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d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) e309–e317

Available online at www.sciencedirect.com

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jo ur nal home p ag e: www.int l .e lsev ierhea l th .com/ journa ls /dema

D-Finite element analysis of molars restored withndocrowns and posts during masticatoryimulation

eata Dejaka,∗, Andrzej Młotkowskib

Department of Prosthetic Dentistry, Medical University of Łódz, Łódz, PolandDepartment of Strength of Materials and Structures, Technical University of Łódz, Łódz, Poland

r t i c l e i n f o

rticle history:

eceived 27 April 2013

eceived in revised form 3 July 2013

ccepted 25 September 2013

eywords:

olar restorations

osts

ore

ndocrown

eramic crown

hewing

inite element analysis

odified von Mises failure criterion

a b s t r a c t

Objective. The objective was to compare equivalent stresses in molars restored with

endocrowns as well as posts and cores during masticatory simulation using finite element

analysis.

Methods. Four three-dimensional models of first mandibular molars were created: A – intact

tooth; B – tooth restored by ceramic endocrown; C – tooth with FRC posts, composite core and

ceramic crown; D – tooth with cast post and ceramic crown. The study was performed using

finite element analysis, with contact elements. The computer simulations of mastication

were conducted. The equivalent stresses of modified von Mises failure criterion (mvM) in

models were calculated, Tsai-Wu index for FRC post was determinate. Maximal values of

the stresses in the ceramic, cement and dentin were compared between models and to

strength of the materials. Contact stresses in the cement–tissue adhesive interface around

restorations were considered as well.

Results. During masticatory simulation, the lowest mvM stresses in dentin arisen in molar

restored with endocrown (Model B). Maximal mvM stress values in structures of restored

molar were 23% lower than in the intact tooth. The mvM stresses in the endocrown did not

exceed the tensile strength of ceramic. In the molar with an FRC posts (Model C), equiva-

lent stress values in dentin increased by 42% versus Model B. In ceramic crown of Model C

the stresses were 31% higher and in the resin luting cement were 61% higher than in the

tooth with endocrown. Tensile contact stresses in the adhesive cement–dentin interface

around FRC posts achieved 4 times higher values than under endocrown and shear stresses

increased twice. The contact stress values around the appliances were several time smaller

than cement–dentin bond strength.

Significance. Teeth restored by endocrowns are potentially more resistant to failure than

those with FRC posts. Under physiological loads, ceramic endocrowns ideally cemented in

molars should not be demaged or debonded.

© 2013 Academy

∗ Corresponding author. Tel.: +48 601411480; fax: +48 426757450.E-mail address: bdejak@poczta.onet.pl (B. Dejak).

109-5641/$ – see front matter © 2013 Academy of Dental Materials. Puttp://dx.doi.org/10.1016/j.dental.2013.09.014

of Dental Materials. Published by Elsevier Ltd. All rights reserved.

blished by Elsevier Ltd. All rights reserved.

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e310 d e n t a l m a t e r i a l

1. Introduction

Crowns significantly damaged after endodontic treatmentwere traditionally restored with metal posts and cores andprosthetic crowns. Post and core comprises a coronal part(core), which acts as a substitute for supragingival tooth struc-tures and provides support for the final prosthetic restoration,and a root part (post), which ensures retention for the restora-tion and is cemented in an adequately prepared root canal.Such a restoration results in a 58.3% loss of tooth structure [1].The preparation of a molar for a post and core involves widen-ing the anatomically complex system of canals, which in theseteeth are narrow, frequently curved and with variable angu-lation [2]. This involves a risk of accidental root perforation[3].

Currently, due to the development of adhesive methods,it is possible to reconstruct damaged posterior teeth withintracoronal restorations – endocrowns [4]. Their advantagesinclude the fact that tooth structures require little preparationcompared with posts and cores and that there is no interfer-ence in the root [5]. Apart from adhesion, retention of ceramiccrowns is based on machromechanical fixation in the pulpchamber [6,7]. Strong bonding between ceramics and tissueusing composite luting cements increases the fracture resis-tance of the restorations [8], and consolidates and stabilizesweakened tooth structures at the same time [9]. What type ofrestoration (endocrown or posts with crown) will provide low-est stresses in molars? Is it possible to restore molars withendocrowns instead of traditional posts and crowns takinginto consideration the strength of restorations?

