima, Cariology and Operative Dentistry, Oral Restitution Department, Graduate School of Medical and Dental Sciences, Tokyo Medical and Dental University, 1-4-45 Yushima, Bunkyo-ku, Tokyo 113-8549, Japan (Tel.: +81 3 5803 5483; Fax: +81 3 5803 0195; e-mail: [email protected]).
© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
Results For the resin post and core with fibre and metallic posts, shear stress at the interface was greater in the cervical area than the post area, depending on the crown height. The resin post and core with metallic post had lower shear stress at the interface of cervical area than that of the fibre post model; however, the metallic post models produced a high concentration of shear stress at the interface between the post and resin composite. On the other hand, for the cast post and core, the shear stress at the interface was mainly produced in the post end area, which increased with decrease of post length. Conclusions For the resin post and core, bonding integrity to the cervical area would play a critical role in the survival of the restored tooth, whereas for the cast post and core, the bond of the post would be essential. Keywords: adhesive, debonding, analysis, fracture, root, stress.
finite
element
Received 28 January 2014; accepted 10 October 2014
caries and access cavity preparation. Nonadhesive traditional post and core with cast or prefabricated metallic posts has been widely used. The survival of teeth restored with crowns supported by posts is dependent on characteristics of the post (length, diameter, shape and its material), crown height and ferrule extension (Rosen 1961, Asmussen et al. 2005, Hayashi et al. 2006, Adanir & Belli 2008, SantosFilho et al. 2008, Chuang et al. 2010, Zicari et al. 2012a). On the other hand, although the insertion depth of a post can contribute to an increase in the
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mechanical retention of a post and core, deeper posts have been reported to cause catastrophic root fracture because a stiff post produces greater stress around the post end (Eskitascioglu et al. 2002, Hayashi et al. 2008). Adhesive resin post and core build-ups incorporating a fibre post are becoming a popular alternative to the traditional nonadhesive cast post and core. It has been demonstrated that using fibre posts can decrease the risk of catastrophic root fracture compared with metallic posts (Akkayan & G€ ulmez 2002, Hayashi et al. 2008). Finite element analysis (FEA) involves a series of computational procedures to predict specific outcomes, including mechanical behaviour, for a complex and specific geometric assembly by integrating results obtained in smaller elements defined by a specific mesh. This analysis is extremely useful for indicating the mechanical aspects of biomaterials and human tissue that can be difficult to measure in vivo. Many studies employing FEA have investigated stress distribution in root filled teeth restored with different post and core techniques, in which fibre posts can avoid stress concentration at the post end because of their similar elastic modulus to dentine (Eskitascioglu et al. 2002, Coelho et al. 2009, Ona et al. 2013). For resin post and cores, adhesion between the cervical canal walls and the resin material is important for improving the retention of the post and core and the fracture strength of the restored tooth. Many studies have demonstrated that shorter posts with good bonding to root dentine do not affect the fracture strength of the restored tooth (Chuang et al. 2010, Schiavetti et al. 2010, Borelli et al. 2012, Zicari et al. 2012b). Moreover, a previous study reported that the absence of adhesion in the post preparation did not affect the fracture strength of the resin post and core reconstructions of pulpless teeth (Nakajima et al. 2010) when sufficient adhesion in the cervical area was provided. These results might indicate that adhesion in the cervical area plays a more critical role in the fracture of resin posts and core-restored teeth than that of the post area. Clinically, the initial debonding at the adhesive interfaces in resin posts and cores would arise partially under the various stresses in the mouth. Partial debonding of the adhesive interface of resin post and cores would change the stress distribution in the restored tooth, which would produce further interfacial failure and/or cohesive failures in the resin composite and/or root dentine. To clarify initial debonding mechanism at the interface between tooth
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structure and resin composite, it is necessary to investigate interfacial stress distribution in the cervical area (loaded or nonloaded side) and post area (cervical, middle or apical part) under loading, which might be influenced by post length and crown height. Therefore, the objective of this study was to investigate equivalent stress concentrations in root filled teeth restored with resin post and cores using fibre and metallic posts, and cast post and cores with various post lengths and crown heights, using FEA, and to assess the regional differences of shear stress at the adhesive interface in restored root filled teeth.
Materials and methods The Finite element models consisted of a mandibular second premolar tooth with a root filling, periodontal ligament and surrounding alveolar bone. The form and the material properties of the components such as tooth and bone are irregular and heterogeneous; therefore, analysis with three-dimensional model structures, not two-dimensional, is necessary to obtain accurate results (Romeed et al. 2006). A threedimensional intact tooth was constructed based on the anatomical image of an adult tooth (Dental Anatomy & Interactive 3-D Tooth Atlas; Brown & Herbranson Imaging, Inc., Portola Valley, CA, USA) (Fig. 1). The stress and strain estimated through the three-dimensional model structures were analysed for prediction of failure risk of the tooth-restoration structures (Wakabayashi et al. 2008). The mandibular bone was modelled as a cancellous block with 2.0mm-thick cortical bone. The post preparation was modelled with a simplified circular external cross section 2.0 mm in diameter in the root. Part of the tooth structure was replaced with a full coverage ceramic crown with shoulder margin form, without ferrule and with three crown heights: 6, 7 and 8 mm. A Ni-Cr alloy cast post and core and resin composite post and core with a glass fibre post or a Ni-Cr alloy metallic post with four post lengths: 4, 6, 8 and 10 mm were used for post and core, in which a fibre post and metallic post 1.0 mm in diameter were completely embedded in the resin post and core. Each model had mesiodistal symmetrical boundary conditions applied and was meshed by approximately 100000 hexahedral elements determined by preliminary convergence tests (ANSYS 11.0; ANSYS Inc., Canonsburg, PA, USA). All materials were considered homogeneous, linearly elastic and isotropic, except for the orthotropic glass fibre post (Table 1). All materials
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were assumed to be perfectly bonded each other. This means that simulations of this study were performed based on linear elastic analysis. A total axial load of 400 N (Kshirsagar et al. 2011) was applied to the tip
of the buccal cusp 45° obliquely from buccal to lingual. In each model, the movement of the outer surface bone was restricted. The shear stress distributions at the interface between post and core and dentine, and the equivalent stress distributions in the tooth and in the post and core were calculated for all simulations. The magnitude of the highest maximum shear stress at the buccal cervical area, lingual cervical area, post end area and proximal post area in the post and core interface was recorded, and the magnitude of highest maximum equivalent stress in the tooth structures and in the post and core materials was also recorded.
