Three-dimensional finite element analysis of molars with thin-walled prosthetic crowns made of various materials

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1 d e n t a l m a t e r i a l s 2 8 ( ) Available online at jo u rn al hom epa ge : Three-dimensional finite element analysis of molars with thin-walled prosthetic crowns made of various materials Beata Dejak a,, Andrzej Młotkowski b, Cezary Langot a a Department of Prosthetic Dentistry, Medical University of Lodz, Poland b Department of Strength of Materials and Structures, Technical University of Lodz, Poland a r t i c l e i n f o Article history: Received 1 April 2011 Received in revised form 24 November 2011 Accepted 24 November 2011 Keywords: Zirconia crowns Leucite-reinforced ceramic crowns Gold alloy crowns Resin composite crowns Strength of molars 3D finite element method Simulation of mastication Contact stresses at a cement tooth adhesive interface Modified von Mises failure criterion a b s t r a c t Objectives. The aim of the study was to compare the strength of thin-walled molar crowns made of various materials under simulation of mastication. Methods. Five 3D FE models of the first lower molar with the use of contact elements were created: intact tooth; tooth with a zirconia crown; tooth with a porcelain crown; tooth with a gold alloy crown and tooth with a composite crown. The computer simulations of mastication were conducted. For the models, equivalent stresseswere calculated using the modified von Mises failure criterion (mvm). Contact stresses at the adhesive interface between the cement and tooth structure under the crowns were analyzed. Results. Equivalent stresses in the crowns, did not exceed the tensile strength of their material. The mvm stresses in resin cement under the zirconia crown were 1.3 MPa, and under the composite crown they increased over 6 times. The tensile and shear contact stressesunder the stiff crowns (ceramics and gold alloy), were several times lower than those under the composite one. The maximum mvm stresses in the tooth structure for the zirconia crown were only 2.8 MPa, whereas for the composite crown were 6.4 MPa. The higher elastic modulus the crown was, the lower the equivalent stresses occurred in the composite luting cement and in the tooth structures. Also contact stresses decreased with the increasing stiffness of the crowns. Significance. Under physiological loads, the thin-walled crowns perfectly luted to molars, made of zirconia ceramic, gold alloys and composite resin are resistant to failure. Prosthetic crowns made of stiff materials are less prone to debonding than those made of composite resin. Prosthetic crowns made of a material with a higher elastic modulus than enamel will strengthen the dental structures of molar teeth Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. 1. Introduction For many years molar prosthetic crowns were fabricated of metal alloys. This is especially true of high noble alloy crowns which were once considered the gold standard in prosthodontic reconstruction of posterior teeth [1]. Long-term observation confirms good performance of gold alloy crowns in clinical practice [2 4]. In recent years metal crowns became less popular purely because of esthetics and rising gold prices. More and more frequently, metal-free ceramic crowns are now used as an alternative to gold alloy restorations. Corresponding author at: Department of Prosthetic Dentistry, Medical University of Lodz, Ul. Pomorska Str. 251, Lodz, Poland. Tel.: ; fax: address: bdejak@poczta.onet.pl (B. Dejak) /$ see front matter 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi: /j.dental

2 434 d e n t a l m a t e r i a l s 2 8 ( ) All-ceramic crowns often are made of leucite-reinforced ceramic [5]. This types of glass ceramic ensures high esthetics and biocompatibility, but it is brittle (fracture toughness K 1C value of 1.3 MPa*m 0.5 ) [6] and has low flexural strength ( MPa) [7,8]. Glass ceramic materials can perform successfully in the anterior region but the long-term outcomes of posterior crowns are not so encouraging [9,10]. Zirconiabased ceramic is characterized by higher flexural strength (up to 1200 MPa) and fracture toughness (K 1C = 9 10 MPa*m 0.5 ) [11]. This material is indicated for posterior crowns but due to its high opacity requires