The effect of ferrule height on stress distribution within a tooth restored with fibre posts and ceramic crown: a finite element analysis.

DENTAL-2446; No. of Pages 12

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The effect of ferrule height on stress distribution within a tooth restored with fibre posts and ceramic crown: A finite element analysis Jelena Juloski a,b,∗ , Davide Apicella a,c , Marco Ferrari a a

Department of Medical Biotechnologies, University of Siena, Policlinico Le Scotte, Viale Bracci, 53100 Siena, Italy Clinic for Pediatric and Preventive Dentistry, School of Dentistry, University of Belgrade, Doktora Subotica 11, 11000 Belgrade, Serbia c Department of Oral and Maxillofacial Sciences, University “Federico II”, Policlinico Via Pansini, 5, 80131 Naples, Italy b

a r t i c l e

i n f o

a b s t r a c t

Article history:

Objectives. To evaluate via finite element analysis the effect of different ferrule heights

Received 6 October 2013

on stress distribution within each part of a maxillary first premolar (MFP) restored with

Received in revised form

adhesively luted glass fiber-reinforced resin (GFRR) posts and a ceramic crown.

16 March 2014

Methods. The solid models consisted of MFP, periodontal ligament and the corresponding

Accepted 18 September 2014

alveolar bone process. Four models were created representing different degrees of coronal

Available online xxx

tissue loss (0 mm, 1 mm, 2 mm and 3 mm of ferrule height). First set of computing runs was performed for in vivo FE-model validation purposes. In the second part, a 200-N force was

Keywords:

applied on the buccal cusp directed at 45◦ to the longitudinal axis of the tooth. Principal

Adhesion

stresses values and distribution were recorded within root, abutment, posts, crown and

Endodontically treated teeth

related adhesive interfaces.

FEA

Results. All FE-models showed similar stress distribution within roots, with highest stress

Ferrule effect

present in the chamfer area. In composite abutments higher stress was observed when

Fiber post

no ferrule was present compared to ferruled FE-models. Stress distribution within crown

Stress distribution

and GFRR posts did not differ among the models. Stress values at the adhesive interfaces decreased with increasing ferrule height. Significance. The stress state at abutment-crown and post-root interfaces was very close to their strength, when ferrule was not present. Similarly, higher ferrule produced more favorable stress distribution at post-abutment and abutment-root interfaces. Endodontically treated teeth with higher ferrule exhibit lower stress at adhesive interfaces that may be expected to lower the probability of clinical failure. © 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

∗ Corresponding author at: Department of Medical Biotechnologies, University of Siena, Policlinico Le Scotte, Viale Bracci, 53100 Siena, Italy. Tel.: +39 0577233131; fax: +39 0577233117. E-mail address: [email protected] (J. Juloski).

http://dx.doi.org/10.1016/j.dental.2014.09.004 0109-5641/© 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: Juloski J, et al. The effect of ferrule height on stress distribution within a tooth restored with fibre posts and ceramic crown: A finite element analysis. Dent Mater (2014), http://dx.doi.org/10.1016/j.dental.2014.09.004


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1.

Introduction

Endodontically treated teeth are generally considered weaker and more susceptible to fracture than vital teeth [1,2]. The main change in the biomechanical behavior is attributed to the considerable loss of tooth structure [1]. Preservation of sound radicular and coronal tooth tissue and especially presence of ferrule are important factors for enhancing the performance of structurally compromised endodontically treated teeth [3,4]. Ferrule is provided by parallel walls of dentin extending coronal to the shoulder of the preparation [5], which after being encircled by a crown produces a protective effect, called ferrule effect, by reducing stresses within a tooth [4]. This topic has been studied over the past years and still represents an interesting field of research. Most of the laboratory studies agree on the beneficial effect of ferrule on the fracture resistance of compromised teeth [6–8]. In addition, the presence of ferrule could reduce the incidence of non-restorable root fractures [9,10]. Regarding the height of ferrule that is necessary to provide the protective effect, various results were reported. While 1-mm was found enough to significantly increase the number of fatigue cycles prior to failure [8], no difference in fracture resistance between teeth with 1-mm ferrule and those with no ferrule was found [10,11]. Additionally, during chewing simulation teeth with 1-mm ferrule exhibited worse performance compared with 2-mm high dentin walls [12]. The minimum heights of ferrule required to significantly improve fracture resistance were 2 mm [11] and 3 mm [10]. Existing clinical trials could not confirm that ferrule was a factor that significantly influenced the survival of endodontically treated teeth [13–15]. When all coronal walls were missing, similar failure risk was found in teeth with complete absence of ferrule and those with 2 mm ferrule [14,15]. Nevertheless, when adequate 2-mm ferrule was included in the preparation design successful treatment outcome was recorded over 2- [16] and 7 year [17] observation period, irrespective of the post type. The impact of ferrule on stress distribution within the restored tooth under stress has been assessed by several finite element analysis (FEA) studies [12,18–20]. It was proved that cervical region of the tooth is indeed exposed to the highest stress [20] and that presence of ferrule reduced the stress level [18,20]. Analyzing von Mises stresses within the central incisor with 0-mm, 1-mm and 2-mm ferrule it was observed that stress decreased with increased ferrule height, regardless of the post material [18]. However, the differences in stress values were small [18]. Another study, investigating metal cast post-and-core restored tooth, suggested that ferrule height should be determined individually based on the bucco-lingual cervical diameter of the root [19]. Therefore, the aim of this study was to evaluate via finite element analysis the effect of different ferrule heights on stress distribution within each part of a maxillary first premolar (MFP) restored with adhesively luted glass fiber-reinforced resin (GFRR) posts and a ceramic crown. The null hypothesis was that different ferrule heights do not affect the stress distribution within the tooth.