Results
Figure 1 Three-dimensional finite element model of the mandibular second premolar tooth (1). Tooth model: root (r), post and core foundation (f), the crown restoration (c), gutta-percha (gp), the periodontal ligament (pdl), the bone block (b), and fibre post (fp), metallic post (mp) was modelled for support of the tooth structures. The loading and boundary conditions (2). Tooth model applied mesiodistal symmetrical boundary conditions and meshed. On the buccal cusp, arrow indicates an off-axis 45° oblique load. The triangles represent the fixation at the lower surface of the bone. This model has 10 mm post length and 6 mm crown height.
Table 1 Material properties used in the study Elastic modulus (MPa)
Poison’s ratio
Dentin
14 700*
0.31**
Porcelain Cortical bone Cancellous bone Gutta-percha Periodontal ligament Ni-Cr alloy Composite resin Glass fibre Transverse Longitudinal
70 000 14 700 490 140 800
0.19 0.3 0.3 0.49 0.45
*Sano et al. (1994) **Farah et al. (1989) €se et al. (1985) Ka Moroi et al. (1993) Moroi et al. (1993) Friedman et al. (1977) Farah et al. (1989)
18 800 12 000
0.27 0.33
Morris (1989) Lanza et al. (2005)
9500 37 000
0.27 0.34
Lanza et al. (2005)
References
© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
Figure 2 shows the equivalent stress distribution in the root dentine structure for a post length and crown height of 6 mm in each combination of post and core materials. The equivalent stress concentration was located at the bottom of the post preparation and at the bone level on the lingual side of the root for all the models. Figure 2-1 presents the maximum equivalent stress at the bottom of the post preparation. The post length affected the magnitude of the equivalent stress at the bottom of the post preparation, whilst crown height did not considerably affect the resultant stress magnitudes. For the cast post and core model, the equivalent stress at the bottom of the post preparation dramatically increased with a reduction in post length (Fig. 2-1a). On the other hand, resin post and core models with fibre and metallic posts had a smaller effect on post length on the equivalent stress at the bottom of the post preparation than the cast post and core model. There was no difference in the magnitude of the equivalent stress at the bottom of the post preparation between the fibre and metallic post models (Fig. 2-1b, 1c). Figure 2-2 presents the maximum equivalent stress concentration at the bone level on the lingual side of the root. The magnitude of the equivalent stress at the bone level in the root became larger in the order of cast post and core model, metallic post model and fibre post model, which were affected by crown height, but not by post length (Fig. 2-2). Figure 3 shows the equivalent stress distribution in the post and core materials for a post length and crown height of 6 mm. For the cast post and core model, the equivalent stress concentration appeared on the lingual (nonloading) side of the middle of the post, whose magnitude was affected by crown heights
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Figure 2 The equivalent stress distributions in the dentine structure and plots of the equivalent stress at the bottom of post preparation in dentin (1) and at the lingual (nonloading) side bone level in dentine (2) for post length 6 mm, crown height 6 mm models. The post and core was made of cast alloy (a), resin composite with fibre post (b) and resin composite with prefabricated metallic post (c). The restorations are not shown in the graphics. Red areas represent the highest stress, as indicated by the scale bars.
(Fig. 3-1a). On the other hand, for the fibre and metallic post models, the equivalent stresses in the post part were very low and uniform, which were not affected by post length and crown height (Fig. 3-1b, 1c). Additionally, in all the models, the equivalent stresses concentrated slightly on the lingual (nonloading) cervical area, whose magnitude was affected by the crown heights (Fig. 3-2).
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Figure 4 shows the shear stress distribution at the interface between the root dentine structure and the post and core materials for a post length and crown height of 6 mm. Figure 5 present the maximum shear stresses at the interfaces of the post end area, proximal post area, lingual (nonloading side) cervical area and buccal (loaded side) cervical area. For the cast post and core model, shear stress concentration at the
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Figure 3 The equivalent stress distributions on the surfaces of the post and core restorations and plots of the equivalent stress at the middle of post length (1) and at the lingual (nonloading) side cervical area (2) for post length 6 mm, crown height 6 mm models. The post and core was made of cast alloy (a), resin composite with fibre post (b) and resin composite with prefabricated metallic post (c). The highest equivalent stress was indicated as the red areas. In the cast alloy models, the equivalent stress concentrated at the middle of the post length. On the other hand, in the fibre post models and metallic post models, the equivalent stress concentrated at the lingual (nonloading) side of the cervical area.
interface was located at the post end area whose magnitude was affected by post length and the proximal area of apical part of the post (Figs. 4 and 5-1a, 2a). On the other hand, for resin post and core models with fibre and metallic posts, the shear stress concentration at the interface was located at the edge of the lingual (nonloading side) cervical area rather
© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
than the post end area, whose magnitude was affected by crown heights (Figs. 4 and 5-3b, 3c). The fibre post model produced larger shear stress at the interface of the lingual (nonloading side) cervical area than the metallic post model (Fig. 5-3b, 3c), whilst at the buccal (loading side) cervical area, the magnitude of the shear stress was almost equal amongst them
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(a)
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Figure 4 The shear stress distributions on the surfaces of the post and core restorations for post length 6 mm, crown height 6 mm models. The post and core was made of cast alloy (a), resin composite with fibre post (b) and resin composite with prefabricated metallic post (c). The highest shear stress was indicated as the maximum (red) or the minimum (blue) stresses dependent on the clockwise and counterclockwise directions. In the cast alloy models, the shear stress concentrated at the both mesial and distal side of the post area. In the fibre post models and the metallic post models, the shear stress concentrated at the lingual (nonloading) side cervical area.
