Biomechanical performance of resin composite on dental tissue restoration: A finite element analysis

Abdelhak Ouldyerou; Hassan Mehboob; Ali Mehboob; Ali Merdji; Laid Aminallah; Osama M Mukdadi; Imad Barsoum; Harri Junaedi

doi:10.1371/journal.pone.0295582

. 2023 Dec 21;18(12):e0295582. doi: 10.1371/journal.pone.0295582

Biomechanical performance of resin composite on dental tissue restoration: A finite element analysis

Abdelhak Ouldyerou ¹, Hassan Mehboob ^2,^*, Ali Mehboob ³, Ali Merdji ¹, Laid Aminallah ¹, Osama M Mukdadi ⁴, Imad Barsoum ^3,^5,^*, Harri Junaedi ²

Editor: Artak Heboyan⁶

PMCID: PMC10734934 PMID: 38128035

Abstract

This study investigates the biomechanical performance of various dental materials when filled in different cavity designs and their effects on surrounding dental tissues. Finite element models of three infected teeth with different cavity designs, Class I (occlusal), Class II mesial-occlusal (MO), and Class II mesio-occluso-distal (MOD) were constructed. These cavities were filled with amalgam, composites (Young’s moduli of 10, 14, 18, 22, and 26 GPa), and glass carbomer cement (GCC). An occlusal load of 600 N was distributed on the top surface of the teeth to carry out simulations. The findings revealed that von Mises stress was higher in GCC material, with cavity Class I (46.01 MPa in the enamel, 23.61 MPa in the dentin), and for cavity Class II MO von Mises stress was 43.64 MPa, 39.18 MPa in enamel and dentin respectively, while in case of cavity Class II MOD von Mises stress was 44.67 MPa in enamel, 27.5 in the dentin. The results showed that higher stresses were generated in the non-restored tooth compared to the restored one, and increasing Young’s modulus of restorative composite material decreases stresses in enamel and dentin. The use of composite material showed excellent performance which can be a good viable option for restorative material compared to other restorative materials.

Introduction

Dental cavities also known as tooth decay are one of the most common dental complications which are distributed among people of every age [1]. Several factors lead to an ecological imbalance between the inorganic components of dental hard tissues and biofilms, including the physical characteristics of the teeth, environmental conditions, and a sugary diet that contribute to creating tooth cavities [2].

However, modern dentistry prioritizes minimal intervention by emphasizing preventative and non-surgical approaches to safeguard tooth hard tissues before the formation of dental cavities. In this regard, the resin infiltration technique is widely used which involves the application of a low-viscosity resin to infiltrate porous and demineralized inter-crystalline spaces within enamel lesions [3]. In an ex vivo study [4], researchers investigated the treatment of non-cavitated and micro-cavitated caries using a modified resin incorporating silver nanoparticles (AgNP) for both internal and external infiltration, aiming to confer antimicrobial properties. The findings revealed that the AgNP-infused resin effectively hindered the regrowth of microbial biofilms while preserving the mechanical integrity of the enamel and preventing the recurrence of caries [3]. Timely intervention to address demineralized and porous enamel lesions is critical, as untreated lesions may progress to dental cavities.

According to the G.V. Black classification system, a demineralization lesion situated within the pits and fissures of the occlusal (biting) surface is denoted as a Class I lesion, whereas a lesion found on the proximal surface of a posterior tooth is classified as a Class II lesion [5]. Within the Class II category, there exist various subtypes such as mesial and occlusal surfaces (MO) and mesial, occlusal, and distal surfaces (MOD) cavities [6].

The primary goal of cavity treatment is the long-term restoration of functional teeth without their removal. In untreated tooth cavities, the depth of the cavity lesion may increase, which may affect the pulp and thus may lead to inflammation and necrosis of the pulp and loss of vitality [7]. Finding a good approach to restoring the tooth cavity is the holy grail for dentistry researchers which is a challenge for dentists to redesign the cavity carefully without encroaching on the pulp tissue or removing too much dental tissue while choosing the right restoration material for balance between function and aesthetics.

Restorative dental materials commonly employed for direct placement, amalgam has traditionally held a prominent position, although concerns regarding its mercury content and non-aesthetic appearance have led to diminished usage in various communities [8]. In response to these concerns, novel resin-based composites have been developed, characterized by unique biomechanical properties such as cost-effectiveness, non-toxicity, prolonged durability, and enhanced aesthetic qualities [9].

Glass ionomer cements (GIC) are now used as both a restorative material and a fissure sealant in dentistry. It represents a relatively recent commercial development aimed at intentionally remineralizing damaged caries of enamel and dentin [10]. Recent advancements in material development have given rise to glass carbomer cement (GCC), an innovative variant of GICs, which incorporates nanoscale particles and introduces fluorapatite as an additional filler [11]. The flexural strength of GCC was found to be comparable to that of conventional glass ionomer cement [12], underscoring the advancements in material development. Despite these improvements, GICs are still not generally considered the top choice for restorative materials compared to amalgam and resin composites. Statistics show that composite materials (44%) are more commonly used than amalgam (40.9%), and glass-ionomers (13.4%) [10].

Nowadays, the development of dental composites with excellent properties is of high interest to academic researchers, and numerous efforts are currently underway to enhance the mechanical characteristics of dental composites [13]. Recently, micro-nano material science has contributed to improving the mechanical and biological properties of restorative composite materials by adding various filler contents to the organic resin matrix, such as silica nanoparticles, ceramic (zirconia, alumina), hydroxyapatite, calcium phosphate, and metals, in diverse sizes and shapes [14].

In a study [15], the mechanical performance of dental resin composite (DRC) was improved by incorporating silica colloidal nanoparticles. The results of this study revealed that these composites have better mechanical properties compared to many commercial products, even with lower filler content, using only a single filler. Similarly, short glass fiber-reinforced dental composites were prepared by adding silane coupling agents. The results showed that the glass fibers improved the strength of the composite [16]. In a different investigation, researchers explored the mechanical properties of resin composites and revealed that Grandio material, a hybrid composite with matrix resin of bisphenol A-glycidyl methacrylate (BisGMA) and triethylene glycol dimethacrylate (TEGDMA), and filler of silanized ceramic and silica particles (63% volume filler), exhibited a higher Young’s (22.15 GPa ± 2.68) [17].

In bioengineering, finite element analyses (FEA) have been widely used [18–21]. FEA can give freedom for researchers to design cavities and consider various restorative materials to investigate their biomechanical performances. The results can be revealed from the analysis of these models to investigate displacements, micro-movements, and stress/strain distribution in teeth, implants, or host bones under mastication forces.

The purpose of this study was to investigate the behavior of dental tissues using alternative restorative materials to fill cavities of varying designs. Three classes of cavities were chosen, Class I, Class II MO, and Class II MOD, and three types of restoration material were selected, amalgam, GCC, and silica-reinforced polymer composites.

The first null hypothesis maintains that no notable disparity exists in stress distribution within enamel and dentin between an infected tooth and a restored or healthy tooth. The second null hypothesis contends that the stiffness of restorative materials holds no consequential influence on the stress distribution observed in restored teeth.

Materials and methods

Construction of 3D finite element models

To generate three-dimensional geometry models, SolidWorks 2020 (Dassault Systèmes, Vélizy-Villacoublay, France) was utilized. A first molar tooth (tooth number 30 in the right mandible) was modeled using a reference image and freeform feature. This tooth has a typical molar shape (a rectangular shape with pits and fissures on it) characterized by multiple cusps and a broad occlusal surface as shown in Fig 1. The poly surfaces were joined using the software’s built-in tools and functions. The enamel part was designed by offsetting 2 mm of the dentin crown from the tooth center. Fig 1(a) displays the 3D model of the intact tooth. Three classes of cavities were created, Class I with 30 mm³, Class II MO with 95.59 mm³, and Class II MOD with 176 mm³.