2.

Materials and methods

2.1.

Finite elements models generation

The solid models consisted of a maxillary first premolar (MFP), the periodontal ligament (PDL) and the corresponding alveolar bone process. The average anatomical dimensions of the alveolar bone and periodontal ligament (PDL) were generated according to the literature data [21]. The external shape of the premolar was obtained by laser-based 3D digitizing (Cyberware, Inc., Monterey, California, USA) of a plaster cast (Thanaka manufacturer, Japan). The scanned profiles were assembled in a 3D wire frame structure using a 3D CAD (Autocad 12, Autodesk Inc.) and exported into a 3D parametric solid modeler (Pro-Engineering 16.0 Parametric Technologies, USA). Arrangement of dentin and enamel internal volumes and morphologies were modeled according to literature data [22]. The solid models of premolar and surrounding alveolar bone are presented in Fig. 1a. The 3D parametric solid modeler software was used to generate four solid-models representing different degrees of coronal tissue loss. The solid-models were represented in a consistent manner, with the ferrule height as the unique geometry variable. Solid-model 0 simulated a premolar restored with a crown in absence of dentin ferrule. Solidmodels 1, 2 and 3 simulated teeth with ferrule heights of 1 mm, 2 mm and 3 mm, respectively. Roots of solid-models 0, 1, 2 and 3 are presented in Fig. 1b. Buccal and palatal glass fiber-reinforced resin (GFRR) post space preparations were modeled in the root canals. GFRR posts had the following dimensions: length 12 mm, coronal diameter 1.5 mm, apical diameter 1.2 mm. Part of the post that was inserted within the root was 9 mm of length, while the remaining 3 mm were incorporated within the abutment. An abutment was modeled according to the dimensions of the MFP prepared for the full crown coverage. The ceramic crown was modeled to fit the abutment. The four solid-models were imported to the Finite Elements Analysis (FEA) software ANSYS rel. 9.0 (Ansys Inc. Houston). The solid-models were meshed with eight nodes brick with 3 degrees of freedom per node, the crown structure was meshed with 4 nodes tetrahedral elements, finally resulting in four 3D FE models made up of 31,240 elements and 35,841 nodes (Fig. 2a). Accuracy of the model was checked by convergence tests [22]. Cement and adhesive interfaces were simulated by layers of solid brick elements: abutment-root and the abutment-post interfaces, average thickness of 10 ␮m [23]; root-post interface, average thickness of 50 ␮m [24]; abutmentcrown interface, average thickness of 50 ␮m [24] (Fig. 2b). Enamel and spongy bone were considered as isotropic linear elastic materials [25]. Cortical bone was considered as an orthotropic elastic material according to the mechanical characterization reported by Schwartz-Dabney and Dechow [26]. Dentin was considered as an orthotropic linear material [27]. Although the elastic moduli of the dentin are similar along its plane of symmetry, it could be safely considered as an isotropic material without a significant influence on the outcome. Management of cortical bone and dentin orthotropicity was previously described by Aversa et al. [28]. Crowns




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Fig. 1 – (a) Schematic representation of a basic model used in the study and (b) schematic representation of the roots of solid models 0, 1, 2 and 3. No ferrule and ferrule of 1, 2 and 3 mm in height was reproduced respectively in solid models 0, 1, 2 and 3.

