Effects of NaOCl, EDTA and MTAD when applied to dentine on stress distribution in post-restored roots with flared canals.

doi:10.1111/iej.12260

Effects of NaOCl, EDTA and MTAD when applied to dentine on stress distribution in post-restored roots with flared canals S. Belli1, O. Eraslan2, O. Eraslan3, M. Eskitascioglu4 & G. Eskitascioglu4 Department of Endodontics, Faculty of Dentistry, Selcuk University, Konya; 2Selcßuklu Oral and Dental Health Center, Konya; Department of Prosthodontics, Faculty of Dentistry, Selcuk University, Konya; and 4Department of Prosthodontics, Faculty of Dentistry, Yuzuncuyil University, van, Turkey 1 3

Abstract Belli S, Eraslan O, Eraslan O, Eskitascioglu M, Eskitascioglu G. Effects of NaOCl, EDTA and MTAD when applied to dentine on stress distribution in post-restored roots with flared canals. International Endodontic Journal, 47, 1123– 1132, 2014.

Aim To evaluate the effect of NaOCl, EDTA and MTAD on the stress distribution and levels in roots with flared canals and three different aesthetic post systems using finite element stress analysis (FEA). Methodology Three-dimensional (3D) FEA models simulating a maxillary incisor with excessive structural loss and flared root canals were created. The dentine of the first models of each post group was assumed as homogenous, whereas the others were deemed as having their elastic modulus affected up to 100 lm deep as a result of irrigation protocol (5.25 NaOCl, 17% EDTA and MTAD for 2 h). A sound incisor tooth model was used as the control. Restorations were created according to the post system used (pre-fabricated fibre post (PFP)), polyethylene fibre (Ribbond) post and core build-up (RBP), and one-piece milled zirconia post and core (ZP). Ceramic crowns were added to the models. A 300-N static load was applied at the centre of the palatal surface of the models to calculate the stress distributions. The SolidWorks/Cosmosworks structural analysis programmes were used for FEA analysis. Results were presented by considering von Mises criteria.

Results The analysis of the von Mises stresses revealed that RBP created less stress in the remaining root dentine when compared to PFP and ZP. ZP maintained the stresses inside its body and reduced stress on the palatal surface of the root; however, it forwarded more stress towards the apical area. NaOCl-, EDTA- and MTAD-treated dentine increased the stresses within the root structure regardless of the effect of the post system used (11–15.4 MPa for PFP, 9.5–13.02 MPa for RBP and 14.2 MPa for ZP). Amongst the irrigation solutions used, EDTA and MTAD increased the stresses more than NaOCl in all models. All the irrigation solutions showed the same stress levels and distributions in the ZP model. Conclusion NaOCl-, EDTA- and MTAD- treated dentine and a rigid post with high elastic modulus may increase fracture risk in roots with flared canals by increasing the stresses within root dentine. Therefore, solutions that alter the elastic modulus of dentine less (such as NaOCl) or an individually shaped post–core system constructed with a material that has an elastic modulus close to dentine (polyethylene fibre) should be used in weak roots. Keywords: EDTA, fibre post, finite element analysis, MTAD, NaOCl, one-piece milled zirconia post. Received 4 March 2013; accepted 3 February 2014

Introduction Correspondence: Dr. Sema Belli, Department of Endodontics, Faculty of Dentistry, Selcuk University Campus, 42079 Konya, Turkey (Tel.: +90 332 2231234; Fax: +90 332 24 10062; e-mail: [email protected]).

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

Since the introduction of fibre posts, studies have revealed that mechanical properties (Cheleux & Sharrock 2009), survival (Butz et al. 2001) and failure

International Endodontic Journal, 47, 1123–1132, 2014

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Effect of irrigation on stresses in post-restored roots Belli et al.