The splint function and extruded cut feature were used to create the cavities and restorative parts with different sizes and dimensions, as shown in Fig 1(b). The thickness of the cortical bone was modeled as 1.5 mm thick using a thickness feature within SolidWorks after designing surfaces to encompass the internal core of the cancellous bone. The PDL (periodontal ligament) and the pulp were not included in our design because it has been established in the literature that when simulating stress distribution at the crown level (regions of interest), the PDL is often excluded due to its well-documented characteristics, including its low stiffness (around 68.9 MPa) and its thin structure (typically 0.2 mm in thickness). These attributes suggest that the PDL’s influence on peak stresses at the tooth crown level is negligible. Therefore, the exclusion of PDL and pulp modeling aligns with established modeling techniques [22]. All models were combined using the Boolean cut feature (Fig 1(c)) and exported in STEP, the standardized CAD file format.

Properties of materials

BisGMA and TEGDMA are resins that are widely used to fill dental cavities [13]. This resin can be reinforced with inorganic ceramic fillers such as silica (SiO₂) nanoparticles [23]. Fig 2 depicts the concept of fabricating resin-reinforced SiO₂ for use in dental fillings. Various theoretical models were employed to predict elastic moduli of micro-filled composite materials, which were compared with experimental results and showed good agreement [24]. Therefore, this study used these models (Eqs 1–5) to predict the elastic moduli of composites.

Isotropic elastic properties were assumed for the composite fillers and the following formulas were used to calculate the composite Young’s modulus:

Einstein model [25]:

\frac{E_{c}}{E_{m}} = 1 + 2.5 V_{f}

(1)

Guth model [26]:

\frac{E_{c}}{E_{m}} = 1 + 2.5 V_{f} + 14.1 V_{f}^{2}

(2)

Counto model [27]:

\frac{1}{E_{c}} = \frac{1 - V_{f}^{1 / 2}}{E_{m}} + \frac{1}{[(1 - V_{f}^{1 / 2}) V_{f}^{1 / 2}] E_{m} + E_{f}}

(3)

Paul model [28]:

E_{c} = E_{m} [\frac{1 - (m - 1) V_{f}^{\frac{2}{3}}}{1 + (m - 1) (V_{f}^{\frac{2}{3}} - V_{f})}]

(4)

Lower bound:

E_{c} = [\frac{E_{f} E_{m}}{E_{f} (1 - V_{f}) + E_{m} V_{f}}]

(5)

Where E_c, E_m, and E_f are Young’s moduli of the composite, resin (BisGMA/TEGDMA) and fillers particles of SiO₂, respectively, and V_f is the volume fraction of the reinforcement particles. Fig 3 shows the comparison of Young’s modulus obtained from the limited experimental [29] results with the micromechanics models (theoretical). The analytical models showed satisfactory validation with the experimental results and can hence be confidently used for the estimation of isotropic elastic properties (e.g. Young’s modulus) with the assumption that they will follow the same experimental pattern. During the validation process, it was noticed that the Guth model prediction was getting better with the increasing fiber volume fraction while the properties with the Counto model started decreasing. The analytical models were used to calculate Young’s modulus of the composite by increasing the volume ratio of the filler (10–70%). Thus, a better Young’s modulus of composites was obtained using the Guth model which was used for the comparative study with higher modulus as of amalgam. Fig 3 shows Young’s modulus versus particle volume fraction (SiO₂) up to 70% fiber volume fraction. Five Young’s moduli of the theoretically calculated composite (10, 14, 18, 22, and 26 GPa) were chosen for the simulation. They were labeled C10, C14, C18, C22, and C26, respectively. Amalgam and GCC were also used in finite element simulations as dental material restoration. All materials were assumed to be isotropic, homogenous, and linearly elastic. Young’s modulus and Poisson’s ratio of all materials are listed in Table 1.

Table 1. Properties of the materials used in FEA.

Components	Materials	Young’s Modulus (GPa)	Poisson’s Ratio (ν)	References
Mandibular Bone	Cortical bone	13.7	0.30	[30]
Mandibular Bone	Cancellous bone	1.37	0.30	[30]
Molar tooth	Enamel	84.1	0.33	[31, 32]
Molar tooth	Dentin	18.6	0.31	[31, 32]
Resin matrix	Bis-GMA/TEGDMA (30/70 mass ratio)	3.29	0.29	[33]
Reinforcement (filler)	Silica (SiO₂)	73	0.17	[33]
Restorative materials	Amalgam	35.0	0.35	[31]
	Composite	10	0.26	[31]
		14
		18
		22
		26
	GCC (Glass carbomer cement)	8.3	0.30	[34, 35]

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Mesh, loading, and boundary conditions

For the FEA, the models were imported into ABAQUS software v6.14 (Dassault Systèmes, Vélizy-Villacoublay, France). All the interfaces were considered perfectly bonded as the amalgam is very hard to de-bond as indicated in the literature [36]. The lower surfaces of the bone were fully constrained and a static uniformly distributed occlusal load of 600 N [37] simulating the maximum bite force was applied vertically on the top surface of the crown [38], as shown in Fig 1(d). Each 3D model of the tooth was meshed by finer linear tetrahedral elements (size of 0.05 for the tooth), and the bone was meshed using coarse elements to reduce computational cost. The good quality of the mesh was ensured by keeping the aspect ratio below 5. To make sure that the mesh seed size does not affect the results a mesh convergence was carried out. A series of simulations were conducted with the intact tooth model, varying mesh size (from larger elements with a size of 0.8 to the optimum number of elements with an element size of 0.05). The stress results converged when the total element number yielded more than 500,000 elements (for the intact tooth model, the maximum elements were (512134). The analyses were performed on three parameters, the condition of the molar (intact tooth, infected tooth, restored tooth), the shape of the cavity (cavities with Class I, Class II MO, Class II MOD), and the dental restorative materials (amalgam, GCC and composites). A total number of 27 simulations were executed.

Results

Finite element models of the molar crown, in all cases (healthy tooth, infected tooth, restored tooth) were constructed. Various types of dental cavities were also modeled. Conventional and new restorative materials were used in these models. Finite element models were used to simulate the cavities with different restorative materials. Results were extracted from the simulations to estimate the biomechanical performance of dental tissue and restorative material as well.

Stresses in different cavities

Three cases of cavities were studied, Class I, Class II MO, and Class III MOD, and they differ in volume sizes and designs. Class I cavity was formed in the occlusal crevice with 30 mm³ in volume. Class II MO and Class II MOD were prepared with 95.59 mm³ and 176 mm³, respectively. Fig 4. shows the stress distribution in enamel and dentin, respectively, with cavity Class I.

The numerical simulation findings are reported in Table 2. It was observed that higher von Mises stress was in the infected tooth with a value of 44.40 MPa in the enamel and 35 MPa in the dentin. Same note for maximum principal stress, 48.06 MPa in the enamel, and 40.20 in the dentin. As for the healthy tooth, it can be noted that von Mises stresses were lower compared to the infected tooth, with 21 MPa in the enamel, and 15.32 MPa in the dentin. The same pattern follows for principal stresses.

Table 2. Max stresses in enamel, dentin, and restorative parts of cavities (in MPa).

	Max stress	Intact tooth	Infected tooth	GCC	C10	C14	C18	C22	C26	Amalgam
		Enamel
Cavity Class I	vM stress	23.11 13.27 24.00	44.40	46.01	45.07	42.10	39.65	37.54	35.70	31.90
	maxP stress		20.43	17.73	17.38	16.72	16.30	16.00	15.70	15.48
	minP stress		48.06	50.87	49.62	46.27	43.41	40.90	38.70	34.40
Cavity Class II MO	vM stress		54.91	43.64	42.16	39.85	38.10	37.02	36.20	34.50
	maxP stress		25.20	15.33	14.70	14.20	13.95	13.69	13.47	13.03
	minP stress		58.27	46.17	43.68	42.00	40.71	39.60	38.66	37.30
Cavity Class II MOD	vM stress		170.80	44.67	40.40	34.26	30.03	26.92	24.50	20.41
	maxP stress		120.00	27.66	23.12	18.40	15.36	13.24	11.68	10.38
	minP stress		202.25	41.06	39.13	34.20	30.52	27.53	25.07	20.24
		Dentin
Cavity Class I	vM stress	15.32 1.97 18.57	35.04	23.61	22.41	19.49	17.50	16.18	15.20	14.03
	maxP stress		7.87	2.68	2.60	2.55	2.48	2.43	2.37	2.34
	minP stress		40.20	26.25	24.49	21.24	19.10	17.44	16.30	15.10
Cavity Class II MO	vM stress		45.19	39.18	37.89	35.98	34.64	33.63	32.87	31.28
	maxP stress		24.09	6.54	5.77	4.57	3.91	3.80	3.72	3.54
	minP stress		46.84	45.91	44.90	42.86	41.39	40.28	39.41	37.60
Cavity Class II MOD	vM stress		72.10	27.50	23.83	19.61	16.61	14.38	13.51	13.70
	maxP stress		28.04	7.37	6.11	4.78	4.06	3.54	3.14	2.76
	minP stress		81.00	22.65	21.00	17.24	14.56	14.07	14.30	14.66
		Restorative part
Cavity Class I	vM stress			10.90	12.50	14.96	16.88	18.45	19.79	21.34
Cavity Class I	minP stress			12.61	13.57	15.95	17.87	19.27	20.53	23.40
Cavity Class II MO	vM stress			16.21	16.40	16.70	17.27	19.28	21.14	23.96
Cavity Class II MO	minP stress			16.25	17.26	19.17	20.46	22.47	24.56	30.00
Cavity Class II MOD	vM stress			13.77	14.00	14.08	13.94	15.54	15.66	16.93
Cavity Class II MOD	minP stress			18.40	18.41	18.71	18.86	18.90	18.99	19.58