(Fig. 5-4b, 4c). Additionally, for the metallic post model, shear stress concentration was also found at the interface between the resin post and core and the post material compared with fibre post model, in which decreasing the post length increased the magnitude of the shear stress (Fig. 6).
Discussion In this study, a ferrule extension was not prepared in the crown-restored tooth model. For a crown restoration, preservation of tooth substrate at the coronal level affects their fracture resistance. In particular, a ferrule extension with at least 2 mm height has been recommended (Zicari et al. 2012a) because increasing ferrule height can reduce distortion of the restored tooth, leading to less stress concentration (Ichim et al. 2006). When a full coverage crown is placed with ferrule retention, post length and the mechanical properties of the post and core materials would hardly affect the fracture strength and the stress distribution of the restored tooth (Pierrisnard et al. 2002, Ichim et al. 2006). On the other hand, without a ferrule extension, post and core materials and post length would strongly affect stress distributions in the restored tooth. Therefore, in this study, a crownrestored tooth model without ferrule extension was
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subjected to FEA to further understand the influence of post and core build-up methods on the stress distribution of root filled teeth. For all the post and core models, the equivalent stress concentration in the root was located at the bottom of the post preparation. The length of post strongly affected the magnitude of the equivalent stress depending upon the post and core methods, although crown height seldom affected them (Fig. 2-1). For the cast post and core model, the equivalent stress at the bottom of the post preparation dramatically increased with a reduction in post length (Fig. 2-1a). This would have been due to the higher elastic modulus for the cast post and core material than root dentine (Coelho et al. 2009, Santos et al. 2010, Ona et al. 2013). On the other hand, the resin post and core models with fibre and metallic posts produced lower equivalent stress at the bottom of the post preparation in the root than the cast post and core model, in which there was smaller effect of post length. Additionally, there was no difference in the magnitude of the equivalent stress at the bottom of the post preparation between the fibre post model and metallic post model (Fig. 2-1b, 1c), although the metallic post had a higher elastic modulus than fibre post and root dentine. These results are in disagreement with previous studies due to differences of the resin post and core models constructed. In this study, the fibre and metallic posts were completely embedded into the resin post and core material; therefore, the stiff post did not make direct contact with the root dentine. The presence of resin composite with a similar elastic modulus to dentine between the root dentine and the post materials would lead to smaller stress concentration in the root. In the analysis of equivalent stress distributions in the post and core materials, the cast post and core model produced equivalent stress at the middle part of the post (Fig. 3-1a). When using a cast post and core with a higher elastic modulus than dentine, the force applied to the crown restoration would be stored in the post and transmitted apically (Hayashi et al. 2006, Ona et al. 2013). This would cause a rotation movement of the cast post and core in the root, setting the middle part of the post as rotational centre and then produce the interfacial stress in the post. Indeed, in this study, the shear stress concentration at the adhesive interface was recorded around the post end area, depending upon the post length and at the proximal area of the post (Figs. 4 and 5-1a, 2a). For similar loads as produced in this study, the initial debonding could occur at the interface of the post
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Figure 5 Plots of the shear stress for post length 6 mm, crown height 6 mm models on the post end area (1), on the proximal post area (2), on the lingual (nonloading) side cervical area (3) and on the buccal (loading) side cervical area (4). (a) Cast alloy models, (b) Fibre post models, (c) Metallic post models.
using cast post and core whose probability would increase with a reduction in post length. The partial debonding would progress to further interfacial failure between the cast post and core and the root, and after complete failure of the interface, the cast post and core may then act as a cantilever beam, which would fracture the root dentine.
© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
For the resin post and core with fibre post and metallic post, the equivalent stress concentration in the root appeared on the bone level of the lingual (nonloading) side, whose magnitude was higher than that of cast post and core model (Fig. 2-2), but lower than that of intact tooth model (not shown). When using resin composite material with a similar elastic
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(a)
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Figure 6 Plots of the shear stress between post and core and post interface for post length 6 mm, crown height 6 mm models. (a) Fibre post models, (b) Metallic post models.
modulus to dentine, the force applied to the crown restoration would not be stored in the post, causing the elastic deformation of the restored tooth with resin post and core. The equivalent stress concentration in the resin post and core was not recorded on the post part, but found on the lingual (nonloading side) cervical area (Fig. 3-2b, 2c). This would indicate that the force applied to the crown restoration would try to cause a bending deformation of the restored tooth, using the bone level as a supporting point, and then generate a distortion within the restored tooth above the bone level. This distortion in the upper part of the restored tooth would produce shear stress at the interface between resin post and core and cervical dentine; therefore, the magnitude of the shear stress would be influenced by crown height, not post length (Figs. 4 and 5-3b, 3c). In this study, for the resin post and core, shear stress concentrations at the interface were recorded on the cervical area, not in the post (Figs. 4 and 53b, 3c). In the restored tooth with a resin post and core, larger shear stress in the cervical area could initially compromise adhesion to the cervical area, and the debonding of cervical area might cause cohesive fracture in the resin post and core material even if maintaining adhesion to the post. A previous study demonstrated that the absence of adhesion in post preparation did not affect the fracture strengths of resin post and core reconstructions of pulpless teeth (Nakajima et al. 2010) when sufficient adhesion to the cervical area was provided. Therefore, adhesion to the cervical area would play a critical role in maintaining the integrity of the restored tooth with resin post and core methods more than the post itself.
