Abstract
Objectives
The aim was to evaluate the stress distribution, comparing an anterior sound tooth with post-endodontic restored teeth under mechanical loading.
Methods
A three-dimensional finite element analysis was performed based on micro-CT scan images of a maxillary canine. Twelve models with different crown properties and post-configurations were simulated. The model of the maxillary sound canine was also created and investigated. A load of 50 N was applied at a 63° angle with respect to the longitudinal axis of the tooth on the palatal surface of the crown. Principal stresses were registered. Numerical FEA results were statistically analyzed to show the influence of post shape and crown materials.
Results
All analyzed models (M1–M12) exhibited a high stress gradient, due to different material stiffnesses present at the various interfaces. The most uniform mechanical behavior of the investigated models, very similar to sound tooth, was the combination of a composite crown and a cylindrical or conical fiber-glass post.
Significance
The results of this study facilitate informed clinical choice between possible material combinations in restorative procedures of endodontically treated anterior teeth.
1
Introduction
Endodontically treated teeth must be adhesively restored as quickly as possible not only to preserve sealing from coronal access but mainly to reduce fracture risk under functional loading . Operative endodontic procedures cause a decrease of rigidity of the tooth due to the pulp chamber opening and to the loss of one or both proximal ridges in posterior teeth . Endodontically treated teeth, however, can sometime be efficiently restored by adhesive techniques without a post. Fracture resistance depends on the adhesive material combination , type of restored tooth and shape of the residual cavity .
Posts have been considered to reinforce weakened teeth when one or two cavity walls remain particularly in larger posterior teeth where compressive forces are present . Also anterior endodontically treated teeth which are adhesively restored with a veneer seem to show in vitro a higher fracture resistance when a fiber-post is cemented in the root . Other authors suggest that the use of post materials conflict with the mechanical resistance of teeth because posts mismatch the stiffness of residual dental structure. When a post is adhesively placed in the root canal it can create a not natural mechanical condition compared with a sound tooth. This is mainly evident looking at the stress-strain redistribution by means of finite element analysis investigations .
Belli et al. showed that differences in mechanical behavior between a sound tooth and an endodontically treated anterior tooth are manifest when they are analyzed under loading. Numerical investigations showed that: (i) the number of interfaces in the restored system, (ii) the post modulus and shape, (iii) the cement thickness and modulus can play a relevant role in crack propagation and fracture of the root or in shock absorbance and stress redistribution within the system . Experimentally, a metallic post in combination with composite resin core had a lower fracture resistance value than a fiber post under static and fatigue loading . The cement layer alone or in combination with dental adhesives used to cement them cannot prevent this effect. Shock absorbance by use of low rigidity posts, such as glass or carbon fiber, may possibly reduce stresses, but it is hard to shun or to annul them completely under loading conditions or to recreate a stress distribution as in a sound tooth . This is particularly true in anterior teeth, where transverse forces play an important role with incisors and canines, more than compressive ones. In such restored teeth, factors such as the natural external and internal dentin diameters and the residual dentin thickness at different levels after the endodontic weakening and post space creation, can influence results on stress absorption.
Most investigations by FEA created one or more CAD models by taking information about the anatomy of anterior teeth from 3D external scanning of the teeth. Data on internal dentin thicknesses acquired from literature could recreate an idealized anterior tooth model without starting from true anatomical tissue information of a single human tooth for the single classes, canine, premolar, molar. This is particularly true without considering the size, the number and the shape of the root. It has been shown that dental micro-CT is the methodology able to produce a highly detailed 3D finite element model starting from a sound natural tooth X-ray scanning. Ausiello et al. confirmed this approach by recreating accurate dental volumes of enamel, dentin, pulp chamber and cement starting from micro-CT data.
The aim of the present investigation was to study the mechanical behavior of a maxillary canine adhesively restored by different material post and crown combinations, under functional loading by means of 3D finite element analysis.
2
Materials and methods
The present paper focuses on an upper human canine before and after endodontic treatment. The tooth was 25 mm long, with about 9.5 mm crown height.
The adopted procedure may be summarized as follows: first of all, the 3D CAD model of the sound canine was built-up starting from micro-CT scan images. Then, the restored tooth was modeled properly. Finally, numerical FEA simulations were performed to understand the influence of different post and crown materials in terms of stress distributions: 12 endodontically treated canine models, restored with different post and crown combinations, were built-up and analyzed. Numerical investigations were conducted under a transverse loading condition looking for the principal stress distribution. Numerical results were also compared with ones coming from the sound canine tooth.
To show the influence of post and crown materials, numerical FEA results were statistically analyzed. PARETO-ANOVA was adopted to calculate the contribution indexes of every factor.
2.1
3D CAD modeling
The sound canine tooth was digitized with a high resolution micro-CT scanner system (1072, SkyScan, Belgium), following the methodology adopted by from the scanning through the tessellated model.
A total of 951 slices were collected (image resolution: 1024 × 1024 pixels). As the aim of this study was just based on the macro-structure of the tooth, there was no need for all slices. Just 252 slices were properly required.
Image data sets were processed by using the ScanIP ® 3.2 module (Simpleware Ltd.). Here, by using image segmentation and filtering procedures, the 3D tessellated model of the tooth was created (see Fig. 1 a and b) .
Tessellated models were then converted into surfaces by means of blending operations through cross-sections ( Fig. 1 c–e).
Such operations were performed within SolidWorks ® 2010 (Dassault Systemes) CAD system. Here, the ScanTo3D ® add-in module was adopted to manage the tessellated geometry. Starting from cross-sections (created by intersecting the tessellated model and cut-planes), lofting surfaces were generated. Boolean operations were then introduced to assure the right congruence between interfacial boundaries at the root–crown interface .