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vM*: Von Mises stress,

maxP*: Maximum principal stress,

minP *: Minimum principal stress in MPa

Fig 5. show von Mises stress distribution in the enamel and dentin with cavity Class II MO. The levels of stress experienced by the diseased tooth were found to be greater when compared to the healthy tooth. Higher von Mises stress was observed in the enamel (54.91 MPa), and 39.18 MPa in the dentin. It was noted that stresses in the case of cavity Class II MO were higher than those obtained with cavity Class I.

Fig 6. depicts the von Mises stress distribution in the enamel and dentin with cavity Class II MOD. When comparing a healthy tooth with an infected tooth with cavity Class II MOD. It is evident that greater levels of stress are present in infected teeth. The maximum stress in the enamel of the infected tooth was 170.80 MPa, and 72.10 MPa for the dentin. Through this comparison, it could be observed that as the size of the cavity increases, the stress on the enamel and dentin increases. Stresses (von Mises and principal stresses) were higher in the tooth with cavity Class II MOD compared to the tooth with cavity Class I and Class II MO, as well stresses were higher in the enamel than dentin in all cases. Enamel and dentin have a compressive strength of around 384 MPa and 297 MPa, respectively [22]. All minimum principal stress values obtained in enamel and dentin under loading of 600 N were below the compressive strength.

Enamel tensile strength is approximately 42 MPa, while the tensile strength of dentin is 44 MPa [22]. Fig 7. shows a comparison between principle stresses in all models, maximum principal stresses in the dentin were below the tensile strength. The same note is for the enamel, except for the infected tooth with cavity type II MOD, where the maximum stress (120 MPa) was greater than the tensile strength of enamel, and thus failure may occur. The comparison and findings in Table 2 demonstrate how the teeth behave differently in different biomechanical conditions.

Effect of dental restoration material

The tooth models with three classes of cavities were restored with 7 different materials (GCC, composite C10-C26, amalgam). The stress distribution in the restored tooth with different cavities and restorative materials is shown in Figs 4–6. The peak von Mises stress in different cavities was at the interfaces between the restorative part and the enamel, as well as between the restorative part and the dentin. The FEA findings (reported in Table 2) revealed that von Mises stress was higher in GCC material, with cavity Class I (46.01 MPa in the enamel, 23.61 MPa in the dentin), and for cavity Class II MO von Mises stress was 43.64 MPa, 39.18 MPa in enamel and dentin respectively, while in case of cavity Class II MOD von Mises stress was 44.67 MPa in enamel, 27.5 in the dentin. Through simulation results, it was noted that lower stresses were in the amalgam-restored tooth for cavity Class I, 31.90 MPa in the enamel, and 14.03 MPa in the dentin. The results indicated that the highest Young’s modulus of the restorative material was associated with the lowest peak stresses observed at the enamel and dentin levels. This highlights the crucial role played by Young’s modulus of the restorative material in determining the stress experienced by enamel and dentin tissues. In contrast, with the composite materials with different Young’s moduli (26, 22, 18, 14, 10 GPa), we noticed that stresses were higher with the lowest Young’s modulus (10 GPa), as we increased Young’s modulus (26 GPa), the stress was decreased in the enamel and dentin. Additionally, it is worth mentioning that all stress levels observed in the restored tooth were lower in comparison to the tooth affected by the cavity. As for the restorative part, it was remarked that increasing the effective stiffness of restorative material increased the stress at the level of the restorative part, von Mises stress was lower in GCC restorative part (10.9 MPa), and it was higher in the amalgam restorative material (21.34 MPa), and this was in the case of cavity Class I. Fig 7. shows the comparison of principal stress in enamel (Fig 7(a)) and dentin tissue (Fig 7(b)). All principal stresses (PS) values reported in restored cavities in enamel and dentin were lower than those of non-restored cases (Infected teeth). Fig 8. shows the maximum von Mises stress in the enamel and restorative part. The greater the stiffness of the restoration material, the lower the stress at the enamel level, and vice versa for the restorative part. The higher the stiffness, the higher the stress at the restorative material level.

Discussion

This study examines three different restorative materials (Amlgam, GCC, Composite) in relation to three categories of dental cavities, specifically Class I and Class II cavities, which include MO and MOD types. Teeth lacking any form of restoration are designated as infected teeth, while teeth with restorations are categorized as restored teeth. In the field of restorative dentistry, understanding the behavior of restored teeth has proven to be a multifaceted challenge. This complexity arises from the wide array of restorative materials available, encompassing both traditional and advanced options as each material type can exhibit distinct properties and behaviors. These advancements have the potential to overcome the limitations of amalgam material, including their ability to control mineral loss and modulate biofilm formation. Regarding GIC, limited evidence [39] suggests that restorations made with this material exhibit a notably superior preventive effect against the development of new caries when compared to other restoration materials.

The results revealed that the first null hypothesis, suggesting no significant difference in stress distribution between infected, healthy, and restored teeth, was not supported and was consequently rejected. The findings indicated that stress levels were notably higher in infected teeth when compared to both restored and healthy teeth. This difference in stress distribution can be attributed to variations in the load application area within the cases under investigation. Specifically, infected teeth exhibited a reduced occlusal area subjected to a 600 N force in comparison to their healthy counterparts. It is important to note that the intensity of a distributed load is contingent upon the force per unit area. Therefore, teeth with cavities transmit a heightened level of stress to the dentin tissue. Consequently, the reduction in tooth structure significantly diminishes tooth stiffness [40]. The findings revealed that as more tooth material was removed, an increased concentration of stresses was observed within the enamel and dentin tissues.

The maximum principal stress in an infected tooth’s enamel was 201 MPa, which is significantly higher than the ultimate tensile strength of enamel at approximately 42 MPa [41]. This means that the enamel is subjected to stress levels that are well beyond its capacity to withstand without exhibiting permanent deformation or damage. Moreover, in various conditions like tooth decay, consumption of acidic foods and drinks or chronic acid reflux may result in cracks, fractures, and even complete failure of the tooth structure [42].

Addressing early detection and treatment of dental infections promptly becomes pivotal in preventing the progression of damage and the subsequent necessity for extensive restorative techniques. Research investigating resin infiltration techniques [3, 43, 44] substantiates this notion, demonstrating their capacity to halt the advancement of white spot lesions. This underscores the importance of timely intervention as a preventive measure against the need for extensive dental restorations.

Additionally, the principal stresses were higher in the infected tooth with Class II MOD (Mesio-Occlusal-Distal) cavity compared to other cavities. Class II MOD cavity preparations involve the removal of a significant portion of the tooth structure, including both the mesial and distal surfaces. This type of preparation is more extensive than Class II MO and Class I Occlusal preparations, which involve the removal of tooth structure from a single surface. The removal of more tooth structure in Class II MOD preparations results in a larger cavity volume and a greater loss of tooth structure, which can lead to increased stresses in the remaining tooth structure. This emphasizes the need for careful consideration and selection of dental materials used for cavity II MOD dental restorations to ensure they can withstand the stresses imposed on them during function. Furthermore, the findings align with previous research indicating that a decayed tooth can generate greater stress than an undamaged tooth [45]. Nowadays, researchers are looking for means to standardize cavity preparations so that the underlying tooth can be preserved.