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In the resin post and core models, the fibre post model had larger shear stress concentrations in the lingual (nonloading side) cervical interface than the metallic post model (Figs. 4 and 5-3b, 3c). Additionally, the fibre post model had larger equivalent stress at the bone level in the root than the metallic post model (Fig. 2-2b, 2c). This would mean that for the fibre post model, larger stress was applied at the bone level in the root as the supporting point for the bending deformation of the restored tooth and that the fibre post model produced larger distortion in upper part of the restored tooth than the metallic post model. This would be a reason why the stiffer metallic post could resist deformation of the restored tooth above the bone level, leading to less shear stress concentration at the cervical interface of resin post and core. However, the metallic post model produced larger shear stress at the interface between the post material and resin composite in the resin post and core compared to the fibre post model (Fig. 6). These stress concentrations at the interface could cause premature fracture of the post and core. Then, a stiffer post material in a resin post and core could maintain the bonding integrity at the cervical interface, but there would be another debonding risk between post material and resin composite, especially with a shorter post length. Recently, Ona et al. (2013) evaluated the effect of absolute bonding failure at the adhesive interfaces of post and core on stress distribution in restored root filled teeth using a nonlinear contact analysis, which can simulate friction and a potential sliding phenomenon in the nonbonded interface. They reported that absolute debonding of the adhesive interface of resin post and cores dramatically changed the stress distribution in a root filled tooth. Also, initial partial debonding at the interface of resin post and cores would change the stress distribution in the restored tooth, following further interfacial failure and/or cohesive failures in resin post and core and/or root dentine. Further research should be undertaken to assess the influence of partial debonding at the interface of the post and core on stress distribution in crown-restored root filled teeth and the fracture patterns. Although the results serve to clarify the critical elements of material selection for post and core restorations, the limitation of the method should be considered, especially if the quantitative assessment of the stresses is to be emphasized. The study design employed only one tooth configuration, loading direction and elastic property of each material. Moreover,
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because the linear elastic analysis is not a time-dependent simulation, the result of this study reveals the stress distribution before the occurrence of initial failure in the model structures. A nonlinear contact simulation would characterize the influence of initial debonding on the post and core stress in tooth models that could dramatically alter the stress distributions in the model. These pending issues should be investigated in further studies. As the scope of the present study was to estimate interfacial stress distributions with various post lengths and crown heights, the purpose of this study was accomplished using the present experimental conditions.
Conclusions For the resin post and core with fibre and metallic posts, shear stress at the interface was higher in the cervical area than in the post area, depending upon the crown height. The metallic post model produced smaller shear stress at the interface of the cervical area than the fibre post model; however, the metallic post produced larger shear stress at the interface between the post material and resin composite within the resin post and core. On the other hand, for the cast post and cores, the shear stress at the interface was mainly produced in the post, which increased with a decrease in post length.
Acknowledgements The authors gratefully acknowledge the financial support received from the Japanese Ministry of Education, Global Center of Excellence (GCOE) Program, International Research Center for Molecular Science in Tooth and Bone Diseases, Tokyo Medical and Dental University.
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© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
Chuang S, Yaman P, Herrero A, Dennison J, Chang C (2010) Influence of post material and length on endodontically treated incisors: an in vitro and finite element study. The Journal of Prosthetic Dentistry 104, 379–88. Coelho C, Biffi J, Silva G, Abrahao A, Campos R, Soares C (2009) Finite element analysis of weakened roots restored with composite resin and posts. Dental Materials Journal 28, 671–8. Eskitascioglu G, Belli S, Kalkan M (2002) Evaluation of two post core systems using two different methods (Fracture strength test and a finite elemental stress analysis). Journal of Endodontics 28, 629–33. Farah JW, Craig RG, Meroueh KA (1989) Finite element analysis of three- and four-unit bridges. Journal of Oral Rehabilitation 16, 603–11. Friedman CE, Sandrik JL, Heuer MA, Rapp GW (1977) Composition and physical properties of gutta-percha endodontic filling materials. Journal of Endodontics 3, 304–8. Hayashi M, Takahashi Y, Imazato S, Ebisu S (2006) Fracture resistance of pulpless teeth restored with post-cores and crowns. Dental Materials 22, 477–85. Hayashi M, Sugeta A, Takahashi Y, Imazato S, Ebisu S (2008) Static and fatigue fracture resistances of pulpless teeth restored with post–cores. Dental Materials 4, 1178–86. Ichim I, Kuzmanovic D, Love R (2006) A finite element analysis of ferrule design on restoration resistance and distribution of stress within a root. International Endodontic Journal 36, 443–52. Kshirsagar R, Jaggi N, Halli R (2011) Bite force measurement in mandibular parasymphyseal fractures: a preliminary clinical study. Craniomaxillofacial Trauma & Reconstruction 4, 241–4. K€ ase HR, Tesk JA, Case ED (1985) Elastic constants of two dental porcelains. Journal of Materials Science 20, 524–31. Lanza A, Aversa R, Rengo S, Apicella D, Apicella A (2005) 3D FEA of cemented steel, glass and carbon posts in a maxillary incisor. Dental Materials 21, 709–15. Moroi HH, Okimoto K, Moroi R, Terada Y (1993) Numeric approach to the biomechanical analysis of thermal effects in coated implants. The International Journal of Prosthodontics 6, 564–72. Morris HF (1989) Veterans Administration Cooperative Studies Project No. 147/242. Part VII: the mechanical properties of metal ceramic alloys as cast and after simulated porcelain firing. The Journal of Prosthetic Dentistry 61, 160–9. Nakajima M, Kanno T, Komada W, Miura H, Foxton R, Tagami J (2010) Effect of bonded area and/or fiber post placement on the fracture strengths of resin-core reconstructions for pulpless teeth. American Journal of Dentistry 23, 300–4. Ona M, Wakabayashi N, Yamazaki T, Takaichi A, Igarashi Y (2013) The influence of elastic modulus mismatch between tooth and post and core restorations on root fracture. International Endodontic Journal 46, 47–52.