characteristics (Torbj€ orner et al. 1995) of these systems are acceptable. However, the use of pre-fabricated fibre posts in flared root canals is compromised because a form-congruence cannot be achieved. Use of dentine-bonded composite to increase dentine wall thickness and reduce resin cement thickness (Grandini et al. 2003), relining the fibre post with composite resin to increase the adaptation of the post to root walls (Grandini et al. 2003) or use of accessory posts (Clavijo et al. 2009), may solve this problem. The application of individually shaped dowels that are formed inside the post space may also provide a closer adaptation of the fibres against the tooth tissue (Eskitasßcio glu et al. 2002). These systems generally involve the use of woven polyethylene or glass fibre to create an endodontic post and core (Eskitasßcio glu et al. 2002). Polyethylene fibre post–core systems are reported to retain all the remaining root structure in the sound roots and therefore can be considered as appropriate materials for the restoration of the roots with thin walls (Ozcopur et al. 2010). Pre-fabricated zirconia posts have positive qualities such as high strength to bending forces and appropriate optical properties (Meyenberg et al. 1995, Rosentritt et al. 2000). On the other hand, several problems have been reported such as core delamination, bonding failures (Cohen et al. 2000, Al-Harbi & Nathanson 2003) and high modulus of elasticity (200GPa) (Fernandes & Dessai 2001). Furthermore, in wide, noncircular, or extremely tapered canals, ceramic post systems that rely on the use of a cylindrical pre-fabricated post may not achieve intimate adaptability of the post to the canal, possibly compromising retention. Streacker & Geissberger (2007) suggested using computer-aided design–computer-aided manufacturing (CAD/CAM) technology for one-piece construction of a milled ceramic post and core when a custom-fabricated post and core was necessary. Awad & Marghalani (2007) reported that this technique creates a post and core with greater toughness and maximum adaptability to the canal and appropriate aesthetic characteristics. When a post is inserted into the root canal, some occlusal forces are directed along the post length and may assist in protecting the remaining tooth structures, decreasing the von Mises equivalent stresses in dentine (Mezzomo et al. 2011). Material properties greatly influence the stress and strain distribution in a structure. The mismatch between stiffness of posts and tooth tissue may cause large stress concentration at the restorative materials/

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tooth interfaces (Genovese et al. 2005), and the interfaces of materials with different moduli of elasticity represent the weak point of a restorative system (Zarone et al. 2006). Concentrations of stress from a biomechanical perspective indicate regions of potential failure (Belli et al. 2011), and biomechanical studies are often used to predict the behaviour of dental restorations to functional forces. Mechanical behaviour of structures and stresses in dentine can be adequately analysed by means of finite elements analysis (FEA). Constructing a computer model using the geometry and physical properties of a structure is essential for FEA (Eskitasßcio glu et al. 2002, Genovese et al. 2005). These properties can be modelled in FEA as isotropic, transversely isotropic, orthotropic and anisotropic (Hsu & Chang 2010). The properties are the same in all directions; therefore, only two independent material constants of Young’s modulus and Poisson’s ratio exist in an isotropic material (Hsu & Chang 2010). Dentine has been characterized as a biological composite with a range of mechanical properties and can be described as a unidirectional array of shafts embedded inside an anisotropic matrix, each of which composed of somewhat different versions of the staggered microstructure (Bar-On & Daniel Wagner 2012). Most of the theoretical models do not consider the staggered microstructure of dentine therefore in most reported studies, and an assumption was made that dentine was homogenous and linearly isotropic (Eskitasßcio glu et al. 2002, Belli et al. 2011, Mezzomo et al. 2011). The modulus of elasticity of dentine was reported as 11–20 GPa (Kinney et al. 2003); however, in clinical conditions, the elastic modulus of inner dentine may change due to the irrigation regimen (Marending et al. 2007). Alterations in mechanical properties of tooth tissue not only change the stress patterns, but also the strength of structure load bearing (Khani et al. 2009). Tang et al. (2010) included the irrigation of the root canal into the list of risks that increased the potential of tooth fracture after endodontic treatment. Sodium hypochlorite (NaOCl), one of the most widely used root canal irrigant, reduced the elastic modulus and flexural strength of dentine after a 2-h exposure (Sim et al. (2001). Machnick et al. (2003) reported that both MTAD, an irrigation solution containing a mixture of a tetracycline isomer, an acid and a detergent (Torabinejad et al. 2003a), and 17% ethylenediaminetetraacetic acid (EDTA) reduced the elastic modulus of dentine after 2 h.