The objective was to compare equivalent stresses in molarsrestored with endocrowns as well as posts and cores duringmasticatory simulation using finite element analysis.

2. Materials and methods

2.1. Geometry of FE models

Double-layer impressions of the upper and lower arch of apatient with normal occlusion were taken using polyvinyl-siloxane material (Express, 3M/ESPE, St. Paul, MN, USA).Occlusal registrations in central and lateral positions of themandible with wax were recorded (Aluwax Dental ProductsCo., Allendale, MI, USA). Working casts with separate dieswere prepared (Girostone, Amann Girrbach GmbH, Pforzheim,Germany). Using a laser scanner (Ceramill Map300 Amann-Girrbach, Koblach, Austria) the occlusal surfaces of three diestone teeth were scanned: the lower right first molar andtwo opposing teeth, the first upper molar and the secondupper premolar. The obtained scans were then processed withsoftware (Ceramill Mind). Full Scan datasets containing coor-dinates of the occlusal surface points of the examined teethwere introduced into the finite element analysis FEA software

(ANSYS v. 10; ANSYS Inc., Canonsburg, PA, USA) [10]. In itspre-processor, occlusal surface points located in frontal layersevery 0.1 mm were selected. These points were connected withsplines and the occlusal surfaces of the teeth were generated.

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In the same patient, a CBCT scan of the first lowermolar under investigation was taken (GXCB-500/i-CAT; Gen-dex Dental Systems, Des Plaines, III, USA). CBCT scans in thehorizontal planes (every 1 mm) provided the base for obtain-ing the circumferential points of the external tooth structurewith roots. Tomography points were used to reconstruct cross-sections of the tooth. By connecting the cross-sections and theocclusal surface we were able to create a solid lower molarmodel (Model A). The cervico-occlusal length of the crownwas 7.5 mm, the bucco-lingual diameter was 10.5 mm, and theroots were 14 mm in length [2]. A 0.2 mm periodontal ligamentwas modeled around the roots (Fig. 1a). The lower molar wasanatomically inclined 15 degrees lingually and 8 degrees ante-riorly [11]. The tooth model was situated in the coordinatesystem in such a way that the Z-axis indicated the mesial sur-face of the tooth, the X-axis the lingual surface, and the Y-axiswas oriented upwards (Fig. 1a).

The tooth model was sectioned perpendicular to its longaxis at a distance of 6.5 mm from the apices of the cusps.In the ANSYS preprocessor, a 3.7 mm × 4 mm × 2 mm cuboidwith rounded edges was created and introduced into thepulp chamber. The solid formed after sectioning part of thecrown was connected with the cuboid, covered with a 0.1 mmthick cement layer and added to the lower molar tooth model(Fig. 1b). In this way we created tooth Model B with anendocrown.

We prepared tooth 46 in a plaster model of the mandible fora crown with a 1 mm wide chamfer. The occlusal surface wasreduced by 1.5–2 mm [12]. The axial walls were prepared witha 6◦ inclination. As was mentioned above, the prepared toothwas scanned. The surface points coordinates were loaded intothe ANSYS application and Model A of the molar tooth wassectioned along this surface. In addition, the tooth modelwas sectioned perpendicular to the longitudinal axis at a dis-tance of 6.5 mm from the apices of the cusps. Then, two10.5 mm × 1.0 cylinders and one 13.5 × 1.0 mm cylinder weregenerated in the Ansys preprocessor. The cylinders were con-nected to core and were introduced in the canals of the firstlower molar model in depth 9 mm and 11.8 mm (Fig. 1c). A0.1 mm thick cement-imitating layer was formed around theroot part of the created post and under the crown. In this way,we created a tooth model with post and core and prostheticcrown (Model C).

