Stress Distribution in Restored Primary Molar Using Finite Element Analysis

doi:10.21203/rs.3.rs-1961745/v1

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Stress Distribution in Restored Primary Molar Using Finite Element Analysis

https://doi.org/10.21203/rs.3.rs-1961745/v1

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The purpose of this study was to evaluate the stress distribution in normal tooth structure and restoration at different preparation designs restored with stainless-steel crown (SSC), zirconia crown (Zr), and amalgam. Six carious primary mandibular second molar were used. The molars were divided into three main groups: Group I (restored with Amalgam), Group II (restored with SSC), and Group III (restored with Zr). Each group was subdivided into Subgroup A (Class II Cavity with MOD extension) and Subgroup B (pulpotomy with MO cavity extension). The restored teeth were imaged for CBCT to create a finite element model for each one. These models were transferred to ANSYS software and subjected to an average simulated masticatory force of 245 N. Regarding the tooth structure, under different force directions and cavity designs, the dentin structure of models restored with amalgam displayed von Mises stress more than models restored with SSC. The lowest von Mises stress value showed in models restored with Zr. Regarding the final restorative material under different force directions and cavity designs, the amalgam recorded the lowest value of von Mises stress than Zr and SSC. The SSC and Zr distribute occlusal stresses significantly more than amalgam restoration. Furthermore, Zr distributes occlusal stresses slightly more than SSC.

Primary molars

stress analysis

preformed zirconia crown

stainless steel crowns

amalgam

Dental caries is a widespread health problem that affects many people with permanent dentition and children with primary teeth (Kassebaum et al. 2015). In the primary dentition stage, preserving the teeth in the mouth is essential because primary teeth are the most suitable space maintainers. In addition, these carious teeth can be restored by different types of restorations. Common options for use in pediatric dentistry include amalgam, composite and prefabricated crowns (Prabhakar et al. 2017).

Dental amalgam is one of the most versatile restorative materials used in dentistry. It has served as a dental restoration for more than 165 years. Other dental restorative materials unmatch the combination of reliable long-term performance in load-bearing situations and low cost. In addition, it has a myriad of uses: rather low technique sensitivity, self-sealing property, and longevity (Bharti et al. 2010). In 2007, Bernardo et al. (Bernardo et al. 2007) reported that 94.4% of all amalgam restorations survived for seven years when placed in permanent posterior molars of children aged 8-12. However, amalgam is still the most durable and cost-effective restorative material, but in preschool children with large proximal carious lesions, preformed metal crowns are preferred to amalgam because of their durability (Mohammadzadeh et al. 2016).

The stainless steel crown (SSC), which is composed of a nickel-chrome alloy (Shinya, Lassila, and Vallittu 2008), was first introduced by Humphrey in 1950 (Attari and Roberts 2006) and is now widely used for the restoration of grossly decayed primary or young permanent teeth in pediatric dentistry (Choi et al. 2016). However, SSC placement is simple and economical with a high success rate and is considered the best treatment modality for teeth with large carious lesions or past endodontic therapy. Eshghi et al. (2012) reported results from a retrospective study of 305 pediatric patients treated under GA 6 to 24 months before the survey was examined. They showed that the SSC restorations had significantly better results vs. Class I and Class II Amalgam and Class I and Class II Tooth color restorations. Unfortunately, SSC is poor aesthetics offered, which limits its use in clinical practice (Atieh 2008). This aesthetic issue has become increasingly important in patients with primary tooth problems (Zimmerman et al. 2009).

Zirconia is a crystalline dioxide of zirconium with mechanical properties similar to those of metals such as stainless steel, and its color is similar to that of teeth. Ready-made zirconia crowns (Zr) are now available for both primary incisors and molars (Alamoudi and Attar 2017). It has sufficient mechanical strength and toughness along with good chemical and dimensional stability. Zr is being evaluated as an alternative to SSCs due to their properties, color, and superior biocompatibility (Bachhav and Aras 2011). Prabhakar et al. (2017) Compared the effectiveness of preformed zirconia crowns with the gold standard SSC for restoring primary teeth through a finite element analysis (FEA). They found that at maximal physiologic masticatory force levels, a grossly destructed tooth restored with a preformed zirconia crown can withstand stress better than a tooth restored with SSC.

