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

Abstract

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), 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.

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 . 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 . This involves a risk of accidental root perforation .

Currently, due to the development of adhesive methods, it is possible to reconstruct damaged posterior teeth with intracoronal restorations – endocrowns . 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 . Apart from adhesion, retention of ceramic crowns is based on machromechanical fixation in the pulp chamber . Strong bonding between ceramics and tissue using composite luting cements increases the fracture resistance of the restorations , and consolidates and stabilizes weakened tooth structures at the same time . 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.

Materials and methods

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) . 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 cross-sections 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 . A 0.2 mm periodontal ligament was modeled around the roots ( Fig. 1 a). The lower molar was anatomically inclined 15 degrees lingually and 8 degrees anteriorly . 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. 1 a).

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.

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. 1 b). 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 . 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. 1 c). 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).

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.

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 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 . Opposing teeth were separated vertically. A 1 mm thick bolus was inserted between them with a Young’s modulus value of 27.57 MPa , 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 . 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 . The buccal cusps of the lower tooth were glided through blouses along the occlusal surfaces of the upper teeth, thereby grinding the bolus ( Fig. 1 e) .

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. 1 c) or a nickel-titanium alloy (Model D) ( Fig. 1 d). 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 , dentin , periodontal ligament , ceramics , nickel-chromium alloy , composite luting cement and core composite . 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) . The compressive and tensile strength values were assumed for enamel (11.5 MPa, 384 MPa) , dentin (105.5 MPa, 297 MPa) , nickel-chromium alloy (710 MPa) , FRC (1200/73 MPa, 1000/160 MPa) , core composite resin (41, 293) , ceramics (48.8 MPa, 162.9 MPa) and composite luting cement (45.1 MPa, 178 MPa) .

Table 1
Data of materials used in models of molars.
Material Modulus of elasticity (GPa) Poisson’s ratio Tensile strength (MPa) Compressive strength (MPa)
Enamel 84.1 0.33 11.5 384
Dentin 18.6 0.31 105.5 297
Periodontium 0.05 0.45
Cast NiCr post 188 0.33 710 710
Glass fiber post E X = 37 ν X = 0.34 R mX = 1200 R cX = 1000
E Y = 9.5 ν Y = 0.27 R mY = 73 R cY = 160
E Z = 9.5 ν Z = 0.27 R mZ = 73 R cZ = 160
Crowns leucite ceramic 65.0 0.19 48.8 162.9
Composite core 14.1 0.24 41 293
Luting resin cement 8.3 0.35 45.1 178

Analysis mode

The study used finite element analysis FEA software (ANSYS v. 10; ANSYS Inc., Canonsburg, PA, USA) . 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 . 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 . 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.

Materials and methods

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) . 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 cross-sections 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 . A 0.2 mm periodontal ligament was modeled around the roots ( Fig. 1 a). The lower molar was anatomically inclined 15 degrees lingually and 8 degrees anteriorly . 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. 1 a).

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.

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. 1 b). 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 . 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. 1 c). 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).

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.

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 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 . Opposing teeth were separated vertically. A 1 mm thick bolus was inserted between them with a Young’s modulus value of 27.57 MPa , 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 . 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 . The buccal cusps of the lower tooth were glided through blouses along the occlusal surfaces of the upper teeth, thereby grinding the bolus ( Fig. 1 e) .

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. 1 c) or a nickel-titanium alloy (Model D) ( Fig. 1 d). 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 , dentin , periodontal ligament , ceramics , nickel-chromium alloy , composite luting cement and core composite . 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) . The compressive and tensile strength values were assumed for enamel (11.5 MPa, 384 MPa) , dentin (105.5 MPa, 297 MPa) , nickel-chromium alloy (710 MPa) , FRC (1200/73 MPa, 1000/160 MPa) , core composite resin (41, 293) , ceramics (48.8 MPa, 162.9 MPa) and composite luting cement (45.1 MPa, 178 MPa) .

Nov 25, 2017 | Posted by in Dental Materials | Comments Off on 3D-Finite element analysis of molars restored with endocrowns and posts during masticatory simulation
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