2.2. Mash

For calculation purposes, each tooth model was divided into10-node structural solid elements (Solid 187). In Model B (withendocrown), 76,000 elements joined at 101,000 nodes wereused. In Model C (post and core) 91,000 elements were joinedat 120,000 nodes. Pairs of bonded contact elements, Targe 170and Conta 174, were applied at the interface of the lutingcement–dentin bond.

2.3. Boundary conditions and masticatory simulations

The models were fixed in the nodes on the upper surface of theupper tooth crowns and in the nodes on the outer surface ofthe periodontal ligament of the lower molar. The study modelswere subjected to loads during the simulated occlusal phase

d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) e309–e317 e311

Fig. 1 – Models of (a) Model A – first mandibular molar tooth with roots and periodontium (mesio-lingual side view) (b)Model B – endocrown (c) Model C – FRC posts and composite resin core (d) Model D – cast posts and core (e) Model of firstmandibular molar tooth with fragments of antagonist’s teeth during the closing phase of the mastication cycle.

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e312 d e n t a l m a t e r i a l

of mastication. The upper tooth crowns (second premolar andfirst molar) and the lower molar models were positioned inthe lateral occlusion using reference points from scans of thelateral occlusal record [13]. Opposing teeth were separated ver-tically. A 1 mm thick bolus was inserted between them witha Young’s modulus value of 27.57 MPa [14], which is charac-teristic for nuts. Pairs of contact elements were used on theocclusal surfaces of the examined teeth and boluses. The coef-ficient of friction between the contact surfaces was assumedto be 0.2 [15]. Displacement of nodes on the outer surfaceof the lower tooth’s periodontal ligament was manipulated.This tooth was moved vertically upwards and at the sametime medially and mesially to the upper teeth, until maxi-mum intercuspation was achieved. Vertical movement waschosen to produce a maximum 200 N reaction force in Y direc-tion for each model [16]. The buccal cusps of the lower toothwere glided through blouses along the occlusal surfaces of theupper teeth, thereby grinding the bolus (Fig. 1e) [17].

2.4. Material properties

The endocrowns and prosthetic crowns examined in thepresent study were made of leucite-reinforced ceramics andluted to tooth structures with a Variolink II composite lut-ing cement (Ivoclar, Vivadent AG, Schaan, Lichtenstein). Theposts and cores were made of fiberglass (model C) (Fig. 1c)or a nickel-titanium alloy (Model D) (Fig. 1d). In the FRCposts, the cores were made of composite, while in the castposts they were made of metal. The values for Young’s mod-ulus and Poisson’s ratio were entered for the enamel [18],dentin [19], periodontal ligament [20], ceramics [21], nickel-chromium alloy [22], composite luting cement [23] and corecomposite [24]. The data are listed in Table 1. The materialsin the model were assumed to be linear, elastic, homogenousand isotropic, but varied in terms of compressive and tensilestrength, with the exception of the nickel-chromium alloy.The material of FRC post was anisotropic (Young’s modulusalong its long axis was 37 GPa, and 9.5 GPa perpendicular tothat axis) [25]. The compressive and tensile strength valueswere assumed for enamel (11.5 MPa, 384 MPa) [26,27], dentin(105.5 MPa, 297 MPa) [27,28], nickel-chromium alloy (710 MPa)[17], FRC (1200/73 MPa, 1000/160 MPa) [29], core compositeresin (41, 293) [30], ceramics (48.8 MPa, 162.9 MPa) [31] and com-posite luting cement (45.1 MPa, 178 MPa) [32].

