Stress Analysis through Finite Element Study in Teeth Reconstructed with Post and Core and Crown

Summary

This study aims, with a method different from those commonly used, to contribute to the controversial issue of "cervical sealing" and the problem of the manufacturing material of posts. To evaluate the distribution of stresses on the remaining dentin, determined by different preparations of the prosthetic margin and the construction materials of the posts, Finite Element Analysis was used.

The materials themselves, which are very rigid and fracture-resistant (steel), can be dangerous because they concentrate stresses on narrow, limited, and very deep dentinal areas. For the prefabricated posts, the distribution of stresses appears more favorable.

The circular bevel reduces stresses in the apical areas of the post, increasing them in the cervical areas.

A narrow and short post with a layer of cement interposed between it and the dentin ("passive post") places very high stress peaks in the thickness of the cement in the middle third of the canal.

By replacing the gold post with materials that have mechanical characteristics similar to dentin, the internal areas of the root canal are free from stress peaks: these are completely located within the thickness of the dentin of the middle third of the canal, saving the critical interface zones between two materials.

Abstract

Introduction

Techniques for the restoration of endodontically treated teeth have been the subject of discussion by researchers for many years. The Finite Element Analysis (FEA) was used to determine stress distribution on residual dentin caused by different types of prosthetic margin design and by post construction materials. FEA is a mathematical model that allows complex structures to be divided into smaller segments with specific properties. Various loading conditions can be applied to the model and stress distributions plotted with a computer. This method provides detailed stress information concerning a nonhomogeneous body such as a tooth.

Materials and methods

Five dimensional models of an upper central incisor were created using the data of Wheeler. These models were the tooth's buccolingual cross sectional representation. All models included dentin with guttapercha, periodontal ligament, cortical and spongeous bone, a post and a crown.

Materials were homogeneous and isotropic with linear elastic behaviour. Mechanical properties correspondent to those described in the literature.

Three different force directions were applied to each model: F1 was applied to simulate a facial trauma; F2 to simulate a vertical force upon the incisor angle; F3 to simulate the masticatory force. All forces were assumed to be of 10 N acting uniformly across a thickness of 1 mm.

Models A and B simulate different types of prosthetic margin design (90° shoulder; 3.5 mm bevel). Model C simulates a 90° shoulder with a 50% longitudinal and axial reduction of the gold post (“passive post”). Models D and E simulate a 90° shoulder, the former with steel post and core, the latter with post and core made of a hypothetical material having dentin-like mechanical characteristics.

The distribution of normal forces in the principal and Von Mises directions were calculated using the SuperSap software for finite elements.

Results

Models A and B: model B (bevel) distributed the stress over a more extensive area; peaks stress in the medium third and in apical dentin were reduced by 25% and 12% compared to model A (a 90° shoulder).

Model C: peak stress occurred in the short cement area between dentin and post.

Model D: very high peak stress in the medium third of the root canal on the interfacing area between post and dentin.

Model E: most favorable, since peak stress occurred in the central area of the residual dentin thickness of the medium third of the inner canal areas. Interfacing areas showed no stress peaks.

Conclusions

This study shows that in endodontically reconstructed teeth extremely rigid materials (steel and gold) should be replaced by materials having the same mechanical properties as dentin.

A circular level is advantageous because it distributes stress over a more extensive dentinal area.

A “passive post” is not advantageous because all stress peaks appear in the short cement area between dentin and post.

Introduction

The techniques for restoring endodontically treated teeth have been the subject of countless discussions and research for many decades. Various studies have been conducted to identify methods that make the root-post-prosthetic reconstruction complex more resistant to the stresses caused by normal masticatory load and potential trauma. In recent years, particular attention has been paid to the shape of endocanal posts (or core posts), their length or width, and their resistance to tensile and oblique loads. As a clinical consequence of this research, there has been a general trend to restore the canal space left empty by endodontic treatment with very rigid and resistant materials, instead of seeking materials with mechanical characteristics as similar as possible to dentin. There has also been little attention to the tooth as a whole, often neglecting the effect of the coverage it receives. The design of the prosthetic margin of this category of teeth has received limited attention in the literature. These issues have been studied in various works through mechanical simulations on extracted teeth subjected to load and with photoelastic models: the results are quite contrasting.