Dentists choose restorative materials according to the ease of use, decrease the chair time, reduce the contamination risk of the cavity, and increase patient cooperation, especially in disabled children (Altan, Göztas, and Arslanoglu 2018). In addition to the properties of the materials such as stress distribution, fatigue resistance, fracture resistance, erosion resistance, degradation, bonding strength, and polymerization shrinkage. These factors are significant in the clinical success of restorative materials (Lambrechts et al. 2006).

In normal teeth, the stresses were predominantly compressive in response to an axial compressive load, but tensile stresses were recorded at the pulpal wall in the tooth with a cavity preparation and restoration. These, combined with heavy compressive stresses in the immediately adjacent area, can cause greater damage to the remaining tooth structure compared with a normal tooth. This change in the type of stresses, from compression to tension, is responsible for an increased fracture potential of a tooth with cavity preparation and restoration. Hegde et al. (2019) compared the stress patterns in the Endodontically Treated second deciduous molars restored with and without Stainless Steel Crown when different loads were applied. They concluded that at higher forces, the tooth and restorative materials such as glass ionomer are bound to fracture under masticatory stress.

One method that analyzes the stress distribution in dental structures is FEA, which is an approximate method for predicting how a product reacts to real-world forces, mechanical stress, and other physical effects. It shows whether a product will break, wear out, or work the way it was designed. It is called analysis, but in the product development process, it is used to predict what will happen when the product is used (Martins and Kövesdy 2012). Danley et al. (2018) measured cuspal flexure and used FEA to assess associated stress levels in amalgam-filled teeth. FEA can provide useful information only if given correct inputs.

However, there are few researches on the effect of stress distribution in these restorations with different cavity designs of teeth when applying the force of mastication. Most of the previous studies mentioned other mechanical properties in restored teeth, such as fracture resistance in the restored teeth. The FEA of the stress helps indicate the physical response of the system. This study aimed to evaluate the stress distribution in normal teeth structure and restorations at different preparation designs with a different restorative material using finite element analysis.

Six sound or initial carious human primary mandibular second molar recently extracted for therapeutic purposes, either about to shed or retained, were selected. The teeth were divided into three main groups, with two molars for each group: Group I: Two molars restored finally with amalgam, group II: Two molars restored finally with SSC, and group III: Two molars restored finally with a Zr.

Each of these groups was also subdivided into two subgroups according to the type of treatment into two subgroups; Subgroup A (One tooth prepared with Class II cavity with MOD extension) and subgroup B (One tooth prepared with pulpotomy with MO cavity extension), then the pulp chamber cavity filled with Intermediate Restorative Materials (IRM).

Sample Preparation

Cavity Preparation and Restoration

Standard Class II amalgam cavity was prepared in three molars with mesial extension and other molars with mesial & distal extension, and the pulpal floor was placed approximately 0.5 mm into the dentin. All walls were connected with a smooth curve, and no catches in the groove area. Next, the standard pulpotomy cavity was prepared in MO Class II teeth. Then, all molars were restored with amalgam.

SSC and Zr Preparation

The standard SSC preparation was made on two molars by decreasing the occlusal surface to 1-1.5 mm depth with a straight fissure bur. The proximal decreasing was accomplished by maintaining vertical walls by a tapered fissure bur. For each tooth, all sharp line angles were rounded, and a prefabricated SSC was selected and tried by seating firstly over the lingual or buccal wall and rolled over onto the opposite wall. After crown preparation, SSC (3M™ ESPE™) was cemented using GIC (GC Fuji I).

Zr preparation was made on two teeth by reducing the occlusal surface to 1-2 mm depth with a diamond flame bur. Next, interproximal contacts were opened, and the entire clinical crown was reduced by 0.5-1.25mm. The resulting preparation was parallel to slightly converging occlusally. After crown preparation, Zr (Nu smile™) was cemented using GIC (GC Fuji I).

