Stress Distribution in Radicular Dentin with Different Post and Core Materials: A 3D Finite Element Analysis

Abstract

This study aims to evaluate the stress distribution of polyetheretherketone (PEEK) and high noble alloy materials in a detailed 3D model of a central incisor using finite element analysis (FEA). A comprehensive 3D model incorporated the crown, crown cement, post and core, post cement, central incisor root, periodontal ligament (PDL), and bone. The PEEK and high noble alloy material properties were input into the model, and the FEA was performed using ABAQUS software. The results showed that while the stresses on the bone, root, and crown increased slightly with the PEEK compared to the high noble alloy, the difference was minimal and attributed to the PEEK’s reduced stiffness. This led to a higher load transfer to surrounding regions around the post. The factor of safety decreased from 16 to 10 when using PEEK, but this reduction was still within acceptable limits and reduced stress-shielding effects. In conclusion, while there was no significant difference in stress magnitudes and distributions between the PEEK and high noble alloys, the PEEK exhibited superior stress-shielding properties, which may offer an advantage in preserving the underlying tooth structure in post and core restorations.

1. Introduction

Dental caries is present in high percentages among people [1]. If dental caries is not controlled or treated, it progresses deeper into the pulp, leading to root canal therapy (RCT). After RCT, it is well known that dentin’s physical and physiologic properties change, with immature collagen experiencing a slight reduction in its levels [2]. Loss of dentinal fluids reduces Young’s modulus of elasticity and eventually causes the loss of the residual tooth structure [2]. Therefore, non-vital teeth are brittle and more susceptible to fracture than vital ones [3].

Posts are commonly used in fixed prosthodontics as restorations cemented into the intra-radicular space of root canal-treated teeth with insufficient remaining tooth structure. These posts are used to retain the core and cover it with a final crown to prevent further fracture. The remaining dentin is a significant factor in enhancing biomechanical performance and the longevity of post and core restorations [4]. Posts are designed to provide intracanal retention for core/crown restoration and distribute the applied load to a greater portion of the surviving coronal and radicular tooth structures. Furthermore, the material used for posts and their components influences the stress distribution within the restoration [5].

A decrease in the elastic modulus of post materials leads to a more favorable stress distribution within the radicular dentin, reducing the risk of excessive stress concentration [6]. In some cases, the tooth structure becomes compromised, and the ferrule effect and the conservation of sound radicular and coronal tooth tissue should be considered in the design to improve the restoration’s performance [3,7,8]. Ferrule design is crucial when preparing teeth for post and core restorations, as it minimizes the fracture risk in root canal-treated teeth [9,10]. A finite element analysis (FEA) study in 2017 examined how a ferrule design combined with specific post material shapes affected the mechanical performance of canine teeth. The study revealed that carbon fiber posts experienced more stress than quartz fiber posts, while the combination of ferrule and quartz fiber posts produced the most homogeneous stress distribution [11]. Another FEA study affirmed the importance of ferrule in weakened root-filled teeth, combined with post systems such as cast post and glass fiber post systems [12]. The cast post system without a ferrule resulted in higher stress concentrations within the root canal. Conversely, the fiber post system showed a more homogeneous stress distribution, similar to a sound tooth [12]. Another study used FEA to investigate the effects of pile materials on the stress distribution between remaining tooth tissue and fracture defects using different elastic moduli and cement materials [13].

The ferrule effect is defined as the remaining supragingival tooth structure surrounding the crown, significantly improving fracture resistance [14]. A 2 mm height of the ferrule is considered the ideal dimension for achieving the optimal circumferential ferrule effect. It lowers stress within the tooth by encircling it with dentin’s parallel walls, extending coronally to the shoulder of the preparation [15]. Non-uniform ferrule lengths still offer greater fracture resistance than teeth without a ferrule [16,17]. The lack of a ferrule may reduce a tooth’s survival rate, depending on the amount of tooth structure loss and the remaining dentin walls. A 1 mm vertical height of the ferrule offers double the fracture resistance compared to teeth without a ferrule [14]. Furthermore, the position of the sound tooth structure is more critical in resisting occlusal stresses than having a 360-degree circumferential axial dentin wall [18].