The second null hypothesis, which stated that the stiffness of restorative materials has no consequential influence on the stress distribution observed in restored teeth, was also not supported and therefore was rejected. The findings indicate that the type of cavity and the varying stiffness of restorative materials do indeed affect the distribution of stress within the enamel and dentin tissues of restored teeth.

Higher stress in enamel and dentin was in the restored tooth with GCC material and the lower stress was in the restored tooth with amalgam material. In the case of composite (C) material, the stress in enamel and dentin was less when Young’s modulus of composite material was lower (10 GPa), and vice versa. Results are in agreement with a previous study [31], which has reported that for a certain Young’s modulus of the restoration material, the first principal stress becomes minimum at the enamel.

When it comes to the stiffness of restoration materials, a study [46] revealed that a higher Young’s modulus of the restorative substance leads to a reduction in stress on both enamel and dentin, even when specifically discussing amalgam. A study [47] demonstrated that restoration with various cavity designs (five distinct Class II restored with composite resin) resulted in different stress magnitudes during the processes of polymerization shrinkage and loading effects on dental tissue. This underscores the influence of cavity geometry on stress distribution.

According to another study [48], endocrown design preparation has a significant impact on long-term success, and restorative materials with a lower modulus of elasticity had more homogeneous stress distribution on the dentin tissue, whereas materials with high young modulus had low stress transmission to the dentin tissue. Another study [35] reported that the GCC material transfers more von Mises stress in the dentin tissue compared to amalgam and composite materials with Class II MOD cavities.

In conjunction with the aforementioned findings regarding the influence of different cavities and restorative materials on stress distribution in teeth, a study [49] explored the impact of restorative material choice on stress distribution within endocrown restorations. The research revealed that the selection of restorative material had a notable effect on stress distribution patterns within endocrown restorations, while the application of fibers did not significantly alter stress distribution in either endocrown group.

The mechanical properties of restorative materials, particularly Young’s modulus, are crucial in determining the clinical performance of endodontically treated teeth that have been restored. In this context, the stiffness of restorative materials is intentionally kept lower than that of enamel to strengthen the tooth structure rather than weaken it.

Composite resins, designed to replicate the natural appearance of teeth and closely mimic their mechanical properties, demonstrate a favorable attribute in adapting to the natural flexure and movement of teeth during function. This adaptability potentially contributes to a more uniform distribution of stress forces, mitigating the likelihood of stress concentration points at the adhesive-tooth interface. An in vitro study corroborated this behavior, demonstrating that the use of composite resin reduces stress concentration at the interface between the adhesive and the tooth compared to materials with a higher Young’s modulus than enamel [42].

Results showed less variation in the peak stresses between the tooth restored with amalgam and the tooth with composite C26 (which has a Young’s modulus of 26 GPa) when compared to other composites with lower Young’s moduli. Biomechanically, there was no statistically significant difference between amalgam and composite in terms of fractures, but the longevity of the composite in posterior teeth remains less. Despite other options being available, composite has emerged as the primary material preferred by dentists for restorative purposes, with favorable attitudes being expressed towards its use [50]. Higher stresses were observed in the enamel compared to the dentin tissue. This difference can be attributed to the fact that enamel is considered to be harder than dentin and possesses higher wear resistance. These two tissues also differ in composition and internal structures and have distinct biomechanical roles [51]. Additionally, in comparison to GCC, composite resins are more effective [52], and they release less fluoride. According to some authors [53, 54], composite resin materials are favored over glass ionomer cement for sealing pits and fissures due to their superior retention properties.

Dentists generally focus on the necessity of preserving dental tissue [55] over quantifying the number of surgical restorative procedures performed. Achieving this goal requires the development of new tools, reimbursement incentives, and collaboration to coordinate the implementation of an improved dental cavity management system across various domains [56].

With the increasing use of digital impressions and 3D printing in dental clinics [57], it is now possible to leverage CAD-CAM techniques to produce nanohybrid restorative materials that are better suited for dental tissue. Furthermore, recent developments in artificial neural network models have led to the creation of predictive tools for post-streptococcus mutants in dental cavities, which can be integrated with digital impressions and 3D printing technologies to enable even more accurate and personalized treatment options for dental patients [58].

FEA stands as a potent tool in the realms of bioengineering and dentistry, and our study’s primary objective was to scrutinize the repercussions of dental cavities and different restorative materials on the performance of enamel and dentin tissues.

It is essential, however, to acknowledge certain limitations inherent to our research. Notably, we employed a simplified assumption by considering all materials as homogenous, isotropic, and linearly elastic. Furthermore, our loading conditions were somewhat idealized, and variations such as oblique or parafunctional loading could impose varying stress patterns on the tooth structure. In this study, finite element models did not include PDL considering that the exclusion of PDL affects minimal to the stresses in the crown and surrounding tissues [22]. Another facet of consideration is the derivation of Young’s modulus for the composite material, which was based on theoretical models rather than empirical testing. Although these models have been substantiated in previous research, the importance of experimental verification of the calculated Young’s modulus cannot be overstated. Hence, prospective studies should prioritize the conduction of such experiments to corroborate the accuracy of the theoretical models employed here, thereby enriching our comprehension of composite material properties.

Conclusion

From this study, it was concluded that the geometry of cavities and different restorative materials affect the biomechanical performance of the restored tooth. Nanocomposite resin is a good alternative material for dental hard tissue restoration especially for patients who are concerned about the potential toxicity of mercury or aesthetic restoration.

Infected or damaged teeth with cavities are prone to higher stresses as compared to healthy teeth.
Larger cavities generate higher stresses in enamel and dentin tissues, thus, to protect the remaining teeth, the larger and smaller cavities should be filled as early as possible.
Without filling the cavity, the stresses may reach higher than the strength of the enamel which may cause further damage to the tooth.
The restoration of Class II MOD cavity is very tricky and complex because of the removal of large tissue, which may require more care and maintenance during their normal function.
The selection of restorative material is the key to efficiently restoring the function of the tooth. Therefore, resin-based composites are good alternative materials due to the tailorable Young’s modulus according to the biomechanical and clinical requirements.
Overall, amalgam and composite C26 (26 GPa) outperformed biomechanically but composites are preferred over amalgam due to aesthetic and clinical concerns of amalgam.

Supporting information

S1 Dataset

(ZIP)

Click here for additional data file.^{(55.7KB, zip)}

Acknowledgments

The authors would like to thank Prince Sultan University for their support.

Data Availability

All relevant data are within the manuscript and Supporting information files.

Funding Statement

The authors received no specific funding for this work.

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PONE-D-23-26356Biomechanical performance of resin composite on dental tissue restoration: A computational analysisPLOS ONE

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Reviewer #1: The present study investigated the biomechanical performance of various dental materials when filled into different cavity designs and their effects on surrounding dental tissues. The subject is intriguing and has the potential to contribute to the scientific literature.

Title:

Please indicate that this is an FEA study.

Abstract:

Loading information is missing.

Introduction:

The introduction lacks an explanation of different cavities and their significance as evaluation factors. Additional information about glass carbomer cement and its comparison with resin composite and amalgam should be introduced. Include a hypothesis at the end of this section.

Methods:

The tooth was modeled using a reference image and freeform features. Provide a description of the tooth number and shape. Explain how cortical bone thickness was defined. Justification for not including the PDL and pulp in the design needs revision. While it's acknowledged that soft tissue could affect stress distribution, the statement claiming no effect should be omitted. During the validation process, it was observed that the Guth model's prediction improved with increasing fiber volume fraction, whereas properties with the Counto model decreased. Provide a justification for this observation. Clarify that Young's Modulus is theoretical. Specify the aspect ratio of your mesh. Explain the choice of focusing on von-Mises stress over the first principal stress.

Discussion:

Enhance the discussion regarding the comparison of different cavity designs. Provide more information about model validation and FEA limitations concerning PDL, soft tissue, and parafunctional loading.

Conclusion:

The conclusion is overly lengthy. Condense the text, remove redundant results, and present only the most clinically significant findings to the readers.