veneering with glass ceramics. High strength zirconia core can be manufactured through CAD/CAM technology and subsequently veneered conventionally. According to in vivo observation, the clinical survival of zirconia-based restorations are comparable to metal ceramic restorations [12]. Recently, a new idea of milling solid monolithic (full-contour) zirconia crowns has occurred [13]. Prosthetic crowns can also be fabricated with composite resin. Although some authors recommend composite crowns as a permanent restoration [14,15], the application of these restorations should be limited to interim purpose [16]. This is due to its occlusal wear [17] especially in molar region [18], gradual loss of marginal adaptation [19], discoloration [20] and increased plaque accumulation [14]. Strength and durability of tooth restoration depends on many factors, such as crown material, its thickness, remaining tooth structure, crown bonding and quality of laboratory fabrication [21]. Standard preparation of a tooth for a monolithic crown requires equal hard tissue reduction of all axial walls and mm of occlusal clearance. Chamfer preparation of 0.8 mm is indicated for both all-ceramic and composite crowns [22,23]. Unfortunately, such preparation leads to 67.5% of tooth structure removal [24]. The authors tried to find the answers for the following questions. Can the amount of removed tooth structures be reduced? Which materials can be used for thin-walled posterior crowns to preserve a crown s strength and reduce marginal leakage during occlusal loading? Which crown s material provides the posterior tooth structure with the highest durability? The objective of this investigation was to compare the strength and adhesion of thin-walled molar crowns made of various materials under masticatory simulation. Our null hypothesis was that molars with crowns made of stiffer materials (zirconia ceramic and gold alloy) are more resistant to failure and debonding than restorations made of low elastic moduli materials (composite resin). Crowns made of materials with higher elastic modulus also better strengthen tooth structures under loads. 2. Materials and methods Double-layer impressions of upper and lower arch of a patient with normal occlusion using polyvinylsiloxane material (Express, 3M/ESPE, St. Paul, MN, USA) were taken. Occlusal registration in central and lateral positions of the mandible with wax (Aluwax Dental Products Co, Allendale, MI, USA) were recorded. Two lower and one upper working casts with separate dies (Girostone, Amann Girrbach GmbH, Pforzheim, Germany) were prepared. Using a laser scanner (Dental 3D Scanner D700, 3ShapeA/S, Copenhagen, Denmark) the occlusal surfaces of three die stone teeth were scanned: first lower molar and two opposing teeth (first upper molar and second premolar). The obtained scans were then processed with software (3Shape Dental Designer CAD; 3Shape A/S). Additional examinations of the first lower molar were made with computerized tomography (GXCB-500/i-CAT; Gendex Dental Systems, Des Plaines, IL, USA). Digital files with coordinates of the occlusal surface points of the examined teeth and the points on the enamel dentin pulp junction of the lower molar (obtained from the CBCT), in horizontal layers (every 1.0 mm), were introduced into the finite element analysis FEA software (ANSYS v. 10; ANSYS Inc., Canonsburg, PA, USA). These points were connected with splines, and the cross-sections of the molar were created. Connecting these cross-sections allowed for the creation of a solid model of the first lower molar (Fig. 1a). The cervico-occlusal length of the crown was 7.5 mm, the bucco-lingual diameter was 10.5 mm, and the length of the roots was 14 mm [25]. A 0.2 mm periodontal ligament was modeled around the roots. The lower molar tooth was anatomically inclined 15 degrees lingually and 8 degrees anteriorly [26]. The lower molar stone model was prepared for a thinwalled crown with a mm chamfer margin. The occlusal surface was then reduced by mm. The axial walls were prepared with 6 of inclination. The prepared tooth was scanned as previously. The coordinates of the surface points Fig. 1 Models of first mandibular molar tooth with roots and periodontium: (a) intact tooth, (b) tooth with crown preparation, and (c) tooth with all-ceramic crown.