Stress studies show that the highest stresses in root dentine occur at the tooth’s circumference, while stress within the root canal is minimal during function [19]. Many studies focus on stress distribution in the root, abutment, post, crown, cement layer, the interfaces between the post–root and post–abutment, and the adhesive layer between the abutment and root or ferrule [3].

Material properties, including Young’s modulus, shear modulus, yield strength, Poisson’s ratio, density, and tensile strength, significantly influence the stress-bearing characteristics of the materials. A 2006 study analyzed both tensile and compressive stresses in relation to ferrule design. The results indicated that higher tensile stresses were observed at the internal and mid-root palatal dentine near the cervical margin compared to preparations without a ferrule. Conversely, the presence of a ferrule led to a notable reduction in compressive stresses, improving the overall stress distribution [5]. Another study found that the maximum principal stresses in dentin with a ferrule were highest in incisors [20]. Nokar et al. showed that fiber-reinforced posts caused greater stress concentration in the root’s middle and cervical thirds than other posts [21]. Retained coronal dentine on the buccal side improved fracture resistance compared to teeth without coronal dentine [22].

Dejak et al. tested various 3D models with and without a ferrule, focusing on post length, and concluded that post length does not affect crown and dentin stresses [23]. Polyetheretherketone (PEEK) is a synthetic polymer with strong mechanical properties, making it suitable for use in dentistry and industry [24]. PEEK is thermoplastic and has a low Young’s elastic modulus, similar to bone [24].

However, only a few studies have focused on using digital dentistry and 3D models to analyze the effectiveness of post and core systems with finite element analysis. Some studies have compared PEEK to other post materials. A 2017 FEA study examined the polyetherketoneketone (PEKK) post–core system. It showed better fracture resistance than metal and fiberglass post–core systems, with a lower elastic modulus and better stress distribution at the intra-radicular surface [25]. Another FEA study in 2020 concluded that carbon-fiber-reinforced polyetheretherketone (CFR-PEEK) is superior for endodontic post fabrication compared to a fiber-reinforced composite (FRC) because it exerts lower stress in the residual dentin. Glass-fiber-reinforced polyetheretherketone (GFR-PEEK) and PEKK materials also provide stress distribution similar to FRC posts [26]. Tekin’s study found that PEEK posts produced less stress than glass fiber posts, particularly in the models with composite veneer crowns [24]. A 2020 study suggested that PEEK posts are preferred over titanium and glass fiber posts, as they provide better stress distribution and lower fracture risk [27]. Finally, Özarslan’s 2021 study found that PEEK posts showed lower stress values than glass fiber posts in central incisor restorations [28].

This study uses finite element analysis (FEA) to analyze displacement, von Mises stresses, maximum principal stresses, the factor of safety (FOS), and stress distribution in 3D models of post and core restored teeth with a ferrule design. The FEA simulation is conducted in an ideal environment to better understand the relative performance of the materials. A post–core-restored tooth with a 2 mm ferrule height is tested under specific loading conditions in FEA simulation software.

The null hypothesis is that the stress magnitudes and distribution in the 3D model’s components are the same for the PEEK and high noble alloy posts.

2. Materials and Methods

The study obtained digitally created 3-dimensional models of maxillary anterior endodontically treated teeth restored with a simulated post, core, and crown designed in computer-aided design (CAD) software called SolidWorks version 2021 (Dassault Systemes, Waltham, MA, USA). The ferrule was designed with a 2 mm vertical height and 2 mm thickness. The models were then exported into the Standard for the Exchange of Product Data (STEP) file format.

The STEP-formatted models were then imported into the ABAQUS unified FEA simulation software version 6.10 (Dassault Systemes, Waltham, MA, USA), which analyzes the static stress simulation study using FEA methods. Two post and core materials were tested: polyetheretherketone (PEEK) and high noble alloy. Therefore, there are two tested groups. Each group has eight components. These components are the bone, the periodontal ligament (PDL), the root, the post cement, the post and core, the crown cement, and the crown, as shown in

Table 1. Material properties of the components used.