Reviewer #2: Intro

- "Several factors lead to an ecological imbalance between (...) that contribute to creating tooth cavities [2]." Please add some short thoughts on the pre-cavity stage. Remember that this would seem even more (or at least equally) important to prevent progress of caries (and cavitation). Refer to https://www.quintessence-publishing.com/deu/de/article/840164/quintessence-international/2009/08/closing-the-gap-between-oral-hygiene-and-minimally-invasive-dentistry-a-review-on-the-resin-infiltration-technique-of-incipient-proximal-enamel-lesions, and to https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0228249. Discuss adequately.

- Provide digestible units/divide into paragraphs.

- Avoid Authors' names with your full text.

- "The purpose of this study is to investigate (...)." Your study has already been finished, right? Must read "The purpose of this study was to investigate (...)."

Results

- "(...) with cavity class I." must read "(...) with cavity Class I."

- Same with "cavity class II". Revise thoroughly.

Discussion

- "The behavior of restored teeth is not well characterized due to the variety of restorative materials (both traditional and advanced materials)." Meaning would seem unclear, please expand your thoughts, and provide references.

- Same with "the stress was greater in the infected teeth". Please clarify.

- Refer to https://journals.sagepub.com/doi/10.1177/00220345890680111401

when explaining your thoughts.

- Again, provide digestible units by paragraphing.

- Add some thoughts on the limitations of your study.

Conclusion

- "The aim of this study was to analyze how (...)." This is not considered a conclusion from your study.

- Same with "Five restorative materials were studied, glass-carbomer cement, amalgam, and dental composite with stiffness variation (10 G Pa to 26 G Pa with an increment of 4)."

- Same with "Nanocomposite resin may be an excellent choice (...)."

- With your Conclusion section, please stick exclusively to your revised aims. Do not simply repeat your results here. Do not speculate. Instead, provide a reasonable and generalizable extension of your outcome.

Refs

- Revise for uniform Journal style. No capital letters with the various Titles.

In total, this would seem an interesting draft, easily intelligible, and considered ready to proceed after some revisions, please see below.

Reviewer #3: The goal of this study is to examine how dental tissues react when cavities of various shapes are filled with alternative restorative materials. Three classes of cavities were chosen, class I (occlusal), class II MO (mesio-occlusal), class II MOD (mesio-occlusal-distal), and three types of restoration material were selected, amalgam, glass carbomer cement (GCC), and silica-reinforced polymer composites with five different Young’s moduli. While it is good that the results have practical impact in terms of application, there are problems in modeling, especially in the creation of finite element models. Therefore, I think it needs to be revised and needs a second check.

The figures and pictures are so blurry that it is difficult to read.Please enrich the quality of the figures and pictures.

Wouldn't the periodental ligament have an effect on stress changes? Not considered in the modeling.

The Author said that ”Each 3D model of the tooth was meshed by finer linear tetrahedral elements (size of 0.05 for the tooth), and the bone was meshed using coarse elements to reduce computational cost”. However, while finite elements are a way of representing the structure as an elastic structure, the element quality has a very important effect on this representation. Three classes of cavities were used. However, there will be geometry changes. How did the same element size suffice for all of them? Linear element was used and compared to quadratic type, tetrahedron element has poor performance and high margin of error. I suggest the authors to do a convergence analysis and quadratic element.

It would be better for comparison if the fringes used in the figures in the stress distributions have the same range.

I recommend the author to add the following publication to the literature search. In this publication "The restorative material type changed the stress distribution of endocrown restorations. The fiber application did not affect the stress distribution in either endocrown group. But, more stress absorption was observed in fiber under IPS-E than C-E." is the conclusion that will contribute to the content of the publication.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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PLoS One. 2023 Dec 21;18(12):e0295582. doi: 10.1371/journal.pone.0295582.r002

Author response to Decision Letter 0

28 Oct 2023

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Partly

________________________________________

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: N/A

Reviewer #3: I Don't Know

________________________________________

3. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes

________________________________________

4. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: No

________________________________________

5. Review Comments to the Author

Reviewer #1:

The present study investigated the biomechanical performance of various dental materials when filled into different cavity designs and their effects on surrounding dental tissues. The subject is intriguing and has the potential to contribute to the scientific literature.

Title:

Please indicate that this is an FEA study.

� Response:

Thank for your comment. The title is revised as per your recommendation.

“Biomechanical performance of resin composite on dental tissue restoration: A finite element analysis”

Abstract:

Loading information is missing.

� Response:

Thank you for your feedback; we have updated the abstract to include the occlusal load information as suggested.

“An occlusal load of 600 N was distributed on the top surface of the teeth to carry out simulations.”

Introduction:

� Response:

Thanks for your comments to strengthen the introduction. The following paragraphs are added to the introduction as per your suggestion to strengthen the manuscript.

“According to the G.V. Black classification system, a demineralization lesion situated within the pits and fissures of the occlusal (biting) surface is denoted as a Class I lesion, whereas a lesion found on the proximal surface of a posterior tooth is classified as a Class II lesion [5]. Within the Class II category, there exist various subtypes such as mesial and occlusal surfaces (MO) and mesial, occlusal, and distal surfaces (MOD) cavities [6].

The first hypothesis posits that an infected tooth will have a significant difference in stress distribution in enamel and dentin compared to a restored or healthy tooth. The second hypothesis suggests that the stiffness of restorative materials significantly affects the stress distribution in restored teeth.”

Methods:

The tooth was modeled using a reference image and freeform features. Provide a description of the tooth number and shape.

� Response:

We have modeled the first molar (tooth number 30) located in the right mandible. The first molar has a typical molar shape characterized by multiple cusps and a broad occlusal surface. Figure 1 shows the shape and location of the modelled tooth.

“A first molar tooth (tooth number 30 in the right mandible) was modeled using a reference image and freeform feature. This tooth has a typical molar shape (a rectangular shape with pits and fissures on it) characterized by multiple cusps and a broad occlusal surface as shown in Fig 1.”

Explain how cortical bone thickness was defined.

� Response:

We established the cortical bone thickness by utilizing thickness features within the SolidWorks software. After designing the surfaces representing the cortical bone layer and the internal architecture of the cancellous bone core, we applied these thickness features to accurately model a cortical bone layer of 1.5 mm, effectively encircling the internal cancellous bone structure.

“The thickness of the cortical bone was modeled as 1.5 mm thick using a thickness feature within SolidWorks after designing surfaces to encompass the internal core of the cancellous bone.”

Justification for not including the PDL and pulp in the design needs revision. While it's acknowledged that soft tissue could affect stress distribution, the statement claiming no effect should be omitted

� Response:

Thanks for highlighting the importance of modelling. It is important to emphasize that our decision aligns with established practices in similar studies. Many research articles in the field of dental biomechanics have consistently omitted the PDL, especially when focusing on stress distribution at the crown level rather than the root. This exclusion is substantiated by the well-documented characteristics of the PDL, including its low stiffness, with a frequently used value of E at 68.9 MPa, and its thin structure, typically measuring 0.2 mm in thickness. These attributes, supported by existing literature, suggest that the PDL's influence on peak stresses at the tooth crown level is negligible. Therefore, based on both precedent and the physical properties of the PDL, its exclusion from our design was a scientifically justified and the justification is added to the manuscript.

https://doi.org/10.1016/j.jmbbm.2022.105305

https://doi.org/10.1080/01694243.2016.1195953

https://doi.org/10.1080/13102818.2015.1015445

https://doi.org/10.1080/13102818.2017.1373600

https://doi.org/10.1016/j.jmbbm.2021.104892

https://doi.org/10.1016/j.dental.2020.11.008

https://doi.org/10.1016/j.jds.2017.03.010

https://doi.org/10.1016/j.dental.2009.07.014

https://doi.org/10.1016/j.dental.2021.01.020

“The thickness of the cortical bone was modeled as 1.5 mm thick using a thickness feature within SolidWorks after designing surfaces to encompass the internal core of the cancellous bone. The PDL (periodontal ligament) and the pulp were not included in our design because it has been established in the literature that when simulating stress distribution at the crown level (regions of interest), the PDL is often excluded due to its well-documented characteristics, including its low stiffness (around 68.9 MPa) and its thin structure (typically 0.2 mm in thickness). These attributes suggest that the PDL's influence on peak stresses at the tooth crown level is negligible. Therefore, the exclusion of PDL and pulp modeling aligns with established modeling techniques [22].”