3 d e n t a l m a t e r i a l s 2 8 ( ) Fig. 2 Models of first mandibular molar tooth with fragments of antagonist s teeth (model A): (a) in lateral position with bolus between the teeth, (b) during the closing phase of the mastication cycle, (c) deformation of bolus, and (d) maximal pressures exerted on tooth occlusal surfaces during closing phase of mastication cycle. were introduced into the ANSYS application, and the surfaces of the prepared crown of the molar were generated in the software (Fig. 1b). The model A of the molar was cut with the above-mentioned surface coordinates. The cut solid, forming a prostethic crown with an additional 0.1 mm thick cement layer was added to the tooth model, thus a 3D model of the first molar with a prosthetic crown was created (Fig. 1c). It was assumed that the crowns were perfectly luted to molar teeth. The upper and lower teeth models were 3D positioned in lateral occlusion using reference points from the scan of the lateral occlusal record and separated vertically. A cuboid bolus of 1 mm thickness was placed between the teeth. The molar was located in a system of coordinates such that the Z-axis indicated the mesial surface of the tooth, the X-axis the lingual surface, and the Y-axis was oriented upward. The models were fixed in the nodes on the upper surface of the maxillary tooth crown and on the external surface of the periodontium around the mandibular molar roots. In this way the computer 3D model A of an intact lower molar tooth and two opposing teeth during the initial phase of chewing movement was created (Fig. 2a). The closing phase of mastication was simulated. Then the nodes on the external surface of the periodontium were displaced. The lower molar tooth was moved vertically upwards, medially and mesially toward the upper teeth until maximum intercuspation was achieved. The vertical movements were chosen to produce a maximum of 200 N reaction force in Y direction for each model. The buccal cusps of the lower tooth were being glided through the boluses along the occlusal surfaces of the upper teeth (Fig. 2b), thereby grinding the bolus (Fig. 2c). On the surface of the lower molar variable pressure was exerted. It reached the highest value at the end of closing phase on the functional cusp (Fig. 2d). It was assumed in the study that prosthetic crowns were made of either zirconia-based ceramic (model B), leucitereinforced ceramic (IPS Empress Ivoclar, Vivadent AG, Schaan, Lichtenstein) (model C), gold alloy type III (model D) or composite resin (Paradigm MZ100, 3M/ESPE, St. Paul, MN, USA) (model E). The crowns were then luted with composite resin cement (Variolink II, Ivoclar, Vivadent AG, Schaan, Lichtenstein). The values for Young s modulus and Poisson s ratio were entered for enamel [27], dentin [28], periodontium [29], zirconia-based ceramic [30], leucite-reinforced ceramic [31], gold alloy [32], composite resin [33] and luting composite resin cement [34]. Data are listed in Table 1. A bolus, with an elastic modulus of MPa (similar properties to a nut) [35], but with a Poisson ratio of 0.45 (similar to a rubber) was used. The following values of ultimate tensile and compressive strength for enamel (11.5 MPa [36], 384 MPa [32]), dentin (105.5 MPa [37], and 297 MPa [32]), zirconiumbased ceramic (745 MPa and 2000 MPa) [38], leucite-reinforced ceramic (48.8 MPa and MPa) [39], gold alloy (457 MPa) [40], composite resin (54.4 MPa [41] and 448 MPa [42]), and composite resin cement (45.1 MPa and 178 MPa) [43] were entered. The models were considered to be linear, elastic, homogeneous, and isotropic but also to have different tensile and compressive strengths. To perform calculations, each tooth model was divided into a structural solid with 10-node elements (Solid 187). The pairs of bonded contact elements were used at the occlusal surfaces of the examined teeth and boluses. The coefficient of friction between the contact surfaces was assumed to be 0.2 [44]. The pairs of bonded contact elements Targe 170 and Conta 174 were used at the cement-tissue junction around the studied prosthetic crowns. In the A tooth model, 24,298 elements joined in the 35,176 nodes were used, whereas in the other models, there were 90,935 elements joined in the 121,582 nodes. Contact simulation of FEA was a nonlinear analysis that required the load and displacement to be applied in a number of steps. Automatic time stepping was applied in this analysis. For the lower first molar models with crowns made of different materials, the components of stresses were calculated using a simulation of masticatory force. Tooth structures, ceramics and composite