3D-Finite element analysis of molars restored with endocrowns and posts during masticatory simulation

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3D-Finite element analysis of molars restored with endocrowns and posts during masticatory simulation Beata Dejak a,∗ , Andrzej Młotkowski b a b

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

a r t i c l e

i n f o

a b s t r a c t

Article history:

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

Received 27 April 2013

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

Received in revised form 3 July 2013

analysis.

Accepted 25 September 2013

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

Keywords:

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

Molar restorations

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

Posts

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

Core

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

Endocrown

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

Ceramic crown

restorations were considered as well.

Chewing

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

Finite element analysis

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

Modified von Mises failure criterion

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), equivalent 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 of Dental Materials. Published by Elsevier Ltd. All rights reserved.

∗

Corresponding author. Tel.: +48 601411480; fax: +48 426757450. E-mail address: [email protected] (B. Dejak). 0109-5641/$ – see front matter © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.dental.2013.09.014

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1.

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Introduction

Crowns significantly damaged after endodontic treatment were traditionally restored with metal posts and cores and prosthetic crowns. Post and core comprises a coronal part (core), which acts as a substitute for supragingival tooth structures and provides support for the final prosthetic restoration, and a root part (post), which ensures retention for the restoration 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 widening the anatomically complex system of canals, which in these teeth are narrow, frequently curved and with variable angulation [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 with intracoronal restorations – endocrowns [4]. Their advantages include the fact that tooth structures require little preparation compared with posts and cores and that there is no interference in the root [5]. Apart from adhesion, retention of ceramic crowns is based on machromechanical fixation in the pulp chamber [6,7]. Strong bonding between ceramics and tissue using composite luting cements increases the fracture resistance of the restorations [8], and consolidates and stabilizes weakened tooth structures at the same time [9]. What type of restoration (endocrown or posts with crown) will provide lowest stresses in molars? Is it possible to restore molars with endocrowns instead of traditional posts and crowns taking into consideration the strength of restorations? 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.

2.

Materials and methods

2.1.

Geometry of FE models

Double-layer impressions of the upper and lower arch of a patient with normal occlusion were taken using polyvinylsiloxane material (Express, 3M/ESPE, St. Paul, MN, USA). Occlusal registrations in central and lateral positions of the mandible with wax were recorded (Aluwax Dental Products Co., Allendale, MI, USA). Working casts with separate dies were prepared (Girostone, Amann Girrbach GmbH, Pforzheim, Germany). Using a laser scanner (Ceramill Map300 AmannGirrbach, Koblach, Austria) the occlusal surfaces of three die stone teeth were scanned: the lower right first molar and two opposing teeth, the first upper molar and the second upper premolar. The obtained scans were then processed with software (Ceramill Mind). Full Scan datasets containing coordinates of the occlusal surface points of the examined teeth were introduced into the finite element analysis FEA software (ANSYS v. 10; ANSYS Inc., Canonsburg, PA, USA) [10]. In its pre-processor, occlusal surface points located in frontal layers every 0.1 mm were selected. These points were connected with splines and the occlusal surfaces of the teeth were generated.

In the same patient, a CBCT scan of the first lower molar under investigation was taken (GXCB-500/i-CAT; Gendex Dental Systems, Des Plaines, III, USA). CBCT scans in the horizontal planes (every 1 mm) provided the base for obtaining the circumferential points of the external tooth structure with roots. Tomography points were used to reconstruct crosssections of the tooth. By connecting the cross-sections and the occlusal surface we were able to create a solid lower molar model (Model A). The cervico-occlusal length of the crown was 7.5 mm, the bucco-lingual diameter was 10.5 mm, and the roots were 14 mm in length [2]. A 0.2 mm periodontal ligament was modeled around the roots (Fig. 1a). The lower molar was anatomically inclined 15 degrees lingually and 8 degrees anteriorly [11]. The tooth model was situated in the coordinate system in such a way that the Z-axis indicated the mesial surface of the tooth, the X-axis the lingual surface, and the Y-axis was oriented upwards (Fig. 1a). The tooth model was sectioned perpendicular to its long axis 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 cuboid with rounded edges was created and introduced into the pulp chamber. The solid formed after sectioning part of the crown was connected with the cuboid, covered with a 0.1 mm thick cement layer and added to the lower molar tooth model (Fig. 1b). In this way we created tooth Model B with an endocrown. We prepared tooth 46 in a plaster model of the mandible for a crown with a 1 mm wide chamfer. The occlusal surface was reduced by 1.5–2 mm [12]. The axial walls were prepared with a 6◦ inclination. As was mentioned above, the prepared tooth was scanned. The surface points coordinates were loaded into the ANSYS application and Model A of the molar tooth was sectioned along this surface. In addition, the tooth model was sectioned perpendicular to the longitudinal axis at a distance of 6.5 mm from the apices of the cusps. Then, two 10.5 mm × 1.0 cylinders and one 13.5 × 1.0 mm cylinder were generated in the Ansys preprocessor. The cylinders were connected to core and were introduced in the canals of the first lower molar model in depth 9 mm and 11.8 mm (Fig. 1c). A 0.1 mm thick cement-imitating layer was formed around the root part of the created post and under the crown. In this way, we created a tooth model with post and core and prosthetic crown (Model C).