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Pierrisnard L, Bohin F, Renault P, Barquinsd M (2002) Corono-radicular reconstruction of pulpless teeth: a mechanical study using finite element analysis. The Journal of Prosthetic Dentistry 88, 442–8. Romeed SA, Fok SL, Wilson NHF (2006) A comparison of 2D and 3D finite element analysis of a restored tooth. Journal of Oral Rehabilitation 33, 209–15. Rosen H (1961) Operative procedures on mutilated endodontically treated teeth. The Journal of Prosthetic Dentistry 11, 973–86. Sano H, Ciucchi B, Matthews WG, Pashley DG (1994) Tensile properties of mineralized and demineralized human and bovine dentin. Journal of Dental Research 73, 1205–11. Santos AF, Meira JB, Tanaka CB et al. (2010) Can fiber posts increase root stresses and reduce fracture? Journal of Dental Research 89, 587–91. Santos-Filho P, Castro G, Silva R, Campos E, Soares J (2008) Effects of post system and length on the strain and
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Stress distribution in root filled teeth restored with various post and core techniques: effect of post length and crown height
K. Kainose1, M. Nakajima1, R. Foxton2, N. Wakabayashi3 & J. Tgami1,4 1
Cariology and Operative Dentistry, Oral Restitution Department, Graduate School of Medical and Dental Sciences, Tokyo Medical and Dental University, Tokyo, Japan; 2Division of Conservative Dentistry, King’s College London Dental Institute at Guy’s, King’s and St Thomas’ Hospitals, King’s College London, London, UK; 3Removable Partial Prosthodontics Department, Graduate School of Medical and Dental Sciences, Tokyo Medical and Dental University, Tokyo; and 4Global Center of Excellence (GCOE) Program, International Research Center for Molecular Science in Tooth and Bone Diseases, Tokyo Medical and Dental University, Tokyo, Japan
Abstract Kainose K, Nakajima M, Foxton R, Wakabayashi N, Tgami J. Stress distribution in root filled teeth restored with various post and core techniques: effect of post length and crown height. International Endodontic Journal.
Aim To investigate interfacial stress distribution in restored root filled teeth with various post lengths and crown heights. Methodology Three-dimensional mathematical models of a root filled mandibular premolar tooth were constructed. Parts of the tooth structures were replaced with ceramic crowns having three crown heights incorporating, either a cast post and core or a resin post and cores with fibre post or metallic post with four post lengths. Finite element linear analysis was performed to calculate equivalent and shear stress distribution at the interfaces between the teeth and post and cores under mesiodistal symmetrical boundary conditions and an oblique static load of 400 N.
Introduction Root filled teeth often require post and core build-ups because of extensive loss of tooth tissue resulting from
Correspondence: Masatoshi Nakajima, Cariology and Operative Dentistry, Oral Restitution Department, Graduate School of Medical and Dental Sciences, Tokyo Medical and Dental University, 1-4-45 Yushima, Bunkyo-ku, Tokyo 113-8549, Japan (Tel.: +81 3 5803 5483; Fax: +81 3 5803 0195; e-mail: [email protected]).
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Results For the resin post and core with fibre and metallic posts, shear stress at the interface was greater in the cervical area than the post area, depending on the crown height. The resin post and core with metallic post had lower shear stress at the interface of cervical area than that of the fibre post model; however, the metallic post models produced a high concentration of shear stress at the interface between the post and resin composite. On the other hand, for the cast post and core, the shear stress at the interface was mainly produced in the post end area, which increased with decrease of post length. Conclusions For the resin post and core, bonding integrity to the cervical area would play a critical role in the survival of the restored tooth, whereas for the cast post and core, the bond of the post would be essential. Keywords: adhesive, debonding, analysis, fracture, root, stress.
finite
element
Received 28 January 2014; accepted 10 October 2014
caries and access cavity preparation. Nonadhesive traditional post and core with cast or prefabricated metallic posts has been widely used. The survival of teeth restored with crowns supported by posts is dependent on characteristics of the post (length, diameter, shape and its material), crown height and ferrule extension (Rosen 1961, Asmussen et al. 2005, Hayashi et al. 2006, Adanir & Belli 2008, SantosFilho et al. 2008, Chuang et al. 2010, Zicari et al. 2012a). On the other hand, although the insertion depth of a post can contribute to an increase in the
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mechanical retention of a post and core, deeper posts have been reported to cause catastrophic root fracture because a stiff post produces greater stress around the post end (Eskitascioglu et al. 2002, Hayashi et al. 2008). Adhesive resin post and core build-ups incorporating a fibre post are becoming a popular alternative to the traditional nonadhesive cast post and core. It has been demonstrated that using fibre posts can decrease the risk of catastrophic root fracture compared with metallic posts (Akkayan & G€ ulmez 2002, Hayashi et al. 2008). Finite element analysis (FEA) involves a series of computational procedures to predict specific outcomes, including mechanical behaviour, for a complex and specific geometric assembly by integrating results obtained in smaller elements defined by a specific mesh. This analysis is extremely useful for indicating the mechanical aspects of biomaterials and human tissue that can be difficult to measure in vivo. Many studies employing FEA have investigated stress distribution in root filled teeth restored with different post and core techniques, in which fibre posts can avoid stress concentration at the post end because of their similar elastic modulus to dentine (Eskitascioglu et al. 2002, Coelho et al. 2009, Ona et al. 2013). For resin post and cores, adhesion between the cervical canal walls and the resin material is important for improving the retention of the post and core and the fracture strength of the restored tooth. Many studies have demonstrated that shorter posts with good bonding to root dentine do not affect the fracture strength of the restored tooth (Chuang et al. 2010, Schiavetti et al. 2010, Borelli et al. 2012, Zicari et al. 2012b). Moreover, a previous study reported that the absence of adhesion in the post preparation did not affect the fracture strength of the resin post and core reconstructions of pulpless teeth (Nakajima et al. 2010) when sufficient adhesion in the cervical area was provided. These results might indicate that adhesion in the cervical area plays a more critical role in the fracture of resin posts and core-restored teeth than that of the post area. Clinically, the initial debonding at the adhesive interfaces in resin posts and cores would arise partially under the various stresses in the mouth. Partial debonding of the adhesive interface of resin post and cores would change the stress distribution in the restored tooth, which would produce further interfacial failure and/or cohesive failures in the resin composite and/or root dentine. To clarify initial debonding mechanism at the interface between tooth
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structure and resin composite, it is necessary to investigate interfacial stress distribution in the cervical area (loaded or nonloaded side) and post area (cervical, middle or apical part) under loading, which might be influenced by post length and crown height. Therefore, the objective of this study was to investigate equivalent stress concentrations in root filled teeth restored with resin post and cores using fibre and metallic posts, and cast post and cores with various post lengths and crown heights, using FEA, and to assess the regional differences of shear stress at the adhesive interface in restored root filled teeth.