resins are materials characterized by different tensile and compressive strengths. One of the criteria used to evaluate the strength of materials under compound stress states is the modified von Mises (mvm) failure criterion [45]. This criterion considers the ratio between the compressive and tensile strength: for example enamel is 33.4; dentin 2.8; zirconia-based ceramic 2.7; leucite-reinforced ceramic 3.3; composite resin 8.2; and composite luting cement 3.9 (Table 1). According to these criteria, the material will fail when the values of the equivalent stresses mvm exceed the tensile strength of the material. The results of the calculation are presented in the form of maps of stress distribution in the ceramic crown, luting cement and on the structures of the computerized molar models. In the study the local media of a region where there was the peak of stress were analyzed: in the occlusal

4 436 d e n t a l m a t e r i a l s 2 8 ( ) Table 1 Mechanical properties of material used in 3D FE models of mandibular molars with crowns made of various materials. Material Elastic modulus (GPa) Poisson s ratio Tensile strength (MPa) Compressive strength (MPa) Enamel Dentin Periodontium Gold alloy Zirconia based ceramic Leucite-reinforced ceramic (Empress, Ivoclar, Vivadent) Composite (Paradigm MZ 100, 3 m/espe) Cement (Variolink II, Ivoclar, Vivadent) Table 2 Maximum value of equivalent stresses according to modified von Mises (mvm) failure criterion in FE models of mandibular molars with thin-walls crowns made of various materials (MPa). Model Models of mandibular molars Stresses mvm (MPa) Crown Cement Enamel Dentin A Intact tooth B Tooth with zirconia crown C Tooth with leucite ceramic crown D Tooth with gold alloy crown E Tooth with composite resin crown surfaces and in distal, cervical regions. The maximum values of mvm stresses of the model materials were compared to one another and to their respective tensile strength. Compressive, tensile, and shear contact stresses at the luting cement dentin interface under the crowns were calculated. They were graphically depicted as maps on the contact surfaces between the restoration and dentin. 3. Results The highest values of the equivalent stresses according to the modified von Mises (mvm) failure criterion in the crowns and the lower molar tooth structures occurred in the final closing phase of mastication during teeth clenching. The values are presented in Table 2 and diagrams 1 3 (Fig. 5a c). Similarly, the highest contact stresses at the luting cement dentin interface under the crowns occurred at the time of maximum intercuspation (Table 3 and Fig. 5d). The higher the elastic modulus of the crown material was, the higher the values were of the equivalent mvm stresses in prosthetic crowns (Table 2 and Fig. 5a). The maximum mvm stresses focused on the occlusal surface of the crowns. In the zirconia crown the highest stress value (51.5 MPa) was observed under the distobuccal cusp (Fig. 3a). In the porcelain crown the maximum stresses concentrated on the same area although their value did not surpass 35.2 MPa. Whereas in the composite crown mvm stresses reached the value of 11.4 MPa in the central groove (Table 2 and Fig. 4a). In the cervical area mvm stresses were several time lower than on the occlusal surface (Fig. 5a). The equivalent stresses in the crowns were 14.5 times lower than the tensile strength of the zirconiabased ceramics. For gold alloy this ratio was 11.9, for composite resin 3.6, and for leucite-reinforced ceramics only 1.4 (Table 1). In none of the studied models did the equivalent stresses in the crowns exceed the strength of the materials of which they were made. The higher elastic modulus the crown was, the lower were the equivalent stresses that occurred in the resin luting cement (Table 2, Fig. 5b). In all cases those stresses concentrated under the functional cusps of the crowns. The lowest values (1.3 MPa) of mvm stresses were observed in the luting cement under the zirconia crown (Fig. 3b), while under the composite crown they increased over 6 times to 8.3 MPa (Fig. 4b). Furthermore contact stresses at the cement dentin interface decreased with the increasing elastic modulus of Table 3 Maximum values of contact tensile, compressive, shear stresses in cement dentin adhesive interface under crowns made of various materials (MPa). Model Models of mandibular molars Contact stresses (MPa) Tensile Compressive Shear B Tooth with zirconia crown C Tooth with leucite ceramic crown D Tooth with gold alloy crown E Tooth with composite resin crown