Fig. 2 – (a) Exploded view of the FEM components of FE-model 0 and (b) detail of adhesive and cement interface solid elements: abutment-root adhesive interface (thickness: 10 ␮m), post-roots and post-abutment cement interface (thickness: 50 ␮m), abutment-crown cement interface (thickness: 50 ␮m). Please cite this article in press as: Juloski J, et al. The effect of ferrule height on stress distribution within a tooth restored with fibre posts and ceramic crown: A finite element analysis. Dent Mater (2014), http://dx.doi.org/10.1016/j.dental.2014.09.004

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d e n t a l m a t e r i a l s x x x ( 2 0 1 4 ) xxx–xxx

Table 1 – Orthotropic and isotropic mechanical properties of the materials coupled to the Finite Elements Models. Young’s modulus (E, expressed in GPa), Shear modulus (G, expressed in GPa) and Poisson’s ratios (␯). Material Cortical bone on facial side Cortical bone on buccal side Dentin Glass fibers reinforced resin post Enamel Cancellous bone Resin cement/Core build-up (Gradia core, GC Corp.) Adhesive material Glass-ionomer cement (GC Fuji PLUS, GC Corp.) Zirconia

Direction of maximum stiffness ◦

E1

E2

E3

G12

G31

G23

␯12

␯31

14.8 17.7

18.3 19.5 23.2 9.5

4.5 4.9 8.6 0.27

4.7 4.9

5.7 5.1 9.4 0.27

0.21 0.16 0.45 3.1

0.25 0.31 0.29 3.5

39.9 with respect to the occlusal plane 4.4◦ with respect to the occlusal plane Normal to dentin tubules Parallel to glass fibers

11.2 12.1 25 37

Isotropic Isotropic Isotropic

84.1 0.91 13

0.33 0.30 0.22

Isotropic Isotropic

1 5.1

0.24 0.27

Isotropic

elements were coupled to the isotropic mechanical properties (IMP) of zirconia. Abutment elements were coupled to the IMP of a dental composite material (Gradia Core, GC Corp. Tokyo, Japan). Post elements were considered as elastic orthotropic material and coupled to the mechanical properties of unidirectional GFRR. Abutment-root and abutment-posts interfaces volumetric elements were coupled to the IMP of a dental adhesive material [23]. Root-post interface elements were coupled to the IMP of a composite cement (Gradia Core, GC Corp. Tokyo, Japan). Abutment-crown interface elements were coupled to the IMP of a glass-ionomer cement (GC Fuji PLUS, GC Corp. Tokyo, Japan). The mechanical properties of the tissues and the materials simulated in the present study (Young’s modulus [E], shear modulus [G] and Poisson’s ratio [␯]) are reported in Table 1. PDL was considered a non-linear vischo-hyper-elastic material [29,30]. The method used to account for the strain-rate dependency of stress required the definition of five visco-elastic materials models based on five different stress–strain curves performed at different straining rates [30]. In the present study, “elastic modulus vs. time” curve was evaluated for each stress–strain curve. Then, data were uploaded in the FEA software. A macro was set up in order to enable a time dependent analysis that computed the strain rate of a given element at each sub-step time. The strain value and the corresponding strain rate were interpolated between the “nearest” visco-elastic material FE-models table to evaluate the corresponding stress value. The full explanation of the method, as well as the adopted phenomenological data (stress–strain curves images), has been previously described by the Authors [28]. PDL stiffness in the direction normal to fibers’ main axis depending by PDL shear modulus (G) was evaluated through the procedure reported by Maceri et al. [31].

2.2. FE-model validation, boundary conditions and applied loads A healthy volunteer with healthy conditions of MFP tissues, MFP periodontal tissues and MFP dimensions comparable with those of the MFP FE-model was selected for the in vivo FEmodel validation. The involvement of a human subject in the study received the ethical approval by an Institutional Review Board (IRB) of the University of Siena (ClinicalTrials.gov number CT01532947). The rights of the enrolled participants have

205

9.5

0.34

␯23 0.42 0.53 3.1

0.30

been protected by the IRB of the University of Siena, Italy, and written informed consent was provided by the participant. A linear strain-gauge self-compensated in temperature (C-980204, Micro-oup, Inc. Raleigh, North Carolina, USA) was bonded (Histoacryl, Braun, Italy) on the buccal aspect of the MFP (Fig. 3a). Strain-gauge was connected to a digital strain measuring hardware (Omicron-T, Battipaglia, Italy) interfaced to a personal computer equipped with a software providing data visualization and storage. The strain state was recorded as a function of time. During the experiments, the MFP was subjected to five loading tests. A force of 5 N was applied 45◦ with respect to the MFP main axis, in a palatal to buccal versus on the palatal aspect of the buccal cusp by a linear dynamometer (MD1000, Pesola, Italy). The force was kept constant for 10 s. The strain state was reported as the mean of 5 loading tests. A preliminary FEA test showed that 3rd principal strain prevailed on the buccal aspect of the MFP and 3rd principal strain direction was parallel to MFP main axis. Accordingly, the strain-gauge was bonded with its main-axis parallel to the MFP. The straingauge signals were recorded in the compressive modalities.