Belli et al. Effect of irrigation on stresses in post-restored roots

The change in elastic modulus of dentine is clinically relevant as a reduced flexural strength and modulus of elasticity may contribute to the weakening of root filled teeth (Sim et al. 2001). Thus, the aim of this FEA study was to evaluate the effect of NaOCl, EDTA and MTAD application on dentine on stress distribution in roots with flared canals that were restored using three different aesthetic post systems. The null hypothesis was that the alterations occur at the inner dentine surface due to the irrigation regimen would not affect the stress values or distribution in roots with flared canals, which were restored using three different aesthetic post–core systems.

Materials and methods A three-dimensional FEA method and SolidWorks 2009 structural analysis program (SolidWorks Corp., Concord, MA, USA) was used. A three-dimensional finite element model of maxillary central incisor was developed. Dimensions of the various dental tissues were allocated based on the anatomical data described by Wheeler (2003). The components included were e: enamel, d: dentine, c: cementum and p: pulp. Three more models were then created simulating root filled maxillary central incisor roots with flared root canals, which were restored using three different post-restorative materials and techniques (pre-fabricated fibre post (PFP); polyethylene fibre post and core build-up (RBP) (Ribbond, Ribbond Inc., Seattle, WA, USA) and one-piece milled zirconia post and core (ZP)). The models included r: resin cement, rc: resin core (rc) (Biscore; Bisco, Vancouver, BC, Canada), d: dentine, g: gutta-percha, Cr: e-max ceramic crown (IPS e.max Press; Ivoclar Vivadent AG, Schaan, Liechtenstein), PFP, RBP and ZP (Fig. 1). Materials used in the study were assumed as homogenous and isotropic except the dentine and pre-fabricated glass fibre post. The glass fibre post was considered as orthotropic and made of long fibres (glass fibre) embedded into a polymeric matrix so that it showed different mechanical properties along the fibre direction (x direction) and along the other two directions (y and z direction; Lanza et al. 2005) (Table 1). For stress analysis, the required elastic properties included Young’s modulus of elasticity, and Poisson’s ratio of the structures is shown in Table 2. The dentine of the first models for each post group was assumed as homogenous, whereas the others were deemed as having their elastic modulus affected up to 100 lm deep (Zou et al. 2010) as a result of


Figure 1 FEA mathematical model simulating a maxillary central incisor. Pink arrows represent the loading area, and the green arrows show the nodes on the outer surface of roots that were assumed as fixed.

Table 1 Mechanical properties of orthotrophic materials. Ex, Ey and Ez represent the elastic moduli along the three directions; NUxy, NUxz, NUyz and Gxy, Gxz, Gyz are, respectively, the Poisson’s ratios and the shear moduli in the orthogonal planes (xy, xz and yz) (Lanza et al. 2005) Property

Glass Post

Ex (GPa) Ey (GPa) Ez (GPa) NUxy NUxz NUyz Gxy Gxz Gyz

37 9.5 9.5 0.27 0.34 0.27 3.10 3.50 3.10

5.25% NaOCl, 17% EDTA and MTAD application treatment (Machnick et al. 2003). The mathematical models included 369 883 nodes and 235 788 tetrahedral solid elements. An occlusal force of 300 N was applied to an area over the cingulum on the palatal surface of the crowns of the models at a 135 angle to the long axis of the tooth (Fig. 2). Nodes at the outer surface of roots were assumed as fixed in all directions to calculate the stress distribution. To simulate adhesion between the structures, all interfaces were considered as completely bonded. The final element on the x-, y- and z-axis for each model was assumed to be fixed for


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Table 2 Mechanical properties of isotrophic structures or materials were acquired from the literature or directly from the manufacturers

Material Dentinea NaOCl-treated dentineb EDTA-treated dentineb MTAD-treated dentineb Resin corec Gutta-perchad IPS e.max corec IPS e.max veneerc Resin cementc Zirconiae Polyethylene fibre post–core

a

Elastic Modulus (E) (GPa)

Poisson’s Ratio (ц)

18.6 9.605 4.437 3.350 12 0.074–0.079 95 65 8 200 23.6

0.31 0.31 0.31 0.31 0.30 0.45 0.24 0.24 0.3 0.33 0.32

lu et al. 2002. Eskitasßciog Machnick et al. 2003. c Manufacturer. d Tay & Pashley 2007. e Christel et al. 1989. a

b

stresses is known as von Mises stresses (Ricks-Williamson et al. 1995). The qualitative stress distribution analyses were recorded in this study using von Mises criteria. A standard view of a mid-saggital section from each model was provided, and the stress distribution scale range was limited to 0–4 MPa. Calculated numeric data were transformed into colour images. As the stress values at the crown structures were very high, the crowns were omitted in the coloured images to better visualize the stress distribution at the remaining dentine structure and the core material.