Materials and methods The Finite element models consisted of a mandibular second premolar tooth with a root filling, periodontal ligament and surrounding alveolar bone. The form and the material properties of the components such as tooth and bone are irregular and heterogeneous; therefore, analysis with three-dimensional model structures, not two-dimensional, is necessary to obtain accurate results (Romeed et al. 2006). A threedimensional intact tooth was constructed based on the anatomical image of an adult tooth (Dental Anatomy & Interactive 3-D Tooth Atlas; Brown & Herbranson Imaging, Inc., Portola Valley, CA, USA) (Fig. 1). The stress and strain estimated through the three-dimensional model structures were analysed for prediction of failure risk of the tooth-restoration structures (Wakabayashi et al. 2008). The mandibular bone was modelled as a cancellous block with 2.0mm-thick cortical bone. The post preparation was modelled with a simplified circular external cross section 2.0 mm in diameter in the root. Part of the tooth structure was replaced with a full coverage ceramic crown with shoulder margin form, without ferrule and with three crown heights: 6, 7 and 8 mm. A Ni-Cr alloy cast post and core and resin composite post and core with a glass fibre post or a Ni-Cr alloy metallic post with four post lengths: 4, 6, 8 and 10 mm were used for post and core, in which a fibre post and metallic post 1.0 mm in diameter were completely embedded in the resin post and core. Each model had mesiodistal symmetrical boundary conditions applied and was meshed by approximately 100000 hexahedral elements determined by preliminary convergence tests (ANSYS 11.0; ANSYS Inc., Canonsburg, PA, USA). All materials were considered homogeneous, linearly elastic and isotropic, except for the orthotropic glass fibre post (Table 1). All materials
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were assumed to be perfectly bonded each other. This means that simulations of this study were performed based on linear elastic analysis. A total axial load of 400 N (Kshirsagar et al. 2011) was applied to the tip
of the buccal cusp 45° obliquely from buccal to lingual. In each model, the movement of the outer surface bone was restricted. The shear stress distributions at the interface between post and core and dentine, and the equivalent stress distributions in the tooth and in the post and core were calculated for all simulations. The magnitude of the highest maximum shear stress at the buccal cervical area, lingual cervical area, post end area and proximal post area in the post and core interface was recorded, and the magnitude of highest maximum equivalent stress in the tooth structures and in the post and core materials was also recorded.
Results
Figure 1 Three-dimensional finite element model of the mandibular second premolar tooth (1). Tooth model: root (r), post and core foundation (f), the crown restoration (c), gutta-percha (gp), the periodontal ligament (pdl), the bone block (b), and fibre post (fp), metallic post (mp) was modelled for support of the tooth structures. The loading and boundary conditions (2). Tooth model applied mesiodistal symmetrical boundary conditions and meshed. On the buccal cusp, arrow indicates an off-axis 45° oblique load. The triangles represent the fixation at the lower surface of the bone. This model has 10 mm post length and 6 mm crown height.
Table 1 Material properties used in the study Elastic modulus (MPa)
Poison’s ratio
Dentin
14 700*
0.31**
Porcelain Cortical bone Cancellous bone Gutta-percha Periodontal ligament Ni-Cr alloy Composite resin Glass fibre Transverse Longitudinal
70 000 14 700 490 140 800
0.19 0.3 0.3 0.49 0.45
*Sano et al. (1994) **Farah et al. (1989) €se et al. (1985) Ka Moroi et al. (1993) Moroi et al. (1993) Friedman et al. (1977) Farah et al. (1989)
18 800 12 000
0.27 0.33
Morris (1989) Lanza et al. (2005)
9500 37 000
0.27 0.34
Lanza et al. (2005)
References
© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
Figure 2 shows the equivalent stress distribution in the root dentine structure for a post length and crown height of 6 mm in each combination of post and core materials. The equivalent stress concentration was located at the bottom of the post preparation and at the bone level on the lingual side of the root for all the models. Figure 2-1 presents the maximum equivalent stress at the bottom of the post preparation. The post length affected the magnitude of the equivalent stress at the bottom of the post preparation, whilst crown height did not considerably affect the resultant stress magnitudes. For the cast post and core model, the equivalent stress at the bottom of the post preparation dramatically increased with a reduction in post length (Fig. 2-1a). On the other hand, resin post and core models with fibre and metallic posts had a smaller effect on post length on the equivalent stress at the bottom of the post preparation than the cast post and core model. There was no difference in the magnitude of the equivalent stress at the bottom of the post preparation between the fibre and metallic post models (Fig. 2-1b, 1c). Figure 2-2 presents the maximum equivalent stress concentration at the bone level on the lingual side of the root. The magnitude of the equivalent stress at the bone level in the root became larger in the order of cast post and core model, metallic post model and fibre post model, which were affected by crown height, but not by post length (Fig. 2-2). Figure 3 shows the equivalent stress distribution in the post and core materials for a post length and crown height of 6 mm. For the cast post and core model, the equivalent stress concentration appeared on the lingual (nonloading) side of the middle of the post, whose magnitude was affected by crown heights
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Figure 2 The equivalent stress distributions in the dentine structure and plots of the equivalent stress at the bottom of post preparation in dentin (1) and at the lingual (nonloading) side bone level in dentine (2) for post length 6 mm, crown height 6 mm models. The post and core was made of cast alloy (a), resin composite with fibre post (b) and resin composite with prefabricated metallic post (c). The restorations are not shown in the graphics. Red areas represent the highest stress, as indicated by the scale bars.