The FE-models were constrained along the x, y and z axis at the top surface of the maxillary bone. First set of computing runs was performed for model validation purposes: • horizontal load applied on the buccal cusp and directed at 90◦ to the longitudinal axis of the MFP in palatal to buccal versus. The horizontal load was gradually increased up to 10 N within an overall interval of 75 s (Fig. 4a). The displacement in the direction of the load was computed and compared to literature experimental data [32,33] (Fig. 4b); • intrusive load applied on the buccal cusp and directed at 0◦ to the longitudinal axis of the MFP. The intrusive load was gradually increased up to 20 N within an overall interval of 75 s (Fig. 4a). The displacement in the direction of the load was computed and compared to literature experimental data [34,35] (Fig. 4c); • oblique load applied on the buccal cusp and directed at 45◦ to the longitudinal axis of the MFP in palatal to buccal versus. The oblique load was gradually increased up to 5 N within a time interval of 75 s (Fig. 4a). Crown 3rd




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Fig. 3 – In vivo experiment compared to FEA test. (a) Strain-gauge bonded on the buccal aspect of a premolar crown; (b) compressive strain values and distribution on the buccal aspect of the premolar FE-models; (c) superimposition of FEA results to the image of the strain-gauges in the in vivo experiment; (d) FEA estimated strain interval and in vivo measured strain values.

principal strain state was computed and compared to in vivo measured strain (Fig. 3b–d). Second set of computing runs was performed to simulate a characteristic MFP loading condition. The models were loaded with a 200 N force applied on the buccal cusp and directed at 45◦ to the longitudinal axis of the tooth in coronal-apical and palatal-buccal directions (Fig. 4a).

2.3.

Presentation of the results

Principals stress analysis was adopted to visualize the computed stress state. Calculated numerical data were transformed into color graphics to visualize mechanical phenomena in the FE models. Principal stresses values and distribution are presented in the following structures: root, abutment, GFRR post, crown, cement layer at the postroot and the post-abutment interface, cement layer between the abutment and the crown, adhesive layer between the abutment and the root or the out-core abutment and the ferrule.

3.

Results

Fig. 3b and c show the 3rd principal strain state on the buccal aspect of the MFP. In the middle area of the buccal aspect of the crown strains ranged from −0.000009 to −0.000015 ␧. In vivo strain state ranged from −0.00001 to −0.000012 ␧. The

computed strain range and strains measured in vivo in the same area are reported in Fig. 3d. The values and the distribution of tensile and compressive stresses within the structures investigated in the present study are presented in Figs. 5 and 6. The color code is indicated in each figure.

3.1.

Stress distribution within the root and the ferrule

Fig. 5a shows the first principal stress – tensile stress – values and distribution in the roots of Model 0, roots and ferrule of FE-models 1, 2 and 3. Tensile stresses prevailed on the palatal side of the roots in all analyzed models. Stress state ranged from 5 to 35 MPa. Peak stresses of 45 and 85 MPa were estimated on the palatal aspect of the apical third of the vestibular and palatal roots respectively. Compressive stresses were estimated on the vestibular aspects of the roots and ranged from −15 to −75 MPa. Peak stresses of −85 and −65 MPa were estimated on the vestibular aspect of the apical third of vestibular and palatal roots and on the crown-root interface margin (Fig. 5b). In the ferrule of FE-models 1, 2 and 3 tensile stress state range from 0 to 15 MPa. Higher tensile stress of 15 MPa was estimated on the palatal aspect in the chamfer area in the 1st mm of ferrule height in all ferruled models. Compressive stress ranged from 0 to −25 MPa. The highest stress was estimated on the buccal aspect of the chamfer area in the 1st mm of ferule height.



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Fig. 4 – (a) Applied loading conditions: red arrow – 45◦ load (200 N) applied in the FEA environment to study stress values and distribution in restored premolars (model 0, 1, 2, 3); dashed black arrow – intrusive force (20 N in a time range of 75.00 s) for PDL FE-model validation; orange arrow – 45◦ load (5 N) applied in the in vivo test for premolar FE-model validation; black arrow – horizontal force (10 N in a time range of 75.00 s) for PDL FE-model validation. (b) Computed horizontal displacement of the premolar FEM compared to in vivo measured data and (c) computed intrusive displacement of the premolar FEM compared to in vivo measured data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

3.2.