Finite Element Model Generation

Cone-beam computed tomography scans were used to obtain three-dimensional images of the prepared teeth. The ANSYS (ANSYS v.19 R2; ANSYS Inc; Houston, USA) software converted the model to a mesh model. Each cloud data point is far 0.5 mm from another point, and these data points were connected to form the surface models of each primary tooth, as seen in Fig.1.

The material properties were assigned in the ANSYS workbench using the elastic modulus and Poisson’s ratio. The material properties of enamel, dentin, amalgam, IRM, GIC, SSC, and Zr were linear, elastic, homogenous, and isotropic. The material properties (Elastic modulus and Poisson’s ratio) of each material are presented in Table 1.

	Table 1: Isotropic material properties.
Material	Elastic modulus in Megapascal unit (MPa)	Poisson’s ratio
Enamel (Bakke et al. 1990)	80,000	0.33
Dentin (Bakke et al. 1990)	20,000	0.31
SSC (Gurbuz, Sengul, and Altun 2008)	200,000	0.33
Zr (Mahmoudi et al. 2012)	240,000	0.26
Amalgam (Musani and Prabhakar 2010)	48,000	0.35
IRM (John 2017)	2,500	0.32
Pulp (Bakke et al. 1990)	2,000	0.45
GIC (Pishevar, Ghavam, and Pishevar 2014)	12,000	0.3

Boundary Condition and Load Application

The root of the tooth was selected as fixed support in all dimensions (x, y, z) as a boundary condition, as seen in Fig. 2. The contact surfaces between the tooth parts and the restorations were taken as bonded, except the amalgam surface was taken as no separation contact.

In this study, an average force of 245N was applied at two load cases (including five different angulations) to each model to simulate the various physiologic masticatory conditions (Rentes, Gavião, and Amaral 2002).

The load cases were considered:

Axial load case:

A nodal force of 245 N parallel to the long axis of the tooth divided equally into three contact areas: on the lingual inclines of the buccal and lingual cusps and the outer inclines of the buccal cusps,2 to simulate maximum masticatory forces in children as seen in Fig. 3-A.

Lateral load case:

The lateral load is divided into four types according to the direction of load cases.

Type I: A nodal force of 245 N at 90◦ on the outer inclines of the buccal cusps was applied.

Type II: A nodal force of 245 N at 45◦ on the outer inclines of the buccal cusps was applied.

Type III: A nodal force of 245 N parallel to the inner inclines of the buccal cusps was applied.

Type IV: A nodal force of 245 N at 45◦ and 90◦ on the outer incline

of the buccal cusps and 0◦ on the inner inclines of the buccal cusps were applied at the same time as seen in Fig. 3-(B-E).

Data Analysis:

Linear static analysis was performed by ANSYS workbench software. Equivalent von Mises stress values were calculated for all models. The images obtained from the Finite Element Analysis are all color graded such that dark blue represents areas experiencing minimal von Mises stress and red represents areas experiencing maximal von Mises stress.

Regarding Model I-A, as seen in Fig. 4, the maximum von Mises stress when applied the force vertically was 64.8 MPa on the marginal isthmus area of amalgam. In contrast, it was 49.5 MPa on enamel, especially on the marginal cavity of enamel. Therefore, the maximum von Mises stress concentrated on the inner cavity area of the dentin, and its value was 31.2 MPa. In addition, the enamel registered 116.93 MPa, which is the highest value of the Maximum von Mises stress when the force direction was applied at the type I lateral loud; it dropped off respectively at type IV, III, and II lateral load recording 103.2 MPa, 94.8 MPa, and 86.1 MPa. The Maximum von Mises stress values on the amalgam at type III, IV, I, and II lateral loads were 97.1 MPa, 84 MPa, 34 MPa, and 20.4 MPa, respectively. In contrast, it was 56.2 MPa, 54.9 MPa, 52.5 MPa, and 32.7 MPa on the dentin at type I, III, II, and IV lateral load directions, respectively.