Results A convenient way of reporting the stress is in the form of colour representation of the stress distributions. A few examples are shown in Figure 3 through 6. The von Mises stresses, which were estimated using the model for each point, are represented using a colour scale. Blue to red colours represent stress values from lower to higher, respectively. The analysis of the von Mises stresses revealed that RBP created less stress at the remaining root dentine when compared to PFP and ZP (Table 3). It is clear that ZP kept the stress inside its body and

Figure 2 Models simulating root filled maxillary central incisor with excessive coronal structure loss and flared root canals, which were restored using three different post-restorative materials and techniques: a: pre-fabricated fibre post (PFP); b: polyethylene fibre (RBP) (Ribbond, Ribbond Inc., Seattle, WA, USA) post and core build-up and c: one-piece milled zirconia post and core (ZP) (r: resin cement; rc: resin core (rc); d: dentine; g: gutta-percha; Cr: e.max ceramic crown).

boundary conditions. The FE modelling was accomplished with the SolidWorks software program, and analyses were run with the CosmosWorks software program that is integrated with SolidWorks. To identify areas of strain and stress concentration where possible failures are more expected to occur, the choice of the pertinent stress representation criterion was based on the evaluation of failure predictive potential of the analysis performed (Sorrentino et al. 2007). The global (x, y and z directional axes) combination of the absolute values squared of all

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Figure 3 Von Mises stress distributions calculated in corresponding finite element control models. Blue to red colours represent stress values from low to high, respectively. PFP and RBP showed almost similar stress distribution although the stress values were different (7.01MPa-8.52MPa, respectively). ZP kept the stress inside its body (black arrow), forwarded less stress towards the palatal surface of the root when compared to RBP and PFP models. Note the increased stress levels at apical side of the post showing that the rigid post forwarded the stress towards the apical region (black circle).



Table 3 Stress values (MPa) found in the models

Pre-fabricated fibre post (PFP)

Crown Resin core Post Dentine Resin cement Gutta

Polyethylene fibre (Ribbond) post and core build-up (RBP)

One-piece milled zirconia post and core (ZP)

NaOCl

EDTA

MTAD

Control

NaOCl

EDTA

MTAD

Control

NaOCl

EDTA

MTAD

Control

16.04 4.10 2.49 11.00 – 1.96

16.04 4.07 2.50 15.40 – 1.94

16.04 4.04 2.50 15.40 – 1.92

16.04 4.10 2.47 8.52 – 1.95

16.67 – 7.01 9.50 – 2.83

16.67 – 7.09 13.01 – 2.79

16.68 – 7.14 13.02 – 2.76

16.67 – 7.15 7.01 – 2.82

19.57 – 25.92 14.22 20.33 7.14

19.57 – 26.01 14.20 20.09 7.00

19.57 – 26.05 14.22 19.94 6.92

19.57 – 25.84 11.40 20.39 7.18

reduced stress on palatal surfaces of the root; however, it forwarded more stress towards the apical area (Fig. 3). NaOCl-, EDTA- and MTAD-treated dentine caused high stress levels and distributions inside the root structure regardless of the effect of the post system used (11.0–15.4 MPa for PFP, 9.5–13 MPa for RBP and 14.2 MPa for ZP). This increase was clearly observed in the palatal middle third of the roots in all the finite models (Figs 4–6). Amongst the irrigation solutions used, EDTA and MTAD increased the stresses more at the buccal cervical region in PFP and RBP post models (Fig. 4) whilst NaOCl increased stress levels at the palatal cervical region of the NaOCl model in the RBP group. All the irrigation solutions caused similar stress levels and distributions in the ZP model (Fig. 6).