Stress distribution within the abutment

The occlusal volume of the abutment had a tensile stress state ranging from 0 to 2 MPa in all models (Fig. 5c). In FE-model 0 tensile stress was assessed on the palatal side of the chamfer area ranged from 8 to 12 MPa. A tensile stress state of 2 MPa was estimated on the buccal side of the chamfer area. In FEmodels 1, 2 and 3 the in-core abutments showed a tensile stress state ranging from 0 to 6 MPa, the highest values were measured on the palatal side. Out-core abutments underwent a stress state ranging from 0 to 6 MPa in FE-model 1, from 0 to 4 MPa in FE-model 2, and from 0 to 2 MPa in FE-model 3. In all tested FE-models the occlusal volume of the abutment had a compressive stress state ranging from 0 MPa to −4 MPa. In FE-model 0 compressive stress was estimated on the buccal side of the chamfer area ranging from −4 to −16 MPa. A compressive stress state of −2 MPa is estimated on the palatal side of the chamfer area. In FE-models 1, 2 and 3 the in-core abutments showed a compressive stress state ranging from around 0 MPa on the palatal side to −8 MPa on the buccal side (Fig. 5d).

3.3.

Stress distribution within the posts

Tensile and compressive stress distribution is presented in Fig. 5e and f. In all tested FE-models peak tensile stress of

31 MPa was assessed in the middle third of the palatal aspect of the palatal post. Tensile stress progressively decreased in coronal direction to a stress value of 1 MPa and in apical direction to a stress state of 9 MPa. Peak compressive stress of −39 MPa is estimated in the middle third of the buccal aspect of the buccal post. Compressive stress progressively decreased in coronal direction to a stress state of −3 MPa and in apical directions to a stress state value of −27 MPa.

3.4.

Stress distribution within the crown

Tensile stresses ranged from 0 to 4 MPa on the occlusal plane and on the palatal and buccal aspects of the crowns (Fig. 5g). Peak stresses of 19 MPa are noticed in the grooves areas of the occlusal plane. Tensile stresses ranged from 4 to 7 MPa in the mesial and distal aspects of the crown with higher stresses estimated close to the crown–cement–root interfaces. Compressive stresses ranged from −0 to −4 MPa on the occlusal plane (Fig. 5h). Compressive stresses were absent on the palatal aspect while they increased from −1 to −16 MPa on the buccal aspect. Peak stress of −16 MPa is noticed close to the crown–cement–root interface. Compressive stresses ranged from 0 to −4 MPa on the mesial and distal aspects.




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Fig. 5 – Distribution of tensile and compressive stress within the restored tooth components: (a and b) root; (c and d) abutment; (e and f) post; (g and h) crown. FE-model 0: no ferrule; FE-model 1: 1 mm high ferrule; FE-model 2: 2 mm high ferrule; FE-model 3: 3 mm high ferrule.



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Fig. 6 – Distribution of tensile and compressive stress within the interfaces: (a and b) cement layer between the abutment and the crown; (c and d) cement layer at the post-root and the post-abutment; (e and f) adhesive layer between the abutment and the root (FE-model 0) and out-core abutment and ferrule (FE-models 1, 2 and 3).

3.5. Stress distribution within the cement layer between the abutment and the crown Tensile stress ranged from 0 to 4 MPa in the buccal, occlusal, mesial, distal and palatal surfaces of the abutment-crown cement interface (Fig. 6a). However, in the chamfer region the peak tensile stress ranging from 7 to 16 MPa was estimated on the palatal aspect of the chamfer area close to the abutmentcrown interface margin. Compressive stress ranged from −1 to −4 MPa in the buccal, occlusal, mesial, distal and palatal surfaces of the abutments. However in the chamfer region compressive stress range from −7 to −16 MPa, peak stress ranging

from −19 to −22 MPa are estimated on the buccal aspect of the chamfer area close to the abutment-crown interface margin (Fig. 6b).

3.6. Stress distribution within the cement layer at the post-root and the post-abutment interface In all tested models higher tensile stresses were noticed on the palatal side of the cement layer of both posts (Fig. 6c). Higher inter-facials tensile stresses were present along the palatal post than those observed on the buccal post. At the palatal post-root interface in FE-models 1, 2 and 3 tensile stresses




ranged from 4 to 8 MPa on the palatal side. In FE-model 0 peak stress of 14 MPa is noticed close to the post-abutment -root interface. At the palatal post-abutment interface in FEmodels 0, 1, 2 and 3 tensile stresses ranged from 0 to 2 MPa. Compressive stress values and distribution in the cement layer interposed in the post-root and post-abutment interfaces of FE-model 0 and post-root and post-ferrule-abutment interface of FE-models 1, 2 and 3 are shown in Fig. 6d. Along the buccal post of FE-models 0, 1, 2 and 3 compressive stress ranged from −4 MPa to −8 MPa on the buccal aspect of the cement layer.