About Model I-B, as seen in Fig. 5, the maximum von Mises stress, when applied the force vertically, was 77.1 MPa on the marginal amalgam in the vertical force direction. In contrast, it was 65.7 MPa on the enamel and 44.6 MPa on the dentin. The lowest value of maximum von Mises stress was recorded on IRM, which was 24.4MPa. The Maximum von Mises Stress was registered 155.4MPa, 146.3MPa, 130.5MPa, and 119.3MPa on enamel at type I, III, IV, and II lateral loads, respectively. The Maximum von Mises stress values on the amalgam were 59.4MPa, 51.3MPa, 50.5MPa, and 46.6MPa type III, I, II, and IV lateral loads, respectively. The maximum von Mises stress on dentin were 59.4MPa, 51.3MPa, 50.5 MPa, 46.6MPa at type III, I, II, and IV lateral loads, and was registered 38.6MPa, 13MPa, 11.6MPa and 17.6MPa on IRM at the same force directions sequence.

Concerning Model II-A, as shown in Fig. 6, the maximum von Mises stress, when applied vertically, records 86.2MPa on the occlusal area of SSC, and it is reduced to 23.9 MPa on dentin, especially on the cervical margin of dentin. The maximum von Mises stress concentrated on the occluso-buccal side of the amalgam, and its value was 21.6 MPa. The SSC registered the highest value of the Maximum von Mises stress, 274.6MPa, when the force direction was applied at the type I lateral load of the tooth. It dropped off respectively at type II, III, and IV lateral loads, recording 273.9 MPa, 245.5MPa, and 196.9 MPa. The Maximum von Mises Stress values on the amalgam at type II, I, IV, and III lateral loads were 66.6 MPa, 26.5 MPa, 16.1 MPa, and 15.9 MPa, respectively. In contrast, 46 MPa, 42 MPa, 39.6 MPa, and 31.2 MPa on the dentin at type I, III, II, and IV lateral loads, respectively.

About Model II-B, as seen in Fig.7, The Maximum von Mises stress was 183.9MPa on the SSC at vertical force direction. While it decreased on the tooth structures, its value was 31.1MPa on the dentin. The lowest value of Maximum von Mises stress was recorded at around 0.4 MPa on IRM and amalgam. The Maximum von Mises Stress was registered 327MPa, 281.8MPa, 203.3MPa, and 191.8MPa on SSC at type I, II, III, and IV lateral loads, respectively, while it was decreased on dentin, and its values were 52.7 MPa, 49.7 MPa, 44.3 MPa and 37.6 MPa at type III, I, II and IV lateral load respectively. On the amalgam and IRM, The Maximum von Mises Stress value is almost 1.0 MPa.

Regarding Model III-A, as shown in Fig. 8, the maximum von Mises stress record 81.1MPa on the occlusal area of Zr, and it is reduced to 21.6 MPa on dentin, especially on the cervical margin of dentin. The maximum von Mises stress concentrated on the occluso-buccal side of the amalgam, and its value was 20.6MPa. The Zr registered the highest value of the maximum von Mises stress, 272.0MPa, when the force direction was applied at the type I lateral load of the tooth. It dropped off respectively at type II, III, and IV lateral loads, recording 271.5 MPa, 224.5MPa, and 174.5 MPa. The maximum von Mises stress values on the amalgam at type III, I, II, and IV lateral loads were 62.8MPa, 25.2MPa, 15.2MPa, and 14MPa, respectively. In contrast, it was 46.5 MPa, 41.7 MPa, 38.5 MPa, and 31.2 MPa on the dentin at type I, III, II, and IV lateral loads, respectively.

Concerning Model III-B seen in Fig. 9, The Maximum von Mises stress was 173.4MPa on the Zr at vertical force direction. While it decreased on the tooth structures, its value was 28.1 MPa on the dentin. The lowest value of Maximum von Mises stress was recorded at around 0.4 MPa on IRM and amalgam. Regarding the lateral force directions, The maximum von Mises stress was registered 294.4MPa, 245.2MPa, 198.8MPa, and 185.7MPa on SSC at types I, II, III, and IV lateral loads, respectively, while it was decreased on dentin. Its values were 49.8MPa, 48.3MPa, 41MPa, and 34.3MPa at type III, I, II, and IV lateral loads, respectively. The maximum von Mises stress value on the amalgam and IRM is almost 1.0MPa.