(Fig. 3-1a). On the other hand, for the fibre and metallic post models, the equivalent stresses in the post part were very low and uniform, which were not affected by post length and crown height (Fig. 3-1b, 1c). Additionally, in all the models, the equivalent stresses concentrated slightly on the lingual (nonloading) cervical area, whose magnitude was affected by the crown heights (Fig. 3-2).
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Figure 4 shows the shear stress distribution at the interface between the root dentine structure and the post and core materials for a post length and crown height of 6 mm. Figure 5 present the maximum shear stresses at the interfaces of the post end area, proximal post area, lingual (nonloading side) cervical area and buccal (loaded side) cervical area. For the cast post and core model, shear stress concentration at the
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Figure 3 The equivalent stress distributions on the surfaces of the post and core restorations and plots of the equivalent stress at the middle of post length (1) and at the lingual (nonloading) side cervical area (2) for post length 6 mm, crown height 6 mm models. The post and core was made of cast alloy (a), resin composite with fibre post (b) and resin composite with prefabricated metallic post (c). The highest equivalent stress was indicated as the red areas. In the cast alloy models, the equivalent stress concentrated at the middle of the post length. On the other hand, in the fibre post models and metallic post models, the equivalent stress concentrated at the lingual (nonloading) side of the cervical area.
interface was located at the post end area whose magnitude was affected by post length and the proximal area of apical part of the post (Figs. 4 and 5-1a, 2a). On the other hand, for resin post and core models with fibre and metallic posts, the shear stress concentration at the interface was located at the edge of the lingual (nonloading side) cervical area rather
© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
than the post end area, whose magnitude was affected by crown heights (Figs. 4 and 5-3b, 3c). The fibre post model produced larger shear stress at the interface of the lingual (nonloading side) cervical area than the metallic post model (Fig. 5-3b, 3c), whilst at the buccal (loading side) cervical area, the magnitude of the shear stress was almost equal amongst them
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(a)
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Figure 4 The shear stress distributions on the surfaces of the post and core restorations for post length 6 mm, crown height 6 mm models. The post and core was made of cast alloy (a), resin composite with fibre post (b) and resin composite with prefabricated metallic post (c). The highest shear stress was indicated as the maximum (red) or the minimum (blue) stresses dependent on the clockwise and counterclockwise directions. In the cast alloy models, the shear stress concentrated at the both mesial and distal side of the post area. In the fibre post models and the metallic post models, the shear stress concentrated at the lingual (nonloading) side cervical area.
(Fig. 5-4b, 4c). Additionally, for the metallic post model, shear stress concentration was also found at the interface between the resin post and core and the post material compared with fibre post model, in which decreasing the post length increased the magnitude of the shear stress (Fig. 6).
Discussion In this study, a ferrule extension was not prepared in the crown-restored tooth model. For a crown restoration, preservation of tooth substrate at the coronal level affects their fracture resistance. In particular, a ferrule extension with at least 2 mm height has been recommended (Zicari et al. 2012a) because increasing ferrule height can reduce distortion of the restored tooth, leading to less stress concentration (Ichim et al. 2006). When a full coverage crown is placed with ferrule retention, post length and the mechanical properties of the post and core materials would hardly affect the fracture strength and the stress distribution of the restored tooth (Pierrisnard et al. 2002, Ichim et al. 2006). On the other hand, without a ferrule extension, post and core materials and post length would strongly affect stress distributions in the restored tooth. Therefore, in this study, a crownrestored tooth model without ferrule extension was
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subjected to FEA to further understand the influence of post and core build-up methods on the stress distribution of root filled teeth. For all the post and core models, the equivalent stress concentration in the root was located at the bottom of the post preparation. The length of post strongly affected the magnitude of the equivalent stress depending upon the post and core methods, although crown height seldom affected them (Fig. 2-1). For the cast post and core model, the equivalent stress at the bottom of the post preparation dramatically increased with a reduction in post length (Fig. 2-1a). This would have been due to the higher elastic modulus for the cast post and core material than root dentine (Coelho et al. 2009, Santos et al. 2010, Ona et al. 2013). On the other hand, the resin post and core models with fibre and metallic posts produced lower equivalent stress at the bottom of the post preparation in the root than the cast post and core model, in which there was smaller effect of post length. Additionally, there was no difference in the magnitude of the equivalent stress at the bottom of the post preparation between the fibre post model and metallic post model (Fig. 2-1b, 1c), although the metallic post had a higher elastic modulus than fibre post and root dentine. These results are in disagreement with previous studies due to differences of the resin post and core models constructed. In this study, the fibre and metallic posts were completely embedded into the resin post and core material; therefore, the stiff post did not make direct contact with the root dentine. The presence of resin composite with a similar elastic modulus to dentine between the root dentine and the post materials would lead to smaller stress concentration in the root. In the analysis of equivalent stress distributions in the post and core materials, the cast post and core model produced equivalent stress at the middle part of the post (Fig. 3-1a). When using a cast post and core with a higher elastic modulus than dentine, the force applied to the crown restoration would be stored in the post and transmitted apically (Hayashi et al. 2006, Ona et al. 2013). This would cause a rotation movement of the cast post and core in the root, setting the middle part of the post as rotational centre and then produce the interfacial stress in the post. Indeed, in this study, the shear stress concentration at the adhesive interface was recorded around the post end area, depending upon the post length and at the proximal area of the post (Figs. 4 and 5-1a, 2a). For similar loads as produced in this study, the initial debonding could occur at the interface of the post
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Kainose et al. Assessment of regional debonding probability
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Figure 5 Plots of the shear stress for post length 6 mm, crown height 6 mm models on the post end area (1), on the proximal post area (2), on the lingual (nonloading) side cervical area (3) and on the buccal (loading) side cervical area (4). (a) Cast alloy models, (b) Fibre post models, (c) Metallic post models.