3.7. Stress distribution within the adhesive layer between the abutment and the root/ferrule interface In FE-model 0 tensile stresses ranged from 5 to 17 MPa on the palatal side of the adhesive interface. Peak tensile stress ranging from 17 to 20 MPa was estimated on the palatal side of the interface close to the root margin. Tensile stresses were absent on the buccal side of the interface. At the “out-core abutment”ferrule interface, in FE-models 1 and 2 tensile stresses ranged from 5 to 8 MPa and 2 to 5 MPa, respectively. In FE-model 3 tensile stresses ranged from 0 to 2 MPa. In Model 0 peak compressive stresses ranging from −22 to −30 MPa were estimated on the buccal side of the interface close to the abutmentroot margin. Compressive stresses progressively decrease in palatal direction. In FE-models 1 and 2 compressive stress range from −6 to −10 MPa and from −2 to −6 MPa, respectively, on the buccal side of the ferrule-abutment adhesive interface. In FE-model 3 compressive stresses ranged from 0 to −2 MPa at the ferrule-abutment interface. Stress distribution within the adhesive layer is presented in Fig. 6e and f.

4.

Discussion

Structural failures of endodontically treated teeth may be due to the fracture of a component or debonding at the adhesive interfaces between the components [14,15]. The failure primarily happens as a result of tensile and shear stresses. The finite element analysis can be used for prediction of fracture by comparing the results to the experimentally determined tensile and shear strength values of a material or an interface. In the present study particular attention was devoted to the modeling of adhesive interfaces between the components of a restored premolar. In particular, interfaces post-root canal dentin, post-abutment, abutment-root, abutment-ferrule and abutment-crown were simulated by direct modeling with volumetric elements of the interfacial space between the components. The interface thickness was simulated according to the literature data reporting the average dimensions of composite cement [24] and adhesive [23] layer. The validation process is an important step in a Finite-Elements-Model generation. Ideally, the results of one particular numerical analysis should be validated by alternative experimental methods. In a typical validation process, experimental strain measurements are used as part of an integrated approach where deformation are measured on a discrete part of a specimen identified for a detailed study by a full field stress analysis technique such as FEA. Ruse [36] described the limits of

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adopting FEA approaches in dental biomechanics neglecting the validation process. Furthermore, in order to reproduce clinical conditions the model adopted to account for the visco-hyper-elastic behavior of the PDL was validated by comparing FE results on the premolar movement within the alveolar socket with data regarding the in vivo premolar displacement under controlled loading conditions [32–35]. A good agreement was observed between the computed displacement data and literature experimental data recorded in vivo (Fig. 4b and c). Compressive strain recorded in vivo is reported in Fig. 3d. Recorded strain values are comprised in the FEA estimated strain-range in the same area of the FE-model. It should be mentioned that strain-gauge length is certainly a critical factor in strain-gauge measurements. In the present study, the adopted strain-gauge was oversized with respect to the size of the premolar crown, and consequently, a detailed full filed strain analysis would bear a significant error. However, the recorded values represents the average strain of the surface covered by the gauge grid and could be considered an indicative data, applicable for model validation in order to verify that no macroscopic errors or flaws were produced in the model set-up. Up-to-date dental biomechanics is missing studies reporting strain measurements on teeth on living subjects. Similarly dental biomechanics literature is missing FEA studies attempting to validate FE-model of a tooth by comparing the mechanical strain estimated in the FE-model to mechanical strain measured on the tooth of a living subject under comparable loading conditions. The present study represents the first attempt to perform an in vivo validation of a tooth FE-model with the direct measurement of mechanical parameters (i.e., strain). In the present study the premolar was made up of brittle materials (either natural or artificial), isotropic (with the exception of dentin and GFRR posts) and with a tensile strength not equal to the compressive strength. The maximum stress/strain criteria are failure criteria developed for brittle materials. The maximum stress criterion assumes that a material fails when the maximum principal stress (1st principal stress) in a material element exceeds the uniaxial tensile strength of the material. Alternatively, the material will fail if the minimum principal stress (3rd principal stress) is less than the uniaxial compressive strength of the material [37]. We adopted the maximum stress criterion to identify and discern the areas where restoring materials and tooth tissues could fail in compression from those where it could fail in tension. This approach was chosen because for simulated materials the value of compressive strength differs from that of tensile strength. The premolar bending in the buccal direction produced tensile stress on the palatal aspect of the tooth. A 200 N load applied to the occlusal surface of the buccal cusp increased tensile stress state of the apical third of the roots to values ranging from 45 to 85 MPa. These stress values are below the tensile failure limit of dentin that is estimated to range from 105 [38] to 135 MPa [27]. Compressive stresses estimated in all tested models did not overcome the compressive strength of dentin (−267 MPa) [39]. Furthermore, the 1 mm, 2 mm and 3 mm-height ferrule FE-models shared similar stress values and distribution patterns in the 1st mm of the ferrule