During the validation process, it was observed that the Guth model's prediction improved with increasing fiber volume fraction, whereas properties with the Counto model decreased. Provide a justification for this observation.

� Response:

We appreciate the reviewer's comment and would like to clarify that in our study, both the Guth and Counto models indeed exhibited an increase in Young's modulus with an increasing fiber volume fraction. The observed discrepancy between the two models arises from their distinct formulas for calculation. The Guth model inherently provides higher Young's modulus values compared to the Counto model due to the mathematical differences in their predictions. It's crucial to recognize that these models are based on unique theoretical foundations and, therefore, yield varying results. The consistent trend of Young's modulus increasing with fiber volume fraction in the Guth model not only supports the validity of our findings but also underscores its utility for comparative purposes. We specifically utilized the Guth model because it provides Young's modulus values at certain volume fractions that closely resemble those of amalgam materials, facilitating a meaningful and relevant comparison within the context of our study.

Clarify that Young's Modulus is theoretical.

� Response:

Thank you for your comment.

“Various theoretical models were employed to predict elastic moduli of micro-filled composite materials, which were compared with experimental results and showed good agreement [24]. Therefore, this study used these models (Eq 1 – 5) to predict the elastic moduli of composites.

Five Young’s moduli of the theoretically calculated composite (10, 14, 18, 22, and 26 GPa) were chosen for the simulation.”

Specify the aspect ratio of your mesh.

The aspect ratio of the mesh was consistently maintained below 5. Thank you for your comment.

“The good quality of the mesh was ensured by keeping the aspect ratio below 5.”

Explain the choice of focusing on von-Mises stress over the first principal stress.

� Response:

Thank you for your valuable comment. Von-Mises stress is a scalar quantity that takes into account the magnitude of stresses (considering both tensile and compressive stresses). Von-Mises stress provides a valuable measure of stress intensity that is particularly useful for assessing material failure, as it considers the combined effect of both the magnitude and the spread of stress in multiple directions, making it a more comprehensive indicator for structural analysis and material design. Moreover, von-Mises stress is commonly used in various biomechanical studies due to its applicability in characterizing stress states. However, it's important to note that we also assessed the first principal stress as part results of our study to provide a more comprehensive understanding of the stress distribution within the dental tissues.

Discussion:

Thank you for your comment. Some references were added in the discussion for the model validation including FE related research. We have incorporated FEA limitations at the end of the discussion as well.

The results revealed that the first hypothesis, which proposed that there would be a significant difference in stress distribution between infected, healthy, and restored teeth, was true. The findings indicated that stress levels were notably higher in infected teeth when compared to both restored and healthy teeth. This difference in stress distribution can be attributed to variations in the load application area within the cases under investigation. Specifically, infected teeth exhibited a reduced occlusal area subjected to a 600 N force in comparison to their healthy counterparts. It is important to note that the intensity of a distributed load is contingent upon the force per unit area. Therefore, teeth with cavities transmit a heightened level of stress to the dentin tissue. Consequently, the reduction in tooth structure significantly diminishes tooth stiffness [40]. The findings revealed that as more tooth material was removed, an increased concentration of stresses was observed within the enamel and dentin tissues.

FEA stands as a potent tool in the realms of bioengineering and dentistry, and our study's primary objective was to scrutinize the repercussions of dental cavities and different restorative materials on the performance of enamel and dentin tissues.

It is essential, however, to acknowledge certain limitations inherent to our research. Notably, we employed a simplified assumption by considering all materials as homogenous, isotropic, and linearly elastic. Furthermore, our loading conditions were somewhat idealized, and variations such as oblique or parafunctional loading could impose varying stress patterns on the tooth structure. In this study, finite element models did not include PDL considering that the exclusion of PDL affects minimal to the stresses in the crown and surrounding tissues [22]. Another facet of consideration is the derivation of Young's modulus for the composite material, which was based on theoretical models rather than empirical testing. Although these models have been substantiated in previous research, the importance of experimental verification of the calculated Young's modulus cannot be overstated. Hence, prospective studies should prioritize the conduction of such experiments to corroborate the accuracy of the theoretical models employed here, thereby enriching our comprehension of composite material properties.

Conclusion:

The conclusion is overly lengthy. Condense the text, remove redundant results, and present only the most clinically significant findings to the readers.

� Response:

The conclusion is revised and key finding are listed in the conclusion. We believe that now conclusion is comprehensive and in a better shape.

• Infected or damaged teeth with cavities are prone to higher stresses as compared to healthy teeth.

• Larger cavities generate higher stresses in enamel and dentin tissues, thus, to protect the remaining teeth, the larger and smaller cavities should be filled as early as possible.

• Without filling the cavity, the stresses may reach higher than the strength of the enamel which may cause further damage to the tooth.

• The restoration of Class II MOD cavity is very tricky and complex because of the removal of large tissue, which may require more care and maintenance during their normal function.

• The selection of restorative material is the key to efficiently restoring the function of the tooth. Therefore, resin-based composites are good alternative materials due to the tailorable Young’s modulus according to the biomechanical and clinical requirements.

• Overall, amalgam and composite C26 (26 GPa) outperformed biomechanically but composites are preferred over amalgam due to aesthetic and clinical concerns of amalgam.

Reviewer #2:

Reviewer #2: Intro

-"Several factors lead to an ecological imbalance between (...) that contribute to creating tooth cavities [2]." Please add some short thoughts on the pre-cavity stage. Remember that this would seem even more (or at least equally) important to prevent progress of caries (and cavitation). Refer to https://www.quintessence-publishing.com/deu/de/article/840164/quintessence-international/2009/08/closing-the-gap-between-oral-hygiene-and-minimally-invasive-dentistry-a-review-on-the-resin-infiltration-technique-of-incipient-proximal-enamel-lesions, and to https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0228249. Discuss adequately.

�Response:

Thanks for your comment. The introduction is revised and the literature from the mentioned papers has been added and cited as per your suggestion.

“However, modern dentistry prioritizes minimal intervention by emphasizing preventative and non-surgical approaches to safeguard tooth hard tissues before the formation of dental cavities. In this regard, the resin infiltration technique is widely used which involves the application of a low-viscosity resin to infiltrate porous and demineralized inter-crystalline spaces within enamel lesions [3]. In an ex vivo study [4], researchers investigated the treatment of non-cavitated and micro-cavitated caries using a modified resin incorporating silver nanoparticles (AgNP) for both internal and external infiltration, aiming to confer antimicrobial properties. The findings revealed that the AgNP-infused resin effectively hindered the regrowth of microbial biofilms while preserving the mechanical integrity of the enamel and preventing the recurrence of caries [3]. Timely intervention to address demineralized and porous enamel lesions is critical, as untreated lesions may progress to dental cavities.”

- Provide digestible units/divide into paragraphs.

�Response:

Thank you for your comment. The introduction has been revised according to your suggestion and divided into paragraphs.

- Avoid Authors' names with your full text.

�Response:

Thanks for your comment. The names of authors were removed from the text as per your suggestion.

- "The purpose of this study is to investigate (...)." Your study has already been finished, right? Must read "The purpose of this study was to investigate (...)."

�Response:

Thank you for pointing out the error; we have now corrected the sentence to read.

"The purpose of this study was to investigate the behavior of dental tissues using alternative restorative materials to fill cavities of varying designs."

Results

- "(...) with cavity class I." must read "(...) with cavity Class I."

- Same with "cavity class II". Revise thoroughly.

�Response:

Thank you for your feedback; we have revised the manuscript to capitalize "cavity Class.. " as suggested.

Discussion

"The behavior of restored teeth is not well characterized due to the variety of restorative materials (both traditional and advanced materials)." Meaning would seem unclear, please expand your thoughts, and provide references.

�Response:

Thank you for your remarkable note. We have revised the discussion section, by adding following paragraphs:

“In the field of restorative dentistry, understanding the behavior of restored teeth has proven to be a multifaceted challenge. This complexity arises from the wide array of restorative materials available, encompassing both traditional and advanced options as each material type can exhibit distinct properties and behaviors. These advancements have the potential to overcome the limitations of amalgam material, including their ability to control mineral loss and modulate biofilm formation. Regarding GIC, limited evidence [39] suggests that restorations made with this material exhibit a notably superior preventive effect against the development of new caries when compared to other restoration materials.”