Upon Comparison of Class II Cavity with MOD Extension, the dentin of the model I-A was significantly higher than the dentin of the model II-A and the dentin of the model III-A under vertical force. While the SSC recorded the highest value of maximum von Mises stress, which was 86.2 MPa, then Zr 81.1MPa was followed by amalgam 64.8MPa, as seen in table 2. Regarding the lateral force directions, the dentin of model I-A recorded the highest values of von Mises stress. Therefore, a significant difference between the dentin of model I-A and other models can be noticed. However, there was no significant difference between model II-A and model III-A. According to the final restorative material, the SSC registered the highest value of maximum von Mises stress, followed by Zr, then amalgam, as shown in Table 2.

Table 2: the maximum von Mises stress in Class II cavity with MOD Models

	Model I-A Amalgam	Dentin	Model II-A SSC Dentin	Model III-A Zr	Dentin
Vertical load	64.842	31.231	86.284 23.93	81.189	21.67
Type I lateral load	34.081	56.264	274.61 46.061	272.09	46.584
Type II lateral load	20.422	52.556	273.99 39.613	271.58	38.526
Type III lateral load	97.184	54.938	245.58 42.028	224.59	41.776
Type IV lateral load	84.055	32.726	196.96 31.206	174.51	31.274

Upon comparison of Pulpotomy with MO cavity extension, it can be observed that the maximum von Mises stress under vertical force in the dentin of model I-B is higher than the dentin of model II-B by 30.28% and higher than the dentin of model III-B by 37% (Table 3). In the lateral force, the dentin of model I-B is significantly higher than model II-B's and model III-B's dentin. Regarding the IRM models part (Table 4), there was a significant difference between model I-B and the other models, while there was no significant difference between model II-B and model III-B in the all-directional force.

Table 3: The maximum von Mises stress in pulpotomy with MO cavity Models

	Model I-B Amalgam	Dentin	Model II-B SSC Dentin	Model III-B. Zr	Dentin
Vertical load	77.117	44.656	183.95 31.13	31.13	173.42
Type I lateral load	40.281	51.342	327 49.787	49.787	294.48
Type II lateral load	27.093	50.55	281.82 44.394	44.394	245.26
Type III lateral load	141.6	59.493	203.37 52.716	52.716	198.82
Type IV lateral load	54.526	46.625	191.84 37.664	37.664	185.79

Table 4: The maximum von Mises stress in IRM.

	Model I-B	Model II-B		Model III-B
Vertical load	24.465		0.3437	0.3137
Type I lateral load	13.068		1.3895	0.4254
Type II lateral load	11.606		0.4882	0.4516
Type III lateral load	38.621		1.4712	1.1942
Type IV lateral load	17.632		1.1968	0.657

In this study, the von Mises stress values on tooth structure and restorative materials for all models were far below the yield strength. The yield strength of dentin is 297MPa, the enamel is 384 MPa (Willems et al. 1993), amalgam is 414MPa (Haque et al. 2019), SSC is 850MPa (Andrea Carpinteri, Francesco Iacoviello, Les p. Pook 2012), Zr is 630MPa (Denry and Kelly 2008), and IRM is 50MPa (M Skoudi 2007). From that, we can conclude that all restorative materials used in this study are safe on the teeth and protect the tooth structure from breaking. It has durability and fracture resistance under the masticatory force, directional force, and cavity designs used in this study. This finding agrees with Arola et al. (2001), who have noticed that stresses within the molar with amalgam restoration were lower than those resulting in the unrestored molar. Prabhakar et al. (2017) and Kist et al. (2019) have found that all Zr and SCC showed a high survival rate during the chewing simulation.