10


volume. Based on this finding, it may be assumed that ferrule height does not influence the stress state in the ferrule structure itself or within the root. Tensile stress state in the ferrule structure of FE-models 1, 2 and 3 does not reach the dentin tensile failure limit ranging from 105 to 135 MPa (Fig. 5a). Previous study demonstrated the extension of the area under tension with increased ferrule height, whereas the maximum nodal stress values showed very little difference among the FE- models with 0.5 mm, 1 mm, 1.5 mm and 2 mm ferrule [19]. Similarly, small differences in dentin stress between the FEmodels without ferrule and those with 1 mm or 2 mm ferrule have been reported [18]. Tensile stress observed in the composite abutment of FEmodel 0 (12 MPa) are higher than those observed in out-core and in-core abutments of FE-models 1, 2 and 3. However, similar stress intensities were estimated in the same area of the dentin ferrule in the FE-models 1, 2 and 3. Accordingly, it could be hypothesized that the stress state in 1st mm of the chamfer volume is not dependent by the material adopted in this area (dentin or composite). Such phenomenon is due to the similar mechanical properties of dentin and composite material used for the abutments. The higher tensile stress state in the 1st mm of the abutment structure is mainly determined by an abrupt variation in mechanical properties along the crown-abutment-root interface. Particularly, the crown has significantly higher geometrical and material rigidity compared to dentin and composite material forming the root and the abutment. Tensile and compressive stresses estimated on the palatal aspect of the abutment of all analyzed models did not overcome the tensile strength (92 MPa) [40] and compressive strength (273 MPa) (GC Gradia Core Brochure, GC Corp. Tokyo, Japan) of the material adopted for the abutment. However, it could be assumed that a different type of finishing line at the crown margin (e.g., knife edge preparation) may have given different results of this part of the study. Also, the current FEA analysis was performed on the model of an upper first premolar and it seems of interest to verify the results on other types of teeth. Tensile and compressive stress values estimated in the crown structure did not overcome the ultimate properties of zirconia (tensile strength 745 MPa; compressive strength 2000 MPa) [41]. In FE-models 0, 1, 2 and 3 tensile and compressive stress values did not overcome the tensile strength (210 MPa) [42] and compressive strength (150 MPa) [43] of fiber-reinforcedcomposite. Unidirectional fiber-reinforced composites are among the very few materials that exhibit greater tensile strength than compressive strength. This behavior stems from a compressive failure mechanism in fiber composites in form of microbuckling. Microbuckling can occur on one side due to a local instability of fibers, and on the other side by yielding of shear deformation in the composite in connection with initially misaligned fibers [44]. The failure of a fiber post during flexural deformation is due to the microbuckling of fibers on the side where the load is applied and where severe fiber compression occurs. Nevertheless, stress values recorded in the present FE-mmodel were significantly below the flexural strength of fiber posts reported in other studies (from 565 to 898 MPa) [45]. The peak tensile stress in the abutment-crown cement interfaces in FE-models 0, 1, 2 and 3 (17 to 21 MPa) is