2.2.

Mash

For calculation purposes, each tooth model was divided into 10-node structural solid elements (Solid 187). In Model B (with endocrown), 76,000 elements joined at 101,000 nodes were used. In Model C (post and core) 91,000 elements were joined at 120,000 nodes. Pairs of bonded contact elements, Targe 170 and Conta 174, were applied at the interface of the luting cement–dentin bond.

2.3.

Boundary conditions and masticatory simulations

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

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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 first mandibular molar tooth with fragments of antagonist’s teeth during the closing phase of the mastication cycle.

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of mastication. The upper tooth crowns (second premolar and first molar) and the lower molar models were positioned in the lateral occlusion using reference points from scans of the lateral occlusal record [13]. Opposing teeth were separated vertically. A 1 mm thick bolus was inserted between them with a Young’s modulus value of 27.57 MPa [14], which is characteristic for nuts. Pairs of contact elements were used on the occlusal surfaces of the examined teeth and boluses. The coefficient of friction between the contact surfaces was assumed to be 0.2 [15]. Displacement of nodes on the outer surface of the lower tooth’s periodontal ligament was manipulated. This tooth was moved vertically upwards and at the same time medially and mesially to the upper teeth, until maximum intercuspation was achieved. Vertical movement was chosen to produce a maximum 200 N reaction force in Y direction for each model [16]. The buccal cusps of the lower tooth were glided through blouses along the occlusal surfaces of the upper teeth, thereby grinding the bolus (Fig. 1e) [17].

2.4.

Material properties

The endocrowns and prosthetic crowns examined in the present study were made of leucite-reinforced ceramics and luted to tooth structures with a Variolink II composite luting cement (Ivoclar, Vivadent AG, Schaan, Lichtenstein). The posts and cores were made of fiberglass (model C) (Fig. 1c) or a nickel-titanium alloy (Model D) (Fig. 1d). In the FRC posts, the cores were made of composite, while in the cast posts they were made of metal. The values for Young’s modulus and Poisson’s ratio were entered for the enamel [18], dentin [19], periodontal ligament [20], ceramics [21], nickelchromium alloy [22], composite luting cement [23] and core composite [24]. The data are listed in Table 1. The materials in the model were assumed to be linear, elastic, homogenous and isotropic, but varied in terms of compressive and tensile strength, with the exception of the nickel-chromium alloy. The material of FRC post was anisotropic (Young’s modulus along its long axis was 37 GPa, and 9.5 GPa perpendicular to that axis) [25]. The compressive and tensile strength values were 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 composite resin (41, 293) [30], ceramics (48.8 MPa, 162.9 MPa) [31] and composite luting cement (45.1 MPa, 178 MPa) [32].

2.5.

Analysis mode

The study used finite element analysis FEA software (ANSYS v. 10; ANSYS Inc., Canonsburg, PA, USA) [10]. FEA contact simulation is a nonlinear analysis that requires the load and displacement to be applied in a number of steps. Automatic time stepping was applied in the ANSYS software. Tooth structures and ceramics are materials characterized by different tensile and compressive strengths. One criterion used to evaluate the strength of materials under compound stress states is the modified von Mises (mvM) failure criterion [33]. This criterion takes into account the ratio between the compressive and tensile strengths for each material; e.g. its value for dentin 2.8; leucite-reinforced ceramics 3.3; composite resin 7.1; and composite luting cement 3.9 (Table 1). The ratio for Cr–Ni alloy is 1

and in that case the criterion takes the form of Von Mises failure criterion. According to the strength criteria, the material will fail when the values of equivalent mvM stresses exceed the tensile strength of the material. The calculation results are presented in the form of maps of stress distribution in molar models. The maximum stress values of materials were compared both to one another and to the tensile strength of individual materials. In order to evaluate the strength of FRC posts, which have strong anisotropic properties, we applied the Tsai-Wu criterion [34]. We calculated the inverse Tsai-Wu ratio index (STWSR) and the index values above 1 indicate material damage. We also calculated the compressive, tensile and shear contact stress values around the examined restorations, on the luting cement–dentin interface and during loading. These were graphically presented as maps on the contact surfaces of restorations and tooth structures. The maximum tensile contact stress values at the interface of cement and tissue surrounding the restorations were compared with the tensile strength of the composite cement–dentin bond.