Two different commercial post geometries were considered: a cylindrical shape (tip diameter: 1 mm; insertion depth: 7 mm – about 2/3 of the root length) and a conical shape (conicity: 6%; tip diameter: 1 mm; insertion depth: 7 mm – about 2/3 of the root length). Fig. 2 depicts the generated CAD models: (a) – treated tooth with conical post; (b) – treated tooth with cylindrical post; and, (c) – sound tooth.
2.2
FE modeling
A linear static structural analysis was performed to calculate the stress distribution in different restoration configurations. All numerical simulations were performed within Comsol Multiphysics ® 4.2 (by COMSOL AB), running on a DELL Precision T7400 workstation (WinXP 64bit, 24GB RAM, 2 Xeon E5420 quad-core processors).
The following assumptions were done:
- •
Dentin was assumed to be an elastic and isotropic material.
- •
Perfect bonding between crown and cement and between post and cement was considered. Perfect bonding was simulated within Comsol Multiphysics ® by defining congruent mesh nodes at the interfacial boundaries (by using the so-called “union assembly” feature): this assures that the same node is shared by two different boundaries and then the displacement fields are there identical.
- •
Rigid constraints at the level of the root (colored surfaces within Fig. 3 a) . Thus, bone tissue was here assumed to be perfectly rigid.
Fig. 3 (a) Load and boundary conditions. (b) Mesh model related to tooth preparation “M1”.
Mastication involves repeated cyclic forces that cause loading of the restored tooth. Literature shows that mastication loads vary greatly from one area of the mouth to another. As previously reported , average forces of about 800 N for male young adults and 600 N for female young adults have been recorded in the molar region. In the premolar region, occlusal forces range from 200 to 600 N. Forces less than 200 N, have been measured in the incisal region. Such a variation may be related to many factors, such as muscle size, bone shape, gender, age and degree of edentulism.
In the present work, a load of 50 N (63 angle degree with respect to the longitudinal axis of the tooth), acting on the palatal surface of the crown (see Fig. 3 a) was applied.
Material properties were derived from the literature . Table 1 reports adopted materials.
| Material | E 1 = E 2 | E 3 | G 13 = G 23 | G 12 = E 2 /[2(1 + ν 12 )] | ν 13 = ν 23 | ν 12 | Reference |
|---|---|---|---|---|---|---|---|
| Enamel | 84.1 | – | – | 0.30 | |||
| Dentin | 18.6 | – | – | 0.32 | |||
| Abutment | 5.2 | – | – | 0.22 | |||
| Cement | 5.1 | – | – | 0.30 | |||
| Zirconia core | 210 | – | – | 0.30 | |||
| Feldspathic ceramics | 69 | – | – | 0.30 | |||
| Composite | 16 | – | – | 0.30 | |||
| Fiber-carbon | 130 | – | – | 0.30 | a | ||
| Fiber-glass | 13.91 | 45.08 | 8.0 | 6.04 | 0.28 | 0.086 | a |
Two different post materials were simulated: fiber-carbon and fiber-glass. Notice that the fiber-carbon was assumed an isotropic material. Instead, the fiber-glass post was considered a transversely isotropic material . “E 3” corresponds to the Young’s Modulus along the longitudinal axis of the post. Finally, three different crown materials were taken into account: zirconia core, feldspathic ceramics and composite.
Table 2 reports the analyzed tooth preparations, obtained by combining different crown materials (F1) and posts, in terms of adopted materials (F2) and shapes (F3). Three levels (from 1 to 3) were assumed for factor F1, whereas, two levels (from 1 to 2) were considered for factors F2 and F3. The configurations “M13” (not showed in Table 2 ) corresponds to the sound tooth. A statistical PARETO-ANOVA analysis was conducted to establish the contribution indexes related to factors F1, F2 and F3.
| Tooth preparation | Crown (F1) | Post material (F2) | Post shape (F3) | Number of elements/nodes |
|---|---|---|---|---|
| M1 | 1 – Zirconia core | 1 – Fiber-carbon | 1 – Cylindrical shape | 268,931/46,486 |
| M2 | 1 – Zirconia core | 2 – Fiber-glass | 1 – Cylindrical shape | 268,931/46,486 |
| M3 | 1 – Zirconia core | 1 – Fiber-carbon | 2 – Conical shape | 250,207/43,337 |
| M4 | 1 – Zirconia core | 2 – Fiber-glass | 2 – Conical shape | 250,207/43,337 |
| M5 | 2 – Feldspathic ceramics | 1 – Fiber-carbon | 1 – Cylindrical shape | 268,931/46,486 |
| M6 | 2 – Feldspathic ceramics | 2 – Fiber-glass | 1 – Cylindrical shape | 268,931/46,486 |
| M7 | 2 – Feldspathic ceramics | 1 – Fiber-carbon | 2 – Conical shape | 250,207/43,337 |
| M8 | 2 – Feldspathic ceramics | 2 – Fiber-glass | 2 – Conical shape | 250,207/43,337 |
| M9 | 3 – Composite | 1 – Fiber-carbon | 1 – Cylindrical shape | 268,931/46,486 |
| M10 | 3 – Composite | 2 – Fiber-glass | 1 – Cylindrical shape | 268,931/46,486 |
| M11 | 3 – Composite | 1 – Fiber-carbon | 2 – Conical shape | 250,207/43,337 |
| M12 | 3 – Composite | 2 – Fiber-glass | 2 – Conical shape | 250,207/43,337 |
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