dangerously close to the tensile strength of the cement at abutment-crown interface (21 MPa) [46]. Based on the stress values measured, interface debonding is expected to occur on the palatal aspect of the abutment-crown interface at level of the chamfer (Fig. 6a), where the highest tensile stress was estimated. Tensile stress estimated at the post-root interfaces of FEmodel 0 (14 MPa) overcame the interface tensile strength on the palatal aspect of the palatal post (12 MPa) [47]. Tensile stress estimated at the post-root interfaces of FE-models 1, 2 and 3 (6 MPa) did not overcome the interface tensile strength of the post-root interface. In FE-model 0 interface debonding is expected to occur in the coronal third of the post-root interface and between the middle and apical third of the post-root interface. In all tested models tensile stresses estimated in the post-abutment interface were lower compared to the interface tensile strength of the cement at the abutment-post interface. Tensile stresses estimated in the abutment-root interface of FE-model 0 (20 MPa) is very close to the tensile strength of the abutment material (22 MPa) [47]. The highest stress value shown in Fig. 6e indicates the area where interface debonding is expected to occur in FE-model 0. In FE-model 1, 2 and 3 tensile stress estimated at the abutment-ferrule interface are lower than the interface tensile strength, and therefore interface failures are not expected to occur in this area. The tensile stress at the abutment-ferrule interface decreases progressively when the height of the ferrule rises. Therefore, the formulated null hypothesis, that different ferrule heights do not affect the stress distribution within the tooth, had to be rejected as it was demonstrated that with increasing ferrule height, the stress decreased. Recently, Ferrari et al. [15] reported results of a randomized clinical trial investigating the contribution of remaining coronal dentin and post placement to the six-year survival of endodontically treated premolars. It was clearly reported that failure risk was lower in teeth restored with prefabricated than customized posts and/or no post placement. Also, it was noticed that the presence of ferrule of around 2 mm was not sufficient to preserve from clinical failures [15]. Present FEA study indirectly confirms this clinical observation, but shows that ferrule height of 3 mm is more desirable amount of residual structure in order to decrease tensile and compressive stresses and consequently preserve the root-post-abutmentcrown system from debonding, the most frequent type of clinical failure [48]. Also the findings of the current study suggest that the palatal bonding interfaces are those subjected to higher stresses and therefore exposed to higher risk of debonding. This specific finding may be due to the type of load applied on the premolar model and it can be considered that under different clinical occlusal loading, as well as parafunctions, stress concentration at bonding interfaces can also be located at vestibular, mesial or distal sides.

5.

Conclusions

Based on the results of the present FEA study it can be concluded that height of the ferrule did not considerably influence the stress state in the ferrule structure itself or




within the root. In all ferruled FE-models the highest stress was estimated in the chamfer area in the 1st mm of ferrule height. When no ferrule was present tensile stress observed in the composite abutment is significantly higher than those observed in out-core and in-core abutments of FE-models with ferrule. Nevertheless, the tensile stress values did not overcome the tensile strength of the abutment material. Similar stress distribution within the ceramic crown and glass-fiber-reinforced-composite post was present in all tested FE-models. Therefore, it can be concluded that the adhesive interfaces are the weakest parts of the tested FE-models and debonding is the most probable cause of failure. The stress state at the abutment-crown and post-root interfaces was dangerously close to the strength of the interfaces in the not-ferruled model. Similarly, at the post-abutment and the abutment-root interface debonding is expected to occur only in teeth without ferrule, whereas lower stresses were estimated in FE-models exhibiting ferrule. Endodontically treated teeth with higher ferrule exhibit lower stresses at adhesive interfaces that may be expected to lower the probability of clinical failure.

[11]

[12]

[13]

[14]

[15]

[16]

[17]

Conflict of interest statement The authors declare that they have no conflict of interest.

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Finite element analysis of stress distribution in ceramic crowns fabricated with different tooth preparation designs.

Effect of increased crown height on stress distribution in short dental implant components and their surrounding bone: A finite element analysis.

Comparison of Stress Distribution in a Maxillary Central Incisor Restored with Two Prefabricated Post Systems with and without Ferrule Using Finite Element Method.

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Stress distribution of oval and circular fiber posts in amandibular premolar: a three-dimensional finite element analysis.

A comparison of intracanal stresses in a post-restored tooth utilizing the finite element method.

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Influence of substructure design and occlusal reduction on the stress distribution in metal ceramic complete crowns: 3D finite element analysis.

Finite element stress analysis of the crowns of normal and restored teeth.

Effects of crown retrieval on implants and the surrounding bone: a finite element analysis.

Comparison of Stresses Generated within the Supporting Structures of Mandibular Second Molars Restored with Different Crown Materials: 3-D Finite Element Analysis (FEA).

abutment connection on stress distribution to implant-surrounding bone: a finite element analysis.

Influence of three different implant thread designs on stress distribution: A three-dimensional finite element analysis.

Biomechanical Stress Analysis of Mandibular First Permanent Molar; Restored with Amalgam and Composite Resin: A Computerized Finite Element Study.

Finite element analysis of the influence of geometry and design of zirconia crowns on stress distribution.

Effect of Integration Patterns Around Implant Neck on Stress Distribution in Peri-Implant Bone: A Finite Element Analysis.

The effect of platform switching on stress distribution in implants and periimplant bone studied by nonlinear finite element analysis.

Effect of core materials on stress distribution of posts.

Three-dimensional finite element analysis of glass-ceramic dental crowns.

Stress Distribution under Commercial Denture Liners- A Finite Element and Clinical Analysis.

Effect of bone distribution on vertebral strength: assessment with patient-specific nonlinear finite element analysis.

Fatigue surviving, fracture resistance, shear stress and finite element analysis of glass fiber posts with different diameters.

Effect of the number of implants on stress distribution of anterior implant-supported fixed prostheses combined with a removable partial denture: a finite element analysis.