5 d e n t a l m a t e r i a l s 2 8 ( ) Fig. 3 Distribution of the equivalent stresses according to the modified von Mises (mvm) failure criterion in molar tooth model with thin-walled zirconia ceramic crown during the closing phase of the mastication cycle (MPa): (a) the crown, (b) resin composite luting cement, and (c) the tooth structure of first molar under the crown. the crown materials (Table 3 and Fig. 5d). The tensile contact stresses occurred along the axial walls of the crowns, reaching a value of 0.4 MPa under the zirconia crown, and 1.5 MPa under the composite crown. The contact shear stresses were 3.3 times higher under the composite crown than under the zirconia one (Table 3 and Fig. 5d). In the intact tooth model A, the maximum equivalent stresses (9.7 MPa) were located in the enamel of the central groove. In the dentin, mvm stresses were concentrated at the cervical area, obtaining a value of 3.4 MPa (Table 2). Among all the studied crown models, the lowest mvm stresses (2.2 MPa) in the dentin occurred under the zirconia crown in the central groove (Figs. 3c and 5c). Whereas under the composite crown, they increased over 2 times to 6.4 MPa (Fig. 4c). The higher the elastic modulus of the crown, the lower were the stresses that occurred in the dentin of central groove (Table 2 and Fig. 5c). In the dentin around the cervical area the mvm stresses were comparable in all investigated cases (Fig. 5c) 4. Discussion This study revealed that during masticatory force simulation, equivalent stresses in molar crown made of zirconia-based ceramics and gold alloy were several times lower than the tensile strength of these materials, whereas the value of mvm stresses in an all-ceramic crown was similar to the tensile strength of leucite-reinforced ceramic. Concentration of those stresses was observed on the inner surface of ceramic crown under the functional cusp. Therefore, the thin-walled crowns in posterior teeth made of zirconia, gold alloy and composite were able to withstand occlusal forces, while under the same forces, porcelain crowns can fail. This is in agreement with the fatigue testing results of Magne et al. [46], indicating that thin-walled leucite-reinforced ceramic molar restorations (1.2 mm occlusal thickness) failed under cyclic loading in 100% of cases, whereas the composite resin restorations resisted such failure. According to findings of Attia and Kern [47], the fracture load of adhesively luted all-ceramic leucite-reinforced crowns reached the value of N. The fracture resistance of zirconia-based ceramic crown is significantly higher than porcelain crowns and similar to PFM crowns [48,49]. The most commonly reported complication of a zirconia crown is chipping of the veneering porcelain [50]. It is for this very reason that led to the development of monolithic posterior zirconia crowns, without a veneering porcelain layer. The fracture resistance of 0.5 mm thick zirconia copings was 1110 N [51], and the use of such a crown will be favorable in view of hard tissue preservation. Unfortunately, zirconia s opacity, milky color and excessive wear of opposing teeth may be the limiting factors for its clinical application. Factorial analysis performed by Rekow et al. [21] showed that material and

6 438 d e n t a l m a t e r i a l s 2 8 ( ) Fig. 4 Distribution of the equivalent stresses according to the modified von Mises (mvm) failure criterion in molar tooth model with thin-walled resin composite crown during the closing phase of the mastication cycle (MPa) (a) the crown, (b) resin composite luting cement, and (c) the tooth structure of first molar under the crown. thickness of prosthetic crowns are of primary importance in stress magnitude. The higher the tensile strength of crown material, the thinner can be the crown s walls. Our results are in accordance with the study by Rekow et al. The higher the elastic modulus of the crown material was, the lower the equivalent stresses were that occurred in composite luting cement and contact shear and tensile stresses at cement dentin interface. It can therefore be presumed that in clinical conditions, all-ceramic and gold crowns will be more resistant to marginal microleakage than composite crowns. The work of Vanoorbeek et al. [52] confirmed that presumption, demonstrating a worse marginal fit and more frequent debonding of composite crowns than all-ceramic crowns after 3 years of function. During simulation of mastication, the mvm stresses in the tooth structures decreased with an increase in the elastic modulus of the crown material used. All-ceramic and gold alloy crowns make the teeth more resistant to damage than composite crowns. The study conducted by Rosentritt et