Figure 5 Stress distribution in the polyethylene fibre post– core build-up (RBP) restored root models when the dentine was assumed to be exposed to NaOCl, EDTA and MTAD. High stress levels are observed at palatal middle third of the roots in NaOCl, EDTA and MTAD models when compared to the control model (red arrows); however, the localization of the stress is smaller in NaOCl model. Control and NaOCl models showed almost similar stress distribution in other parts of the tooth. EDTA and MTAD models showed high stress levels at buccal cervical region of the core structure. Green arrows show the point where the maximum stresses were occurred in EDTA and MTAD models.

Discussion

Figure 4 Stress distribution in the pre-fabricated fibre post (PFP) restored root models when the dentine was assumed to be treated with NaOCl, EDTA and MTAD. Irrigation regimens increased the stresses at core structures and especially inside the middle third palatal side of the roots (red arrows). NaOCl increased the stress levels at palatal cervical region of the crown (yellow arrow) whilst EDTA and MTAD models showed high stress levels at buccal cervical region of the crowns (green arrows).


In this FEA study, the effect of root dentine affected by 5.25% NaOCl, 17% EDTA and MTAD irrigation on stress distribution in roots with flared canals that were restored using three different aesthetic post systems was evaluated. The global combination of the absolute values squared of all stresses, which are known as von Mises criterion (Okamoto et al. 2008, Belli et al. 2011), was used to indicate the bounds for principal stress. Three-dimensional modelling was used as two-dimensional modelling may neglect several important details (Toparli et al. 1999). The results indicated that 5.25% NaOCl-, 17% EDTA- and MTAD-treated dentine increased the stresses inside the root structure


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Figure 6 Stress distribution in the one-piece milled zirconia post and core (ZP) restored root models when the dentine was assumed to be treated with NaOCl, EDTA and MTAD. All the tested irrigation solutions changed the stress patterns inside the tooth model when compared to the control model, and this change is similar to each other. NaOCl-, EDTA- and MTAD-treated dentine reduced the stresses inside the ZP post (control model, red arrow), however, forwarded more stress towards the root dentine (yellow arrows). High stress values are also observed at the buccal cervical region of the crown and at the apical side of the post in NaOCL, EDTA and MTAD models (black circles).

regardless of the effect of post system used. Thus, the null hypothesis that alterations within the inner dentine surface due to irrigation regimens would not affect the stress values or distribution in weakened roots, which were restored using three different aesthetic post–core systems, was rejected. Loss of tooth tissue, altered physical properties of dentine and altered proprioception/nociception are listed as the main factors that interact cumulatively to influence tooth loading and distribution of stresses (Gulabivala 1995). Intracanal irrigants, medicaments and materials play a part in influencing the physical and mechanical properties of dentine (Sim et al. 2001). NaOCl irrigation promotes a deleterious effect on collagen and proteoglycans, reducing the mechanical resistance of dentine (Lee et al. 2004). In a study by Sim et al. (2001), the effect of different concentrations of NaOCl was evaluated by the application of the four-point flexural test, and the results revealed a negative effect on the properties of dentine only at high concentrations by reducing its flexural strength, thus indicating that far less force is required for cohesive bonds to fail. In this study, confirming the results of previous studies, 5.25% NaOCl increased the stress distribution inside the root structure regardless of the effect of the post system used when compared to the control model.