3.

Results

We calculated the equivalent mvM stress values in tissues and prosthetic restorations during masticatory simulation. Variable forces were transferred onto the occlusal surfaces of the examined teeth by the boluses. The highest stress values in the structures of the examined lower teeth and restorations occurred in the final closing phase of mastication during teeth clenching (Table 2). Similarly, the highest contact stress values in the luting cement–tooth tissue interface occurred at the time of maximum intercuspation, and their values are presented in Table 3. During masticatory simulation, mvM stress values did not exceed the tensile strength of any individual material in any model. In the intact tooth model (Model A), maximum stress values (10.7 MPa) were located in the enamel of the central groove. In dentin, mvM stress was concentrated at the cervical area and achieved a value of 3.4 MPa (Table 2). In tooth Model B with endocrown, maximum mvM stress values of 2.6 MPa were recorded in the distal region of the prepared pulp chamber and were 23% lower than in the intact tooth (Model A) (Fig. 2a). In the ceramic endocrown, mvM stress did not exceed 16.5 MPa and was concentrated on the functional cusp of the endocrown (Fig. 2b). In the luting resin cement, equivalent stress values around the distal region of the endocrown reached 1.8 MPa (Fig. 2c) (Table 2). Contact stress values at the endocrown-tooth tissues interface did not exceed 1 MPa (Table 3; Fig. 2d and e). In the tooth with an FRC posts (Model C), equivalent stress values in dentin increased to 3.7 MPa and increased in relation to the Model B with endocrown (Table 2). The stress concentration in the dentin occurred under the crown shoulder, in the distal region of the tooth (Fig. 3a). The mvM stress values in the molar 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 FRC posts, the STWSR index did not exceed 0.018 (Fig. 3d). Contact tensile and shear stress values along the post and core-dentin

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Fig. 2 – Distribution of the equivalent stresses according to the modified von Mises (mvM) failure criterion and contact stresses 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 side view); (c) equivalent stresses mvM in resin composite luting cement (distal side view); (d) contact tensile and compressive stresses distribution between endocrown and dentin (distal side view) (contact tensile stresses are marked in blue color and their 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 indicates maximal shear stresses). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 3 – Distribution of the equivalent stresses according to the modified von Mises (mvM) failure criterion and contact stresses in molar tooth model with FRC posts, composite resin core and ceramic crown during the closing phase of the mastication cycle (MPa). (a) Equivalent stresses mvM distribution in dentin (distal side view); (b) equivalent stresses mvM distribution 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 compressive stresses distribution between post and dentin (mesio-lingual side view) (contact tensile stresses are marked in blue color and their values are negative; contact compressive stresses are marked in red and yellow color and their values are positive); (f) contact shear stresses distribution between post and dentin (mesio-lingual side view) (MX and red color indicates maximal shear stresses). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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

Modulus of elasticity (GPa)

Enamel Dentin Periodontium Cast NiCr post Glass fiber post

Crowns leucite ceramic Composite core Luting resin cement

Poisson’s ratio

84.1 18.6 0.05 188 EX = 37 EY = 9.5 EZ = 9.5 65.0 14.1 8.3

Tensile strength (MPa)

0.33 0.31 0.45 0.33 X = 0.34 Y = 0.27 Z = 0.27 0.19 0.24 0.35

Compressive strength (MPa)

11.5 105.5

384 297

710 RmX = 1200 RmY = 73 RmZ = 73 48.8 41 45.1

710 RcX = 1000 RcY = 160 RcZ = 160 162.9 293 178

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

Models of mandibular molars

Maximal stresses mvM (MPa) Enamel/Ceramic of restoration

A B C D

Intact tooth Tooth with endoctown Tooth with FRC post and resin composite cores Tooth with cast post and cores

Dentin

Posts

10.7 16.5 21.0

3.4 2.6 3.7

– – 0.18 STWSR

– 1.8 2.9

17.6

3.2

49.5

2.1

interface were higher than around endocrowns (Fig. 3e and f; Table 3). The application of a metal post and core (Model D) caused lower stress in the dentin, the ceramic crown and cement as compared to the stress noted in the dentin of the tooth with an FRC post (Table 2). Contact stress values at the metal posttooth tissue interface were also slightly lower in relation to Model C (Table 3). However, stress values in the tooth with the metal post continued to be higher than in the tooth with the endocrown restoration (Model B) (Table 2).

4.