2.5. Analysis mode

The study used finite element analysis FEA software (ANSYSv. 10; ANSYS Inc., Canonsburg, PA, USA) [10]. FEA contact sim-ulation is a nonlinear analysis that requires the load anddisplacement to be applied in a number of steps. Automatictime stepping was applied in the ANSYS software. Tooth struc-tures and ceramics are materials characterized by differenttensile and compressive strengths. One criterion used to eval-uate the strength of materials under compound stress states isthe modified von Mises (mvM) failure criterion [33]. This crite-

rion takes into account the ratio between the compressive andtensile strengths for each material; e.g. its value for dentin 2.8;leucite-reinforced ceramics 3.3; composite resin 7.1; and com-posite luting cement 3.9 (Table 1). The ratio for Cr–Ni alloy is 1

( 2 0 1 3 ) e309–e317

and in that case the criterion takes the form of Von Mises fail-ure criterion. According to the strength criteria, the materialwill fail when the values of equivalent mvM stresses exceedthe tensile strength of the material. The calculation resultsare presented in the form of maps of stress distribution inmolar models. The maximum stress values of materials werecompared both to one another and to the tensile strength ofindividual materials. In order to evaluate the strength of FRCposts, which have strong anisotropic properties, we appliedthe Tsai-Wu criterion [34]. We calculated the inverse Tsai-Wuratio index (STWSR) and the index values above 1 indicatematerial damage.

We also calculated the compressive, tensile and shear con-tact stress values around the examined restorations, on theluting cement–dentin interface and during loading. Thesewere graphically presented as maps on the contact surfacesof restorations and tooth structures. The maximum tensilecontact stress values at the interface of cement and tissuesurrounding the restorations were compared with the tensilestrength of the composite cement–dentin bond.

3. Results

We calculated the equivalent mvM stress values in tissues andprosthetic restorations during masticatory simulation. Vari-able forces were transferred onto the occlusal surfaces of theexamined teeth by the boluses. The highest stress values inthe structures of the examined lower teeth and restorationsoccurred in the final closing phase of mastication during teethclenching (Table 2). Similarly, the highest contact stress valuesin the luting cement–tooth tissue interface occurred at thetime of maximum intercuspation, and their values are pre-sented in Table 3. During masticatory simulation, mvM stressvalues did not exceed the tensile strength of any individualmaterial in any model. In the intact tooth model (Model A),maximum stress values (10.7 MPa) were located in the enamelof the central groove. In dentin, mvM stress was concentratedat the cervical area and achieved a value of 3.4 MPa (Table 2).

In tooth Model B with endocrown, maximum mvM stressvalues of 2.6 MPa were recorded in the distal region of the pre-pared pulp chamber and were 23% lower than in the intacttooth (Model A) (Fig. 2a). In the ceramic endocrown, mvMstress did not exceed 16.5 MPa and was concentrated on thefunctional cusp of the endocrown (Fig. 2b). In the luting resincement, equivalent stress values around the distal region ofthe endocrown reached 1.8 MPa (Fig. 2c) (Table 2). Contactstress values at the endocrown-tooth tissues interface did notexceed 1 MPa (Table 3; Fig. 2d and e).

In the tooth with an FRC posts (Model C), equivalent stressvalues in dentin increased to 3.7 MPa and increased in relationto the Model B with endocrown (Table 2). The stress concentra-tion in the dentin occurred under the crown shoulder, in thedistal region of the tooth (Fig. 3a). The mvM stress values in themolar restored with FRC posts were 31% higher in the crown

ceramics (Fig. 3b) and 61% higher in the luting resin cement(Fig. 3c) than in the tooth with endocrown (Table 2). In FRCposts, the STWSR index did not exceed 0.018 (Fig. 3d). Contacttensile and shear stress values along the post and core-dentin

d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) e309–e317 e313

Fig. 2 – Distribution of the equivalent stresses according to the modified von Mises (mvM) failure criterion and contactstresses in molar tooth model with ceramic endocrown during the closing phase of the mastication cycle (MPa). (a)Equivalent stresses mvM in dentin (distal side view); (b) equivalent stresses mvM in ceramic endocrown (mesio-lingual sideview); (c) equivalent stresses mvM in resin composite luting cement (distal side view); (d) contact tensile and compressivestresses distribution between endocrown and dentin (distal side view) (contact tensile stresses are marked in blue color andtheir values are negative; contact compressive stresses are marked in red and yellow color and their values are positive); (e)contact shear stresses distribution between endocrown and dentin post (distal side view) (MX and red color indicatesmaximal shear stresses). (For interpretation of the references to color in this figure legend, the reader is referred to the webversion of this article.)