al. [53] on fracture performance of 96 teeth restored with metal ceramic, alumina-based, and zirconia-based crowns demonstrated only one case of fracture. It is obviously impossible for a computer simulation to include all of the factors encountered in the oral environment. The applicability of FEA results to oral conditions depends upon, among other factors, the similarity between the shape, dimensions, material data, load application of the models, and the natural teeth. In this study, calculations were made on the 3D tooth models patterned after intact natural molars. It was assumed that the materials used in the models were linearly elastic, homogeneous, and isotropic, but they had different compressive and tensile strengths. Unfortunately, the properties of tooth structures are not homogeneous and are anisotropic like dentin (due to its capillary morphological structure) or enamel (due to its prismatic structure). Furthermore, during laboratory fabrication of prosthetic crowns some material artifacts can occur that were not taken into consideration in our study. Because of difficulties in numerical analysis the isotropic linear characteristic of the bolus was assumed. Applied load can significantly influence the outcomes of FEA studies. In the majority of tooth performance in vitro examinations, static loads were applied directly to the occlusal surfaces [54]. This was a considerable simplification of real occlusal forces. In our study the computer model was created on the basis of the natural interarch relationship (upper and lower teeth were 3D positioned using occlusal records). The 3D simulations of one cycle of bolus mastication with the use of contact elements on occlusal surfaces were performed. This innovative approach allowed us to reproduce complex and variable loads applied on a tooth during mastication and to investigate the 3D stresses in the teeth. In the examined models, bonded contact elements at the cement dentin interface were used. It allowed us to calculate contact tensile and shear stresses and to visualize their

7 d e n t a l m a t e r i a l s 2 8 ( ) Fig. 5 Graph of maximal stresses: (a) Graph 1. 1.Maximal mvm stresses in crowns made of various materials (MPa), (b) Graph 2. 2.Maximal mvm stresses in dentin under crowns made of various materials (MPa), (c) Graph 3. 3.Maximal mvm stresses in luting cement under crowns made of various materials (MPa), and (d) Graph 4. 4.Maximal contact stresses under crowns made of various materials (MPa). distribution at the whole cement tooth structure interface. Thanks to application of this method, potential debonding areas were able to be assessed. Our hypothesis was therefore partially proven. Prosthetic molar crowns made of stiffer materials (ceramics and gold alloy) are less prone to debonding than those made of low elastic modulus materials (composite resin). Crowns made of higher elastic modulus materials protect tooth structures from damage better than those made of low elastic modulus materials. Such a direct dependence was not observed when studying just a crown s strength. Damage of a crown is determined by the relation of stresses generated in the material to their tensile strength. For that reason, a porcelain crown is prone to failure because high stresses occur in it but tensile strength of a leucite-reinforced ceramic is low. 5. Conclusion Within the limitations of this study it can be concluded that: 1. Under physiological loads, the thin-walled crowns made of zirconia ceramic, gold alloys, and composite resin are all resistant to failure. The leucite-reinforced ceramic molar crowns are more susceptible to damage. 2. Prosthetic crowns made of low elastic modulus materials (composite resin) are more prone to debonding than those made of stiffer materials (ceramics and gold alloy). 3. Prosthetic crowns made of a material with a higher elastic modulus than enamel will strengthen the dental structures of molar teeth. Ceramic and gold alloy crowns protect tooth structures from damage better than composite resin ones. r e f e r e n c e s [1] Small BW. Material choice for restorative dentistry: inlays, onlays, crowns, and bridges. Gen Dent 2006;54: [2] Wagner J, Hiller KA, Schmalz G. Long-term clinical performance and longevity of gold alloy vs. ceramic partial crowns. Clin Oral Investig 2003;7:80 5. [3] Christensen GJ. Longevity of posterior tooth dental restorations. J Am Dent Assoc 2005;136: [4] Encke BS, Heydecke G, Wolkewitz M, Strub JR. Results of a prospective randomized controlled trial of posterior ZrSiO(4) ceramic crowns. J Oral Rehabil 2009;36:

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