Discussion

The present study showed that dentin mvM stress levels in tooth with an endocrown were smaller than in the intact tooth. It can be acknowledged that rigid ceramic endocrowns reinforce tooth structures. Simultaneously the mvM stress levels in endocrown did not exceed the ceramic tensile strength [31]. During physiological loading, ceramic endocrowns in molars should not fail. These results are convergent with FEA studies by Lin et al. [35], in which calculations showed

Resin composite luting cement

that stress levels in teeth with endocrowns were lower than in teeth with prosthetic crowns [36]. Authors have concluded that endocrowns and conventional prosthetic crowns should demonstrate similar longevity in the oral cavity [37]. It was confirmed by clinical research. During a 5-year clinical follow-up period, 87.1% of endocrowns in molars successfully performed their function [38]. Other studies report a 5-year failure rate of 9.7% for ceramic reconstructions on non-vital teeth [39]. Taking into consideration the strength and longevity of endocrowns, minimal invasive preparation of tooth structures and no roots damage, these restorations are recommended to use in molars. Equivalent stress levels in the dentin of molars restored with posts and cores and ceramic crowns were higher than stress levels in the tooth with the endocrown, as well as stress levels in the intact tooth. The highest mvM stresses in dentin and crown occurred in molar restored with FRC posts. This type of restoration seems to be the least beneficial in molar teeth. According to Morgano [40], composite posts and cores do not reinforce the structure of endodontically treated teeth, but only ensure retention for the supragingival part. Biacchi and Basting [41] found that molars with endocrowns are

Table 3 – Maximum values of contact tensile, compressive, shear stresses in cement–dentin adhesive interface under various restorations in molars (MPa). Model

B C D

Models of mandibular molars

Tooth with endoctown Tooth with FRC post and resin composite cores Tooth with cast post and cores

Contact stresses (MPa) Compressive

Tensile

5.9 9.0

0.4 1.6

Shear 0.9 1.7

8.3

1.4

1.1

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more fracture resistant than teeth restored with FRC posts and cores and ceramic crowns. On the other hand, experimental strength study by Forberger and Göhring [42], have shown no significant differences between teeth restored with posts and endocrowns 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), unlike incisors [2]. According to Shillingburg et al. [43], a loaded tooth can be compared to a cantilever with the rotation axis located at the cervix. Masticatory forces are applied at an oblique direction to cusps and lever the restoration. The lever-arm of forces is longer (approx. 10.5 mm) than in incisors (6–7 mm). According to the level equilibrium formula, smaller forces are exerted on restorations in molars than in incisors. In addition, the mean area of the endocrown-molar tooth interface is 60 mm2 and is 2 times higher than in incisors (30 mm2 ) [2]. Smaller lever forces exerted on restorations and good bonding strength between endocrowns and tooth structures make these restorations possible to apply in molars. However, damaged anterior tooth crowns should be preferably restored with posts and cores. Results from Rathke et al. [44] studies suggest that the tensile strength of the bond between Variolink II cement and dentin is 29.9 MPa. In the present study, contact stress levels around any of the investigated restorations were not higher than 1.6 MPa, and so were far from exceeding the bonding strength of the cement with tooth tissue (Table 3). Contact stress levels around endocrowns were 4 times lower than around FRC posts and cores, while shear stresses were 2 times lower. In light of the present study and assuming that the endocrown in a molar tooth is made from ceramics without artifacts and is ideally bonded to tooth tissue, it should neither become damaged nor debond under physiological loads in the oral cavity. However, the most common failures affecting extensive ceramic restorations in molars are porcelain fractures or microleakage [42]. In clinical practice, effective bonding between ceramics and teeth depends on multiple factors. Adhesive cementation of glass ceramics requires etching its surface [45], silanization [46], applying bonding systems [47] and ensuring appropriate treatment of the enamel and dentin surface [48]. Any contamination of the surfaces to be bonded (with saliva, blood) or procedural errors prevent good adhesion from being achieved. In addition, bond strength between ceramics and tooth tissue decreases over time as an effect of periodical loads and temperature changes [49,50]. These phenomena are essential bearing in mind the failures that occur when restoring teeth with endocrowns.

5.

Conclusions

Within the limitations of this study during masticatory simulation:

1. Ceramic endocrowns in molars caused the lowest mvM stress levels in dentin compared to posts and cores. Molars restored with endocrowns are less prone to fracture than those with posts.

2. Under physiological loads, ceramic endocrowns ideally cemented in molars should not be demaged or debonded. Endocrowns may be used to restore molars. 3. The highest equivalent stresses occurred in molar restored with FRC post. The unfavorable molar reconstructions in biomechanical terms are an FRC posts with a composite cores.

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