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Fig. 3 – Distribution of the equivalent stresses according to the modified von Mises (mvM) failure criterion and contactstresses in molar tooth model with FRC posts, composite resin core and ceramic crown during the closing phase of themastication cycle (MPa). (a) Equivalent stresses mvM distribution in dentin (distal side view); (b) equivalent stresses mvMdistribution in ceramic crown (bottom view); (c) equivalent stresses mvM distribution in resin composite luting cement(mesio-lingual side view); (d) inverse of Tsai-Wu strength ratio index in FRC posts (STWSR) (mesio-lingual side view); (e)equivalent stresses mvM distribution in resin composite luting cement around post contact tensile and compressivestresses distribution between post and dentin (mesio-lingual side view) (contact tensile stresses are marked in blue colorand their values are negative; contact compressive stresses are marked in red and yellow color and their values arepositive); (f) contact shear stresses distribution between post and dentin (mesio-lingual side view) (MX and red colorindicates maximal shear stresses). (For interpretation of the references to color in this figure legend, the reader is referred tothe web version of this article.)

d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) e309–e317 e315

Table 1 – Data of materials used in models of molars.

Material Modulus ofelasticity (GPa)

Poisson’s ratio Tensile strength (MPa) Compressivestrength (MPa)

Enamel 84.1 0.33 11.5 384Dentin 18.6 0.31 105.5 297Periodontium 0.05 0.45Cast NiCr post 188 0.33 710 710Glass fiber post EX = 37 �X = 0.34 RmX = 1200 RcX = 1000

EY = 9.5 �Y = 0.27 RmY = 73 RcY = 160EZ = 9.5 �Z = 0.27 RmZ = 73 RcZ = 160

Crowns leucite ceramic 65.0 0.19 48.8 162.9Composite core 14.1 0.24 41 293Luting resin cement 8.3 0.35 45.1 178

Table 2 – Maximum values of equivalent stresses according to modified von Mises (mvM) failure criterion in FE models ofmandibular molars with various restorations (MPa).

Model Models of mandibularmolars

Maximal stresses mvM (MPa)

Enamel/Ceramic ofrestoration

Dentin Posts Resin composite lutingcement

A Intact tooth 10.7 3.4 – –B Tooth with endoctown 16.5 2.6 – 1.8C Tooth with FRC post and 21.0 3.7 0.18 STWSR 2.9

iT

lcatMme

4

TtIfi[mF

resin composite coresD Tooth with cast post

and cores17.6

nterface were higher than around endocrowns (Fig. 3e and f;able 3).

The application of a metal post and core (Model D) causedower stress in the dentin, the ceramic crown and cement asompared to the stress noted in the dentin of the tooth withn FRC post (Table 2). Contact stress values at the metal post-ooth tissue interface were also slightly lower in relation toodel C (Table 3). However, stress values in the tooth with theetal post continued to be higher than in the tooth with the

ndocrown restoration (Model B) (Table 2).

. Discussion

he present study showed that dentin mvM stress levels inooth with an endocrown were smaller than in the intact tooth.t can be acknowledged that rigid ceramic endocrowns rein-orce tooth structures. Simultaneously the mvM stress levels

n endocrown did not exceed the ceramic tensile strength31]. During physiological loading, ceramic endocrowns in

olars should not fail. These results are convergent withEA studies by Lin et al. [35], in which calculations showed

Table 3 – Maximum values of contact tensile, compressive, shevarious restorations in molars (MPa).

Model Models of mandibular molars

B Tooth with endoctown

C Tooth with FRC post andresin composite cores

D Tooth with cast postand cores

3.2 49.5 2.1

that stress levels in teeth with endocrowns were lower thanin teeth with prosthetic crowns [36]. Authors have con-cluded that endocrowns and conventional prosthetic crownsshould demonstrate similar longevity in the oral cavity [37]. Itwas confirmed by clinical research. During a 5-year clinicalfollow-up period, 87.1% of endocrowns in molars success-fully performed their function [38]. Other studies report a5-year failure rate of 9.7% for ceramic reconstructions onnon-vital teeth [39]. Taking into consideration the strengthand longevity of endocrowns, minimal invasive preparationof tooth structures and no roots damage, these restorationsare recommended to use in molars.