This study aims, with a methodology different from those commonly used, to contribute to the controversial issue of "cervical sealing" and regarding the problem of the material used for manufacturing pins. Finite Element Analysis (FEA) is used, a numerical method of stress analysis that is not widely used in dentistry.

The finite element analysis method relies on a mathematical model that approximates the geometry of the object to be created. The latter is divided into a finite number of small elements, with 3 or 4 nodes, each with a separate description of the displacement field (and therefore of the stresses and strains). Various loading conditions are applied to the model, and the constraints are modeled by appropriate boundary conditions. The equations, derived based on linear elastic behavior and the mechanical characteristics of the materials, are solved with complex computing algorithms using personal computers. The advantage of this methodology is to provide detailed information on the stress occurring in a non-homogeneous body like the tooth.

This type of analysis was introduced by Turner and is used in mechanical, thermal, electromagnetic simulations, and in some fields of medical biomechanics research.

In the field of endodontically treated teeth, this methodology has been used, albeit in a limited number of studies, to evaluate the internal stress of roots housing different shaped posts with normal or varied supporting tissue levels.

This work aims to evaluate the influence of the prosthetic margin preparation on the distribution of stresses on the remaining root dentin. Furthermore, using this analysis system, it aims to assess whether the mechanical characteristics of the material used to fabricate the post can favorably change the resistance of this category of teeth.

Materials and Methods

Starting from a two-dimensional model of a maxillary central incisor (according to Wheeler's data), 5 different models were created representing its vestibulo-palatal midsection and measuring 24 mm in length. All include the root canal with dentin and gutta-percha in the apical 4 mm, periodontal ligament, spongy bone, and cortical bone. A reconstruction of the internal part of the root canal type post was designed (with a 12° inclination): the coronal area was restored with a gold crown (Fig. 1).

All materials are considered homogeneous, isotropic, and with linear elastic behavior. The mechanical properties of the materials are those commonly used in the literature (Tab. 1). The thickness of the cement between the post and dentin and between the post and crown is considered negligible due to the small thickness and for limits imposed on the complexity of the model.

Three different loading force directions were applied to each model: F1 simulates a traumatic force acting at the center of the crown, horizontally and vestibularly to it; F2 is a vertical force acting at the incisal angle: F3 represents the masticatory load and is at a 45° palatal alignment with respect to the incisal angle. All forces act uniformly through a thickness of 1 mm and have an intensity of 10 Newtons (1 Kgf).

The apical bone at the apex is assumed to be completely fixed with constraints that prevent any movement. An IBM personal computer with an Intel 486DX2-66 microprocessor and a finite element calculation program, SuperSap (Algor, Pittsburgh), was used.

The midsection in the vestibulo-palatal direction of the upper central incisor was studied.

The distributions of normal stresses in the principal directions and Von Mises stresses, commonly used in engineering, were calculated. From these distributions, the maximum and minimum values of the stresses were derived.

Two models simulating two different types of prosthetic margin preparation designs (90° shoulder, bevel 3.5 mm long with 12° inclination) have been prepared. They present the same reconstruction (gold post and crown) (models A and B) (Figs. 1-2).

These two types of prosthetic margin designs were chosen to provide an original contribution to the controversial issue of the effect of "cervical encirclement." In model C, which has a prosthetic margin preparation design identical to model A (90° shoulder), the influence of longitudinal and axial reduction by 50% of the gold post has been simulated and calculated (Fig 3). This model was chosen to verify, with this methodology, the results of an interesting approach to these issues ("passive post").

Models D and E also simulate a preparation of the prosthetic margin with a 90° shoulder, but they have different characteristics of the material used for the stump pin: model D, steel; model E, hypothetical material with mechanical properties equivalent to dentin.