- Same with "the stress was greater in the infected teeth". Please clarify.

- Refer to https://journals.sagepub.com/doi/10.1177/00220345890680111401

when explaining your thoughts.

�Response:

Thank you for your valuable feedback. We have taken your suggestion into consideration and have now added a clarification regarding the higher stress observed in infected teeth. Additionally, we have included the reference you provided.

The findings indicated that stress levels were notably higher in infected teeth when compared to both restored and healthy teeth. This difference in stress distribution can be attributed to variations in the load application area within the cases under investigation. Specifically, infected teeth exhibited a reduced occlusal area subjected to a 600 N force in comparison to their healthy counterparts. It is important to note that the intensity of a distributed load is contingent upon the force per unit area. Therefore, teeth with cavities transmit a heightened level of stress to the dentin tissue. Consequently, the reduction in tooth structure significantly diminishes tooth stiffness [40]. The findings revealed that as more tooth material was removed, an increased concentration of stresses was observed within the enamel and dentin tissues.

- Again, provide digestible units by paragraphing.

�Response:

Thank you for your suggestion. The discussion has been revised.

- Add some thoughts on the limitations of your study.

Thank you for your comment. We have added some limitations at the end of discussion section.

“It is essential, however, to acknowledge certain limitations inherent to our research. Notably, we employed a simplified assumption by considering all materials as homogenous, isotropic, and linearly elastic. Furthermore, our loading conditions were somewhat idealized, and variations such as oblique or parafunctional loading could impose varying stress patterns on the tooth structure. In this study, finite element models did not include PDL considering that the exclusion of PDL affects minimal to the stresses in the crown and surrounding tissues [22]. Another facet of consideration is the derivation of Young's modulus for the composite material, which was based on theoretical models rather than empirical testing. Although these models have been substantiated in previous research, the importance of experimental verification of the calculated Young's modulus cannot be overstated. Hence, prospective studies should prioritize the conduction of such experiments to corroborate the accuracy of the theoretical models employed here, thereby enriching our comprehension of composite material properties.”

�Response:

Conclusion

- "The aim of this study was to analyze how (...)." This is not considered a conclusion from your study.

- Same with "Five restorative materials were studied, glass-carbomer cement, amalgam, and dental composite with stiffness variation (10 G Pa to 26 G Pa with an increment of 4)."

- Same with "Nanocomposite resin may be an excellent choice (...)."

�Response: Thank you for your continued guidance and feedback on our conclusion section. We have carefully revised it to ensure that it aligns with your recommendations:

• Infected or damaged teeth with cavities are prone to higher stresses as compared to healthy teeth.

• Larger cavities generate higher stresses in enamel and dentin tissues, thus, to protect the remaining teeth, the larger and smaller cavities should be filled as early as possible.

• Without filling the cavity, the stresses may reach higher than the strength of the enamel which may cause further damage to the tooth.

• The restoration of Class II MOD cavity is very tricky and complex because of the removal of large tissue, which may require more care and maintenance during their normal function.

• Overall, amalgam and composite C26 (26 GPa) outperformed biomechanically but composites are preferred over amalgam due to aesthetic and clinical concerns of amalgam.

We hope these revisions better address your concerns and appreciate your diligence in helping us improve the focus and clarity of our conclusion.

Refs

- Revise for uniform Journal style. No capital letters with the various Titles.

�Response:

Thank you for pointing out the need for uniform journal style with no capital letters in various titles.

In total, this would seem an interesting draft, easily intelligible, and considered ready to proceed after some revisions, please see below.

�Response:

Thank you for your positive assessment of the draft. We appreciate your feedback. We have already made the necessary revisions to the manuscript based on your suggestions.

Reviewer #3:

�Response:

We appreciate your comment and checked other studies similar to this study and found that the models are correct based on reasonable assumptions. Besides that, the authors possess well established techniques in finite element modelling and analysis of implants.

The figures and pictures are so blurry that it is difficult to read. Please enrich the quality of the figures and pictures.

�Response:

Your comment is greatly valued. The system of PLOSOne journal reduces the quality of the figures on the website, which is indicated during the submission process, however, high resolution figures can be download to the given link on the top right side of each figure. Below is the example of download and submitted high-resolution figure.

System generated PDF file figure.

Submitted and downloaded high quality figure from right side link.

Wouldn't the periodental ligament have an effect on stress changes? Not considered in the modeling.

�Response:

Thank you for your thoughtful comment. It's important to note that many similar studies have also excluded the PDL in their simulations (see following articles), particularly when the cavities are located at the crown rather than the root. Additionally, the PDL's low stiffness (the most frequently used value of E is 68.9 MPa) and thin structure (0.2 mm thickness) make it unlikely to significantly impact peak stresses at the tooth crown level, as supported by the literature.

https://doi.org/10.1080/01694243.2016.1195953

https://doi.org/10.1080/13102818.2015.1015445

https://doi.org/10.1080/13102818.2017.1373600

https://doi.org/10.1016/j.jmbbm.2021.104892

https://doi.org/10.1016/j.dental.2020.11.008

https://doi.org/10.1016/j.jds.2017.03.010

https://doi.org/10.1016/j.jmbbm.2022.105305

https://doi.org/10.1016/j.dental.2009.07.014

https://doi.org/10.1016/j.dental.2021.01.020

The following text is added to the manuscript for clarification.

“The PDL (periodontal ligament) and the pulp were not included in our design because it has been established in the literature that when simulating stress distribution at the crown level (regions of interest), the PDL is often excluded due to its well-documented characteristics, including its low stiffness (around 68.9 MPa) and its thin structure (typically 0.2 mm in thickness). These attributes suggest that the PDL's influence on peak stresses at the tooth crown level is negligible. Therefore, the exclusion of PDL and pulp modeling aligns with established modeling techniques [22]”

�Response:

Thank you for your valuable comment. We acknowledge the importance of element quality in finite element analysis and appreciate your suggestion regarding a convergence analysis using quadratic elements. In our study, we maintained a consistent element size for all models to ensure uniform meshing conditions. We appreciate your suggestion and will consider it for future work to further refine our modeling and analysis. It's worth mentioning that the authors possess well established techniques in finite element modelling and analysis of implants including the advantages of quadratic elements for structures with complex geometries like bones and teeth. However, in this particular study, mesh convergence was rigorously conducted using both linear tetrahedral and quadratic elements with the same seed size to ensure consistency across all models. Interestingly, the results from both element types yielded similar outcomes. This suggests that, for the specific focus of this study, the linear tetrahedral elements were adequate in capturing the relative differences in biomechanical performance among the different cavity classes.

It would be better for comparison if the fringes used in the figures in the stress distributions have the same range.

�Response:

Thank you for your suggestion. While using the same legend for all stress distributions may aid in direct comparison, it's important to note that it can make it challenging to discern peak stresses, particularly in regions with small elements. To maintain clarity and readability in our figures, we opted to use legends with different ranges for stress distributions, which allows us to emphasize critical stress variations and make them more apparent to the reader.

�Response:

Thank you for your valuable suggestion, and we appreciate your input. We have now included the recommended publication in our literature search to enhance the content of our manuscript.

“In conjunction with the aforementioned findings regarding the influence of different cavities and restorative materials on stress distribution in teeth, a study [47] explored the impact of restorative material choice on stress distribution within endocrown restorations. The research revealed that the selection of restorative material had a notable effect on stress distribution patterns within endocrown restorations, while the application of fibers did not significantly alter stress distribution in either endocrown group.”

________________________________________

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Attachment

Submitted filename: Comments 1909.docx

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PLoS One. doi: 10.1371/journal.pone.0295582.r003

Decision Letter 1

Artak Heboyan

7 Nov 2023

PONE-D-23-26356R1Biomechanical performance of resin composite on dental tissue restoration: A finite element analysisPLOS ONE

Dear Dr. Mehboob,

Please submit your revised manuscript by Dec 22 2023 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

We look forward to receiving your revised manuscript.

Kind regards,

Artak Heboyan, Ph.D.

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Reviewer #1: I am thoroughly satisfied with the current version as it fulfills all my requirements and expectations to the fullest extent of this paper.

Reviewer #2: With the help of the reviewers, this revised and re-submitted manuscript has been considerably improved. Notwithstanding, still some minor issues would seem in need of revision, please see below.