The outcome showed that the lateral force in each model gives a higher value of von Mises stress than vertical force. Because the masticatory forces in the lateral direction create two types of stress on tooth structure; the first is compressive stress that is located primarily on the side toward which the tooth is being bent; the second, tensile stress, acts on the side away from the direction of bending (Lee and Eakle 1984). This finding agrees with Musani et al. (Musani and Prabhakar 2010) and Prabhakar et al. (2017); they found the best stress distribution pattern with minimal stress values seen when the tooth was loaded at the center of the occlusal surface axially. However, as the force angle increased, the stress value increased, and high magnitudes of stress were seen in the cervical third of the crown. That is because the lateral direction is restricted to a smaller surface area.

Regarding the lateral force directions, the type I lateral force recorded the highest stress in the dentin of Class II with MOD models. This finding agrees with Musani and Prabhakar (2010) and Prabhakar et al. (2015), who reported that if the force angle increased, the stress values also increased. In addition, high magnitudes of stresses were seen in the cervical third of the crown. On the other hand, the type III lateral force recorded the highest stress in the dentin of pulpotomies models. That is because by removing the pulpal floor, the force directly affects the lingual wall of the dentin(Mamoun and Napoletano 2015).

The results of this study showed that the value of von Mises stress in pulpotomies models is higher than in class II models. This result was in agreement with Jiang et al. (2010), who reported that the tooth's structural integrity is diminished with endodontic treatment, resulting in higher von Mises stress concentration in the tooth structure. Thus, it is indicated that if the tooth structure is modified by endodontic treatment, the tooth’s structural integrity cannot be fully restored, no matter what type of restoration material is used.

The amalgam restoration in this study recorded the lowest value of von Mises stress when compared with SSC and Zr restorations. This finding agrees with Hegde et al. (Hegde et al. 2019). Furthermore, the authors indicated that covering the complete teeth leads to more surfaces exposed to the load, a finding with SSC and Zr in contrast to amalgam restoration. On the other hand, the stress generated within the SSCs was much higher than that within the Zr. That is because the stress generated in the material depends on the elastic modulus of that material (Seo et al. 2009). This finding is in agreement with Prabhakar et al. (2017). They have found that the inherently lesser stress development leads to the Zr being better suited to resist bite forces.

In this study, the dentin of Group I models recorded the highest values of von Mises stress. This finding agrees with Danley et al. (2018), who concluded that the amalgam expansion pushed cavity walls outward, creating expansion stresses. Saito et al.(1973) have concluded that the enamel portion of the restored tooth carries a significant portion of the load and is transferred into the surrounding tooth structure remarkably high on the dentin portion. Studies by Einwag and Dünninger (1996), Randall et al. (2000), and Braff (1975) also obtained similar results. The high efficacy of SSC could be explained since it has a greater stress distribution than most restorative materials used in pediatric patients. Another study similar to our outcome is by Hegde et al. (2019), who reported that the stress and strain values in models covered with SSC were within the safe levels indicated in the occlusal surface compared to those without SSC.

In this study, all the situations showed reduced stress generation in the dentine by Zr than by the other restorative materials. This indicates higher protection conferred by the Zr to the underlying tooth than is possible by others. This finding also agrees with Prabhakar et al. (2017). They have found that even at maximal physiologic bite force levels, a grossly destructed tooth restored with Zr can withstand stress better than a tooth restored with SSC.

The von Mises stress in IRM recorded the highest value in the amalgam group since the SSC and Zr are loaded with a force of constant intensity; the stress is not transmitted continuously and is concentrated on the peri-cervical dentin. However, in amalgam restorations, it was attached mechanically to tooth surfaces, so the masticatory force pushes amalgam apically, which creates stress concentrations at pulp champers (Arola et al. 2001). From that, we can conclude that SSC and Zr reduce the stress in the pulp champers and roots, reducing the possibility of a tooth fracture.

Within the limitation of this study, we can conclude that amalgam restorative material transfers and concentrates the stress significantly in the small area of dentin, particularly in pulpotomies treated molars where the possibility of tooth fracture is high. However, the SSC and Zr distribute occlusal stresses, which helps minimize possible breakages and protect the underlying tooth structures. Furthermore, Zr distributes occlusal stresses slightly more than SSC, especially in pulpotomies treated teeth.

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No competing interests reported.

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Stress Distribution in Restored Primary Molar Using Finite Element Analysis

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