Results

In a tooth treated endodontically and reconstructed with a post and crown, a bevel of 3.5 mm with an inclination of 12° (model B) results, compared to a shoulder preparation at 90° (model A), in a better distribution of stresses, particularly reducing stress peaks in the areas of apical dentin at the post by 12% and in the areas of dentin in contact with the post in the middle third of the canal by 25%. The distribution of stresses appears to encompass much larger dentinal areas and additionally loads the area of dentin beneath the bevel more. This different distribution of stresses can be evaluated in the two models subjected to traumatic force (F1) and masticatory force (F3) (Figs. 4, 5, 6, 7). These quantitative data are consistent with our previous research that used the finite element analysis method and with a study through in vitro mechanical simulations. The vertical force (F2) gives comparable results in all five different models studied: not providing useful information for the purposes of this research, it is not examined here.

If in the model to be subjected to simulated load (forces F1 and F3), the post is reduced by 50% both axially and transversely (passive post, model C) and the space between the post and dentin is filled with a material (cement) that has the same mechanical characteristics as dentin (Young's modulus and Poisson's coefficient), very high stress peaks are concentrated in the middle third of the canal in the wide area of cement that lies between dentin and post. This area shows stress values that are 200% higher compared to models A and B (Figs. 8, 9).

Maintaining the preparation of the prosthetic margin with a 90° shoulder, variations in the mechanical characteristics of the material used to construct the post have been simulated. Compared to a traditional gold post (Young's modulus: 98 GPA; Poisson's coefficient: 0.33), if it is made of steel (210 GPA; 0.30 Poisson's coeff.) (model D), we have a purely unfavorable situation. The applied forces (FL and F3) produce stress peaks with very high values in the dentin areas of the middle third and apical to the post along the entire interface area between the post and dentin (compared to the traditional gold post, there is an increase in stress values in these two areas of 100% and 30% respectively) (Figs. 10. 11).

If the post is constructed with a material that has the same mechanical characteristics as dentin (18.6 GPA; 0.31 Poisson's ratio) (Model E), the stress peak, for forces F1 and F3, is located in the central area of the remaining dentin thickness of the coronal third and middle of the canal. The more internal areas are free from stress peaks. This is the most favorable situation among those studied as the stress peak is entirely located in a more external area of root dentin compared to the other models. There are also no stresses in the critical interface area between different materials (Figs. 12, 13).

In this type of analysis of the tooth's cross-section, there is a maximum representation of the post simultaneously with a minimum representation of the dentin: the post is therefore overrepresented. This data is important for better understanding the results of this two-dimensional study.

Discussion conclusions

This study can provide clinical guidelines for the reconstruction of elements treated endodontically. The use of materials to reconstruct the space left empty by endodontic therapy should probably be reconsidered: materials that are very resistant to fracture and therefore very rigid (for example, steel) can be dangerous because they concentrate stresses on narrow, limited, and very deep dentinal areas. Similar considerations can be made for traditional gold posts, although the distribution of stresses appears more favorable compared to the previous case. Preserving even a small amount of cervical dentin, in order to achieve a cervical collar, seems advantageous. The circular bevel allows for better distribution of stresses, decreasing them in the apical areas of the post and increasing them in the cervical areas.

A narrow and short gold post with a thick layer of cement interposed between it and the dentin (a "passive" stump post, which has a cement with mechanical characteristics as close as possible to dentin) does not seem advantageous because it critically places stress peaks within the thickness of the cement in the middle third of the canal.

The replacement of the traditional gold post with a material that has mechanical characteristics similar to dentin appears to be the best solution for the restoration of this category of teeth. The internal areas of the root canal are free from stress peaks: these are entirely located within the thickness of the root dentin in the middle third of the canal, thus sparing the critical interface zones between the two materials.

Computer simulation with stress analysis of various models of endodontically treated teeth therefore indicates new avenues for development in dental material research.

The reconstruction of the endodontically treated tooth with a steel or gold post seems to be abandoned in favor of materials that have mechanical characteristics as close as possible to dentin. A restoration of this type of the internal part of the root canal, in turn covered by a traditional gold-resin or gold-ceramic crown, seems to offer significant advantages. Cervical reinforcement, if feasible, can provide further benefits for a longer lifespan of these elements.

Authors: Giovanni Cavalli, Pio Bertani, Paolo Generali

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