- "The first hypothesis posits that (...)" and "The second hypothesis suggests that (...)" - please provide a sound and valid NULL HYPOTHESIS. The latter must be deducible from the forgoing thoughts.

- "The results revealed that the first hypothesis, which proposed that there would be a significant difference in stress distribution between infected, healthy, and restored teeth, was true." Please note that a hypothesis never will be "true". Again, please provide a sound NULL hypothesis (see comments given above), and remember that H0 can be rejeceted or not rejected.

- Same with "The second hypothesis of the study (...) was also true." Revise carefully.

- "This highlights the importance of early detection and treatment of dental infections to prevent the progression of damage and the need for extensive restorative procedures." Sound references missing. Again, please stick to https://pubmed.ncbi.nlm.nih.gov/19639091/, to https://doi.org/10.13140/RG.2.2.36646.37443, and to https://pubmed.ncbi.nlm.nih.gov/28294198/. Please discuss.

- "An in vitro study reported that the use of composite resin reduces the amount of stress concentration at the interface between the adhesive and the tooth in comparison with other materials that have a higher Young modulus than enamel [42]." Remember that one sentence does not constitute one paragraph. Please provide digestible units.

This re-submitted manuscript will be worth following after some further revisions.

Reviewer #3: Although there are points about the number of elements, convergence study and quadratic element that I disagree with the author, I think that it is acceptable due to relative comparisons within itself. Other explanations and arrangements are sufficient and I think that the article can be published in your journal.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

**********

PLoS One. 2023 Dec 21;18(12):e0295582. doi: 10.1371/journal.pone.0295582.r004

Author response to Decision Letter 1

17 Nov 2023

Reviewer #1:

I am thoroughly satisfied with the current version as it fulfills all my requirements and expectations to the fullest extent of this paper.

�Response:

Thank you for accepting the revised version; I appreciate your approval for the article's publication in the journal.

Reviewer #2:

With the help of the reviewers, this revised and re-submitted manuscript has been considerably improved. Notwithstanding, still some minor issues would seem in need of revision, please see below.

1- “The first hypothesis posits that (...)" and "The second hypothesis suggests that (...)" - please provide a sound and valid NULL HYPOTHESIS. The latter must be deducible from the forgoing thoughts.

� Response:

Thank you for your valuable suggestions to enhance the manuscript. The introduction has been revised incorporating the following paragraph:

“The first null hypothesis maintains that no notable disparity exists in stress distribution within enamel and dentin between an infected tooth and a restored or healthy tooth. The second null hypothesis contends that the stiffness of restorative materials holds no consequential influence on the stress distribution observed in restored teeth.”

2- “The results revealed that the first hypothesis, which proposed that there would be a significant difference in stress distribution between infected, healthy, and restored teeth, was true." Please note that a hypothesis never will be "true". Again, please provide a sound NULL hypothesis (see comments given above), and remember that H0 can be rejected or not rejected.

� Response:

Thanks for your comments to improve the manuscript. We have revised carefully as suggested by reviewer.

3- Same with "The second hypothesis of the study (...) was also true." Revise carefully.

� Response:

The study's findings led to the rejection of both null hypotheses. Thank you for your valuable insights.

“The second null hypothesis, which stated that the stiffness of restorative materials has no consequential influence on the stress distribution observed in restored teeth, was also not supported and therefore was rejected.”

4- "This highlights the importance of early detection and treatment of dental infections to prevent the progression of damage and the need for extensive restorative procedures." Sound references missing. Again, please stick to https://pubmed.ncbi.nlm.nih.gov/19639091/, to https://doi.org/10.13140/RG.2.2.36646.37443, and to https://pubmed.ncbi.nlm.nih.gov/28294198/. Please discuss.

� Response:

We appreciate your valuable input in enhancing the manuscript. Following your guidance, the references mentioned above have been incorporated to strengthen and improve the manuscript.

“Addressing early detection and treatment of dental infections promptly becomes pivotal in preventing the progression of damage and the subsequent necessity for extensive restorative techniques. Research investigating resin infiltration techniques [3,43,44] substantiates this notion, demonstrating their capacity to halt the advancement of white spot lesions. This underscores the importance of timely intervention as a preventive measure against the need for extensive dental restorations”.

3. Kielbassa AM, Muller J, Gernhardt CR. Closing the gap between oral hygiene and minimally invasive dentistry: a review on the resin infiltration technique of incipient (proximal) enamel lesions. Quintessence Int. 2009;40: 663–81.

43. Kielbassa AM, Ulrich I, Werth VD, Schüller C, Frank W, Schmidl R. External and internal resin infiltration of natural proximal subsurface caries lesions: A valuable enhancement of the internal tunnel restoration. Quintessence Int (Berl). 2017;48.

44. Kielbassa AM, Ulrich I, Treven L, Mueller J. An updated review on the resin infiltration technique of incipient proximal enamel lesions. Med Evol. 2010;16: 3–15.

� Response:

We appreciate your guidance to enhance the manuscript; the paragraph below has been revised accordingly

“Composite resins, designed to replicate the natural appearance of teeth and closely mimic their mechanical properties, demonstrate a favorable attribute in adapting to the natural flexure and movement of teeth during function. This adaptability potentially contributes to a more uniform distribution of stress forces, mitigating the likelihood of stress concentration points at the adhesive-tooth interface. An in vitro study corroborated this behavior, demonstrating that the use of composite resin reduces stress concentration at the interface between the adhesive and the tooth compared to materials with a higher Young's modulus than enamel [42].”

Reviewer#3:

�Response:

Thank you for approving the revisions and for your recommendation to publish the article in the journal.

The authors thank all the reviewers for their valuable comments to improve the paper quality.

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PLoS One. doi: 10.1371/journal.pone.0295582.r005

Decision Letter 2

Artak Heboyan

23 Nov 2023

Biomechanical performance of resin composite on dental tissue restoration: A finite element analysis

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2. Is the manuscript technically sound, and do the data support the conclusions?

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PLoS One. doi: 10.1371/journal.pone.0295582.r006

Acceptance letter

Artak Heboyan

12 Dec 2023

PONE-D-23-26356R2

Biomechanical performance of resin composite on dental tissue restoration: A finite element analysis

Dear Dr. Mehboob:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

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PERMALINK

Biomechanical performance of resin composite on dental tissue restoration: A finite element analysis

Abdelhak Ouldyerou

Hassan Mehboob

Ali Mehboob

Ali Merdji

Laid Aminallah

Osama M Mukdadi

Imad Barsoum

Harri Junaedi

Roles

Abstract

Introduction

Materials and methods

Construction of 3D finite element models

Fig 1. Models configuration; (a) CAD modeling of the intact tooth, (b) Designs of cavities, (c) Assembly of the models, and (d) Loading, mesh, and boundary condition.

Properties of materials

Fig 2. Representative scheme of the use of SiO2-reinforced resin nanoparticle composites in FEA.

Fig 3. Comparison of Young’s modulus obtained from the experimental [29] and theoretical models for predicting composite Young’s modulus with increased fiber volume fraction.

Table 1. Properties of the materials used in FEA.

Mesh, loading, and boundary conditions

Results

Stresses in different cavities

Fig 4. Von Mises stress distribution in; (a) enamel and (b) dentin tissue with cavity Class I (in MPa).

Table 2. Max stresses in enamel, dentin, and restorative parts of cavities (in MPa).

Fig 5. Von Mises stress distribution in; (a) enamel and (b) dentin tissue with cavity Class II MO (in MPa).

Fig 6. Von Mises stress distribution in; (a) enamel and (b) dentin tissue with cavity Class II MOD (in MPa).

Fig 7. Comparison of principal stress in the restored tooth with different cavities and different restorative materials; (a) enamel, and (b) dentine.

Effect of dental restoration material

Fig 8. Maximum von Mises stress in the enamel and restorative material with different cavities.

Discussion

Conclusion

Supporting information

Acknowledgments

Data Availability

Funding Statement

References

Decision Letter 0

Artak Heboyan

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Author response to Decision Letter 0

Decision Letter 1

Artak Heboyan

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Author response to Decision Letter 1

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Artak Heboyan

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Fig 2. Representative scheme of the use of SiO₂-reinforced resin nanoparticle composites in FEA.