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The recommended concentration of sodium hypochlorite ranges from 0.5% to 5.25% (Baumgartner & Cuenin 1992); however, Sim et al. (2001) showed that a 5.25% concentration had a negative effect on the properties of dentine. The flexural strength and elastic modulus of dentine were reduced, and this effect was noticeable in a ‘whole’ tooth (without enamel) as increased strain under standard cyclic nondestructive loading. Similarly, Machnick et al. (2003) reported that NaOCl significantly lowered the flexural strength and modulus of elasticity of dentine bars after a 2-h exposure. However, Moorer & Wesselink (1982) did not report a greater effect on the mechanical properties of dentine with higher concentration of NaOCl (5.25%) than lower concentration (2.6%). In the present study, an aggressive regimen (5.25%) was selected in order that the effect was guaranteed, and the dentine was considered as treated for 2 h to simulate ‘maximum exposure time’ a tooth would be exposed to an irrigant for multivisit root canal treatment (Machnick et al. 2003). The elastic modulus of dentine was reported as 9.34, 8.79 and 9.61 when affected with 1.3%, 2.6% and 5.25% NaOCl, respectively (Machnick et al. 2003); thus, the results of this FEA study would not change if the root dentine was assumed to be exposed to different concentrations of NaOCl. MTAD has similar solubilizing effects on pulp and dentine to those of EDTA (Torabinejad et al. 2003b, Zhang et al. 2003) and significantly more effective than 5.25% NaOCl in eradicating bacteria from the infected root canals (Torabinejad et al. 2003c). The results of present study indicated that both MTAD and 17% EDTA changed the stress dynamics within root dentine. Machnick et al. (2003) reported that 2-h exposure with 30 mL MTAD significantly reduced the flexural strength and modulus of elasticity of dentine bars; however, this decrease was less than that with 17% EDTA-treated bars. When MTAD is used as recommended (20 min 1.3% NaOCl/5 min MTAD, Torabinejad et al. 2003a,b,c), it does not have an adverse effect on flexural strength and modulus of elasticity of dentine (Machnick et al. 2003). In the present study, the MTAD clinical protocol was not simulated. If the clinical protocol was simulated (elastic modulus: 9.15GPa), the stress patterns would be the same as the 5.25% NaOCl group. Based on these findings, it can be speculated that using the clinical protocol for MTAD, the stresses at the remaining root structure can be reduced. During and after root canal instrumentation, it is necessary to remove the organic and inorganic



remnants together by the use of chelating agents (EDTA), followed by NaOCl (Baumgartner & Mader 1987). EDTA chelates with Ca2+ and other divalent cations, demineralizes dentine and leads to tubular erosion if used extensively (Calt & Serper 2002, Sayin et al. 2007). In this study, the inner dentine surface was assumed to be exposed to 17% EDTA for 2 h. Confirming previous studies that report the effect of EDTA on structural alterations in human dentine, EDTA treatment increased the stresses in remaining root dentine (Table 3). When the stress distribution and stress levels in NaOCl, EDTA and MTAD models were compared, it was observed that the effect of NaOCl-affected dentine on stress distribution was lower than the others except the models that include ZP post. This result can be explained by the reduced effect of NaOCl on the elastic modulus of root dentine (Table 2). On the other hand, NaOCl, EDTA and MTAD models showed similar stress accumulation when compared to the control model in the ZP group. Zirconia has an elastic modulus of 200GPa. High rigidity of the post material might have made the differences between the elasticity of root dentine structure in NaOCl, EDTA and MTAD models insignificant. The other important result of this study was that polyethylene fibre post–core build-up restoration (RBP) created the least stress in the remaining root dentine when compared to the others (Fig. 3). The fracture strength of root filled, thin-walled teeth is affected by the remaining dentine thickness (Kivancß et al. 2009). Newman et al. (2003) compared the fracture resistance of pre-fabricated posts and polyethylene fibre post core both in narrow and flared canals and concluded that RBP was less fracture resistant than the others. The application of individually shaped dowels that are formed inside the post space provides a closer adaptation of the fibres against the tooth substrate and a better stress transfer (Karbhari & Wang 2007). There is no consensus on the superiority of fibrereinforced aesthetic posts when compared with metallic rigid posts. The advantages of RBP in terms of stress distribution when compared to a rigid post have been reported previously (Eskitasßcio glu et al. 2002). Use of zirconia posts has been questioned because of its high modulus of elasticity (200 GPa), which could result in catastrophic failures of roots (Bittner et al. 2010). One-piece zirconia posts provided a post and core with greater toughness, maximal adaptability to the canal and adequate aesthetics (Fernandes &