using cast post and core whose probability would increase with a reduction in post length. The partial debonding would progress to further interfacial failure between the cast post and core and the root, and after complete failure of the interface, the cast post and core may then act as a cantilever beam, which would fracture the root dentine.
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For the resin post and core with fibre post and metallic post, the equivalent stress concentration in the root appeared on the bone level of the lingual (nonloading) side, whose magnitude was higher than that of cast post and core model (Fig. 2-2), but lower than that of intact tooth model (not shown). When using resin composite material with a similar elastic
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(a)
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Figure 6 Plots of the shear stress between post and core and post interface for post length 6 mm, crown height 6 mm models. (a) Fibre post models, (b) Metallic post models.
modulus to dentine, the force applied to the crown restoration would not be stored in the post, causing the elastic deformation of the restored tooth with resin post and core. The equivalent stress concentration in the resin post and core was not recorded on the post part, but found on the lingual (nonloading side) cervical area (Fig. 3-2b, 2c). This would indicate that the force applied to the crown restoration would try to cause a bending deformation of the restored tooth, using the bone level as a supporting point, and then generate a distortion within the restored tooth above the bone level. This distortion in the upper part of the restored tooth would produce shear stress at the interface between resin post and core and cervical dentine; therefore, the magnitude of the shear stress would be influenced by crown height, not post length (Figs. 4 and 5-3b, 3c). In this study, for the resin post and core, shear stress concentrations at the interface were recorded on the cervical area, not in the post (Figs. 4 and 53b, 3c). In the restored tooth with a resin post and core, larger shear stress in the cervical area could initially compromise adhesion to the cervical area, and the debonding of cervical area might cause cohesive fracture in the resin post and core material even if maintaining adhesion to the post. A previous study demonstrated that the absence of adhesion in post preparation did not affect the fracture strengths of resin post and core reconstructions of pulpless teeth (Nakajima et al. 2010) when sufficient adhesion to the cervical area was provided. Therefore, adhesion to the cervical area would play a critical role in maintaining the integrity of the restored tooth with resin post and core methods more than the post itself.
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In the resin post and core models, the fibre post model had larger shear stress concentrations in the lingual (nonloading side) cervical interface than the metallic post model (Figs. 4 and 5-3b, 3c). Additionally, the fibre post model had larger equivalent stress at the bone level in the root than the metallic post model (Fig. 2-2b, 2c). This would mean that for the fibre post model, larger stress was applied at the bone level in the root as the supporting point for the bending deformation of the restored tooth and that the fibre post model produced larger distortion in upper part of the restored tooth than the metallic post model. This would be a reason why the stiffer metallic post could resist deformation of the restored tooth above the bone level, leading to less shear stress concentration at the cervical interface of resin post and core. However, the metallic post model produced larger shear stress at the interface between the post material and resin composite in the resin post and core compared to the fibre post model (Fig. 6). These stress concentrations at the interface could cause premature fracture of the post and core. Then, a stiffer post material in a resin post and core could maintain the bonding integrity at the cervical interface, but there would be another debonding risk between post material and resin composite, especially with a shorter post length. Recently, Ona et al. (2013) evaluated the effect of absolute bonding failure at the adhesive interfaces of post and core on stress distribution in restored root filled teeth using a nonlinear contact analysis, which can simulate friction and a potential sliding phenomenon in the nonbonded interface. They reported that absolute debonding of the adhesive interface of resin post and cores dramatically changed the stress distribution in a root filled tooth. Also, initial partial debonding at the interface of resin post and cores would change the stress distribution in the restored tooth, following further interfacial failure and/or cohesive failures in resin post and core and/or root dentine. Further research should be undertaken to assess the influence of partial debonding at the interface of the post and core on stress distribution in crown-restored root filled teeth and the fracture patterns. Although the results serve to clarify the critical elements of material selection for post and core restorations, the limitation of the method should be considered, especially if the quantitative assessment of the stresses is to be emphasized. The study design employed only one tooth configuration, loading direction and elastic property of each material. Moreover,
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because the linear elastic analysis is not a time-dependent simulation, the result of this study reveals the stress distribution before the occurrence of initial failure in the model structures. A nonlinear contact simulation would characterize the influence of initial debonding on the post and core stress in tooth models that could dramatically alter the stress distributions in the model. These pending issues should be investigated in further studies. As the scope of the present study was to estimate interfacial stress distributions with various post lengths and crown heights, the purpose of this study was accomplished using the present experimental conditions.
Conclusions For the resin post and core with fibre and metallic posts, shear stress at the interface was higher in the cervical area than in the post area, depending upon the crown height. The metallic post model produced smaller shear stress at the interface of the cervical area than the fibre post model; however, the metallic post produced larger shear stress at the interface between the post material and resin composite within the resin post and core. On the other hand, for the cast post and cores, the shear stress at the interface was mainly produced in the post, which increased with a decrease in post length.
Acknowledgements The authors gratefully acknowledge the financial support received from the Japanese Ministry of Education, Global Center of Excellence (GCOE) Program, International Research Center for Molecular Science in Tooth and Bone Diseases, Tokyo Medical and Dental University.
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© 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd
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