Material	Young’s Modulus (GPa)	Poisson’s Ratio
Bone	13.7	0.3
PDL	0.0689	0.45
Root	18.6	0.31
Post Cement	18.3	0.3
Post (PEEK)	3.95	0.3931
Post (High Noble Alloy)	100	0.31
Gutta-Percha	6.9 × 10−4	0.45
Crown Cement	18.3	0.3
Crown (Zirconia)	250	0.32

.

Table 2. Component’s materials, sizes, and number of elements and nodes.

Component	Element Size (mm)	No. of Elements	Node
	No. Nodes
Crown	0.5	45,246	68,222
Bone	0.5	116,642	170,358
Crown Cement	0.4	11,728	22,881
Post	0.5	19,982	31,060
Gutta-Percha	0.2	5607	8820
Post Cement	0.4	11,513	22,967
Root	0.5	54,607	80,895
	Total	265,325	405,203

shows each component’s size and number of elements and nodes of these components. Figure 1 shows the components of the model. The crown is subjected to an angled force, F, with a magnitude of 100 N on the mid-lingual surface of the central incisor at a 45-degree angle to the long axis of the crown [8,21]. The bottom and side surfaces of the bone, shown as the boundary condition region in Figure 2, are fixed from movement. The material properties used for each component in the model are shown in Table 1. The model used 265,326 quadratic tetrahedral elements with 405,204 nodes (a total of 1,215,612 degrees of freedom). The performance of both PEEK and the high noble alloy were evaluated in terms of the total displacement of the crown and the generated stresses on the other components.

3. Results

The results show minimal differences between the two tested materials. However, the PEEK material showed a slight increase in the root, crown, and bone stress values compared to the high noble alloy. This increase in stress is attributed to the lower stiffness (elastic modulus) of the PEEK material, which is less rigid than highly noble alloys, resulting in higher stress concentrations in the surrounding structures. This leads to the transfer of higher loads to neighboring regions surrounding the post. Furthermore, the factor of safety (FOS) decreased from 16 to 10 with the utilization of the PEEK material. However, this reduction remains within acceptable limits and contributes to mitigating stress shielding effects due to the post exhibiting relatively similar stiffness to its surrounding regions. Moreover, the principal stresses were notably higher in magnitude when utilizing the high noble alloy material. Therefore, the performance of the PEEK material was better than that of the high noble alloy material. Total displacement and the stresses are illustrated in Figure 3, Figure 4, Figure 5 and Figure 6 and summarized in

Table 3. Total displacement, stresses, and FOS of the tested groups.

			Stresses
Component	Material	Strength (MPa)	Von Mises (MPa)	Principal Stress (MPa)	FOS
Root	Dentin	86	31.77	43.82	1.96
Post	PEEK	192	19.08	0.6456	10.01
Crown	Zirconia	1100	79.47	50.53	13.84
Bone			199.4	225.2
			Displacement (um)	4.925
Root	Dentin	86	29.98	42.63	2.02
Post	High Alloy	310	18.35	13.41	16.89
Crown	Zirconia	1100	66.18	42.01	16.62
Bone			190.9	216.5
			Displacement (um)	4.724

.

4. Discussion

This study tested the null hypothesis that there were no differences in the stress distribution on the root using different post materials: the PEEK material post or the high noble alloy post. The results showed that the tested null hypothesis should be accepted because the PEEK post material was similar to the high noble alloy post material in stress distribution and von Mises and principal stresses.

We found the following key outcomes based on the studies mentioned earlier compared to our methodology. Dejak et al. used FEA with contact elements to explore the effects of the ferrule, length of cast, and FRC posts on the stresses on anterior teeth in a study. For instance, 120,000 elements were used for each of the thirteen tooth models, with 150,000 nodes connecting them [23]. Compared to our study, the number of elements and nodes enrolled in our study, 265,325 and 504,203, respectively, were higher than the inputs in Dejak’s study [23]. Moreover, that study used two types of posts: cast nickel chrome (NiCr) and glass fiber posts with composite core build-up and crowns made of leucite ceramic cemented with luting resin cement. In contrast, in our study, we used posts of high noble alloy and PEEK materials luted with resin cement. The result of that study showed that there were minimal tensile stresses around ferrule posts in the teeth. Moreover, it was concluded that teeth restored with cast posts have lower von Mises stresses than teeth restored with FRC posts. Regardless of the post material, the von Mises stresses in teeth with varying lengths of posts were identical. Accordingly, our study results show increased stresses on the bone and the root using the PEEK post compared to the high noble alloy. As for the FOS, it was reduced from 16 to 10 when using the PEEK post.