Dessai 2001). Furthermore, this system avoids potential core delamination by eliminating interfaces between the post and core (Bittner et al. 2010). However, with rigid systems, fractures commonly occur in the apical half of the root (Assif & Gorfil 1994). Although an opposite finding was reported by Bittner et al. (2010), the model of the one-piece milled zirconia post showed that ZP kept the stress inside its body and reduced stress on the palatal surface of the root; however, it forwarded more stress towards the apical area and increased the risk of catastrophic failure as previously reported by Eskitasßcıo glu et al. (2002). The results also indicated that dentine that was affected by irrigation solutions reduced the stresses inside the zirconia post material; on the other hand, it increased the stresses in the apical and on the palatal side of the root dentine and at cervical-buccal side of the core material (Fig. 6). One of the limitations of FEA studies is that when creating models, the structures are generally assumed to be homogeneous and isotropic (Belli et al. 2011). In most of these studies, dentine has been modelled as a homogeneous/isotropic material (Eskitasßcio glu et al. 2002, Borcic et al. 2005), thus the effects of dentinal tubules, intrapulpal hydrostatic pressure and the elastic modulus gradient on the mechanical properties of dentine are ignored (Kishen & Vedantam 2007). In the present study, the elastic modulus of dentine in the control model was considered as 18.6 GPa (Eskitasßcio glu et al. 2002, Belli et al. 2011). On the other hand, an additional layer has been created in the models to simulate the effects of the irrigation regimen. The rapid invasion of bacteria into the tubules is well known (Haapasalo & Orstavik 1987, Ando & Hoshino 1990); therefore, the depths the irrigants can penetrate into tubules are an important factor. Longer exposure time results in deeper penetration of NaOCl (Zou et al. 2010). Kuga et al. (2011) reported the penetration depth of 2.5% NaOCl as between 94 and 120 lm, whilst according to Zou et al. (2010) the depth was 77 lm for 1% NaOCl when used for 2 min. and 300 lm for 6% NaOCl when used for 20 min. In this study, whilst modelling the irrigation solution affected dentine, the penetration depth was considered as 100 lm. Kuga et al. (2011) reported that association with acid solutions did not promote an increase in dentine penetration by NaOCl; therefore, the irrigation solutions were used separately. When a structure is subjected to a load, stress is induced in the structure, which may lead to deformation of the latter. These stresses may occur as tensile,


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compressive, shear or a stress combination. The stresses generated within a structure can be accurately analysed by evaluating the stress concentration areas by means of FEA. FEA allows detailed visualization of the distribution of stresses. The von Mises failure criterion that demonstrates the energy transmission in the structure (Verıssimo et al. 2013) was used in this study to indicate the bounds for principal stress. Von Mises stress is a comprehensive stress of each point in material and is widely used as an indicator of the possibility of damage occurrence (Pegoretti et al. 2002, Okamoto et al. 2008, Belli et al. 2011). Dentine is brittle, and its compressive strength is 5–6 times higher than its tensile strength. Therefore, the von Mises stress criterion was chosen to assess the risk of tooth fracture after the residual root was restored with a post and core. This criterion has already been shown to successfully indicate stress distribution in post-restored roots with flared canals (Belli et al. 2013). It is difficult to extrapolate the results of this FEA study directly to a clinical situation. The limitations of FEA studies such as the several assumptions made regarding the simulated structures (Borcic et al. 2005, Kishen & Vedantam 2007, Belli et al. 2011) are well known. Clinical experience indicates that most fractures occur after several years, and generally, such failures are unrelated to episodes of acute overload, but result from fatigue failure (Chen et al. 1999). The absence of dynamic loading is another limitation of this study. Besides these limitations, FEA studies provide clinicians with a prediction of the success of a restoration from a biomechanical perspective, and it has been shown to be a useful tool when investigating complex systems (Chen et al. 1999, Asmussen et al. 2005).

Conclusions Within the limitations of this FEA study, the following conclusions were drawn: ● NaOCl, EDTA and MTAD increased the fracture risk in roots with flared canals by increasing the stresses within the root dentine regardless of the effect of the post system used. ● Considering the reduced effect on the elasticity of root dentine, NaOCl is preferred as the irrigation solution before constructing a post-restoration to reduce stresses. ● Polyethylene fibre posts retain the remaining root structure by reducing stresses, whilst one-piece milled zirconia posts may cause catastrophic failure

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by forwarding the stresses towards the apical region in roots with flared canals.

Acknowledgements This study was performed in the Research Center of the Dental Faculty, Selcuk University and supported in part by Scientific Research Projects Coordination Center (BAP) of Selcuk University, Konya, Turkey.

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