Equivalent stress levels in the dentin of molars restoredwith posts and cores and ceramic crowns were higher thanstress levels in the tooth with the endocrown, as well as stresslevels in the intact tooth. The highest mvM stresses in dentinand crown occurred in molar restored with FRC posts. Thistype of restoration seems to be the least beneficial in molar

teeth. According to Morgano [40], composite posts and coresdo not reinforce the structure of endodontically treated teeth,but only ensure retention for the supragingival part. Biac-chi and Basting [41] found that molars with endocrowns are

ar stresses in cement–dentin adhesive interface under

Contact stresses (MPa)

Compressive Tensile Shear

5.9 0.4 0.99.0 1.6 1.7

8.3 1.4 1.1

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more fracture resistant than teeth restored with FRC posts andcores and ceramic crowns. On the other hand, experimentalstrength study by Forberger and Göhring [42], have shown nosignificant differences between teeth restored with posts andendocrowns in terms of fracture resistance.

Biomechanics in incisors are different than in molars.Molars height (7.5 mm) is smaller than width (10.5 mm), unlikeincisors [2]. According to Shillingburg et al. [43], a loaded toothcan be compared to a cantilever with the rotation axis locatedat the cervix. Masticatory forces are applied at an obliquedirection to cusps and lever the restoration. The lever-arm offorces is longer (approx. 10.5 mm) than in incisors (6–7 mm).According to the level equilibrium formula, smaller forces areexerted on restorations in molars than in incisors. In addi-tion, the mean area of the endocrown-molar tooth interfaceis 60 mm2 and is 2 times higher than in incisors (30 mm2) [2].Smaller lever forces exerted on restorations and good bond-ing strength between endocrowns and tooth structures makethese restorations possible to apply in molars. However, dam-aged anterior tooth crowns should be preferably restored withposts and cores.

Results from Rathke et al. [44] studies suggest that the ten-sile strength of the bond between Variolink II cement anddentin is 29.9 MPa. In the present study, contact stress levelsaround any of the investigated restorations were not higherthan 1.6 MPa, and so were far from exceeding the bondingstrength of the cement with tooth tissue (Table 3). Contactstress levels around endocrowns were 4 times lower thanaround FRC posts and cores, while shear stresses were 2 timeslower. In light of the present study and assuming that theendocrown in a molar tooth is made from ceramics withoutartifacts and is ideally bonded to tooth tissue, it should nei-ther become damaged nor debond under physiological loadsin the oral cavity. However, the most common failures affect-ing extensive ceramic restorations in molars are porcelainfractures or microleakage [42]. In clinical practice, effectivebonding between ceramics and teeth depends on multiple fac-tors. Adhesive cementation of glass ceramics requires etchingits surface [45], silanization [46], applying bonding systems [47]and ensuring appropriate treatment of the enamel and dentinsurface [48]. Any contamination of the surfaces to be bonded(with saliva, blood) or procedural errors prevent good adhe-sion from being achieved. In addition, bond strength betweenceramics and tooth tissue decreases over time as an effectof periodical loads and temperature changes [49,50]. Thesephenomena are essential bearing in mind the failures thatoccur when restoring teeth with endocrowns.

5. Conclusions

Within the limitations of this study during masticatory simu-lation:

1. Ceramic endocrowns in molars caused the lowest mvMstress levels in dentin compared to posts and cores. Molarsrestored with endocrowns are less prone to fracture thanthose with posts.

( 2 0 1 3 ) e309–e317

2. Under physiological loads, ceramic endocrowns ideallycemented in molars should not be demaged or debonded.Endocrowns may be used to restore molars.

3. The highest equivalent stresses occurred in molar restoredwith FRC post. The unfavorable molar reconstructions inbiomechanical terms are an FRC posts with a compositecores.

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