In a study by Savychuk et al., they applied their model bone, and the number of elements and nodes was much smaller than in the current study. They used a gold-cast post and core and fiber posts only and a metal–ceramic crown, and they did not show the FOS in their study [20]. In our study, we used a PEEK material and zirconia crown in the tested model, and the FOS was demonstrated in our study.

A previous study used gold post and core and Ni-Cr post and core and metal–ceramic restorations and a stainless-steel post, titanium post, carbon fiber post, glass fiber post, and quartz fiber post with composite cores restored with metal–ceramic restorations (MCRs). The third group included a zirconia post and core restored with all-ceramic restorations (ACRs), zirconia post, carbon fiber post, glass fiber post, and quartz fiber post with composite cores and ACRs. Meanwhile, PEEK was not simulated in the model. The finite element meshes were composed of nearly 4300 elements and 6000 nodes. That study showed the von Mises stresses but did not mention the FOS of the tested model [21].

Mechanical properties, Young’s modulus of elasticity, and Poisson’s ratios, entered in the FEA model for analysis, are different between the PEEK and high noble alloy posts.

We found no differences in the stress distribution pattern or strength of the crown or roots. Usually stress distribution patterns are related to structural and shape differences in the models. This is true for our model and can be explained by the fact that the only difference is in the material properties rather than in the shapes of the model.

If both models are similar in shape but different in properties, strengths, and stress values, the FOS would be different in our comparison. We are concerned with four components: bone, root, crown, and the post itself. Therefore, we found slight differences in only the von Mises stresses, and principal stresses of roots and bones are usually higher in PEEK than in high noble alloys. This means that the values of stresses are not affected so much in those two components by the differences in the mechanical properties of those two posts. This indicates that bones and roots are not affected by those differences. Therefore, roots will not fracture differently by changing the materials of the posts from alloys to PEEK. Also, bones might not be stressed differently, which might not cause problems in the surrounding bones.

Meanwhile, the strengths are different within the two compared posts, which are higher for the alloys than for the PEEK. It is also noticed that the safety factor is higher for the high noble alloys than for the PEEK in the post and within the covering crown due to the alloy’s high strength. This might indicate that the PEEK posts might withstand less stresses than the alloy, and their strength is much less than that of the alloy. And the safety factor is less for the PEEK than for the alloy, making it more prone to failure than the alloy. Given that information, the PEEK posts may break more easily than in the alloy’s case. Regarding the retrievability of post, given that the PEEK hardness is less than the alloy’s, it can be drilled easier than the hard alloy, making reposting much easier clinically.

The shift between the PEEK and alloy affects the covering crown von Mises and principal stresses. They are higher in the PEEK than in the alloy. This may indicate that having PEEK in the background base or under the crown can dampen the forces subjected onto the crown, making it more resistive to failure in PEEK than in alloy posts. This is an essential protective mechanism for the crown.

We did not vary the force values; therefore, we cannot show the effects on these components with varying force values by simulating the varying force values within the oral cavities at different locations.

Therefore, having PEEK posts under zirconia crowns may offer a protective mechanism to the overlying crown. If failure occurs in the system, it may happen in the PEEK post in an easily retrievable way, with not much stress on the root and surrounding bone.

The current study’s limitations were that we used only one ferrule design on a central incisor tooth. The only material used was PEEK compared to a high noble alloy. We implemented only one post design: the custom post and core. Prefabricated post and core materials were not modeled in the current study. Only static loads, not dynamic loads, were applied to the tested model.

Future studies will include dynamic stresses, various ferrule designs, different materials, and other tooth types.

5. Conclusions

The PEEK demonstrated better stress-shielding properties compared to the high noble alloy, potentially reducing the risk of residual root fractures. These findings suggest that PEEK could be a more favorable alternative for post and core restorations, particularly in enhancing the longevity and durability of endodontically treated teeth.