Finite Element Analysis of Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section Running title:Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section

Finite Element Analysis of Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section Running title:Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Finite Element Analysis of Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section Running title:Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section Niloofar Sadat Kashfi, Mohammad Mahdi Jalili, Mina Soltanianzadeh, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6009419/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Jun, 2025 Read the published version in BMC Oral Health → Version 1 posted 10 You are reading this latest preprint version Abstract Background & Objective: The cervical region of dentin plays a crucial role in the distribution of masticatory forces, with vertical root fractures often initiating and spreading from this area. This study investigates the distribution of occlusal stresses in the cervical region of root dentin, considering varying thicknesses and cross-sections, using Finite Element Analysis. Materials & Methods: Sections from central and premolar teeth were imported into CAD to create 3D models. The tooth structure and surrounding tissues were modeled using mechanical properties such as Young's modulus and Poisson's ratio. Four cross-sectional shapes—circular, oval, sand clock, and kidney—were designed. A force of 50 Newtons, representing the occlusal force of the opposing tooth, was applied to the palatal surface of the models at a 60° angle for anterior teeth and a 45° angle for premolars. The stress distribution in the cervical dentin was then analyzed. Results: Von Mises stress values indicated that stress points were highest in the kidney, sand clock, oval, and circular cross-sections, respectively. Increased thickness of the residual dentinal wall resulted in reduced maximum and minimum stress and a smaller area of stress regions. In all cross-sections, the minimum and maximum stress points were predominantly on the palatal and buccal sides of the cervical dentin, respectively. Conclusion: The study demonstrated that stress distribution in teeth varies with different root cross-sections, with higher stress observed in the sand clock and kidney cross-sections. Thinner dentin in the cervical region leads to greater stress concentration, especially in the buccal area of the tooth. Dental stress analysis finite element analysis root canal therapy (RCT) dental pulp cavity dentin Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Root canal therapy (RCT) is conducted to thoroughly clean and shape the root canal, eliminate existing microorganisms, fill the canal, ensure a proper seal, and prevent the re-entry of microbes into the periapical bone space ( 1 ). Mechanical-chemical preparation is essential for cleaning, disinfecting, and shaping the root canal. This step is crucial in treating a tooth with pulpitis, as successful treatment relies on the thorough removal of bacteria, their by-products, and necrotic tissues, which could otherwise support bacterial regrowth ( 2 ). Root canal shaping is another critical and predictive step in root canal treatment, particularly during the final stages. It plays a crucial role in ensuring proper root canal disinfection ( 3 ). Numerous clinical experiences and studies have highlighted the benefits of conical canal preparation during shaping, including enhanced cleaning efficiency, improved control of root apical instrumentation, reduced reliance on precise working length measurement, and more consistent apical resistance form ( 4 ).The use of highly tapered rotary instruments can cause changes in the volume and geometry of the root canal, hence increasing the risk of vertical root fracture due to excessive dentin removal from the middle and cervical third of the canal ( 5 ). In general, the canal tapering should be adequate to enable deep penetration of the sealer and filling material, while avoiding excessive tapering that could lead to procedural errors and unnecessary weakening of the root ( 6 ). Canal preparation, particularly the tapering rate, involves the removal of dentin from the canal wall. This process can compromise the root's structural integrity, significantly weakening the tooth root and potentially causing the formation of microcracks and fractures in the root dentin ( 7 , 8 ). Studies suggest that the shape of the root canal cross-section and the dentin thickness may influence the susceptibility of roots to vertical root fractures. It has been observed that an oval-shaped cross-section, as opposed to a circular one, results in asymmetric stress distribution within the canal, with a greater tendency for stresses to occur in the buccal-lingual direction on the canal's inner wall ( 9 – 11 ). The role of root cross-section in stress distribution within the cervical dentin is a critical factor in understanding mechanical behavior under occlusal forces. Variations in root cross-sectional shape influence how stress is concentrated and dispersed across the cervical region. Studies employing finite element analysis (FEA) have demonstrated that elliptical or irregular root cross-sections tend to exhibit higher stress concentrations compared to circular cross-sections, due to uneven geometry that may amplify localized stress ( 9 , 12 ). Additionally, the thickness of dentin in different cross-sectional regions impacts its ability to endure mechanical stress; thinner sections are more prone to deformation and failure under load ( 13 , 14 ). These insights underscore the importance of root morphology and dentin thickness in assessing the biomechanical performance and susceptibility to structural compromise under physiological conditions. Enhancing the understanding of these factors may contribute to improved clinical strategies for dental restorations and preventive care. Attempts have been made to explore the correlation between simulated morphometric parameters of root segments and susceptibility to root fracture using finite element modeling/finite element analysis (FEM/FEA)( 10 , 15 ). Finite element analysis is a computational technique that predicts the response of different materials to a range of forces ( 16 , 17 ). This technique has been used in dentistry primarily for implant design and testing ( 18 ). Using FEA, a direct relationship has been demonstrated between the amount of stress applied to the radicular region and the diameter of the simulated canals ( 7 ). The cervical region of dentin is crucial for the distribution of masticatory forces. Studies have shown that vertical root fractures due to these forces typically initiate and spread from this area ( 7 , 10 , 15 ). Therefore, this study examined the distribution of occlusal stresses in the cervical region of root dentin with varying thicknesses and cross-sections using the Finite Element Analysis (FEA) method. Methodology In this descriptive study utilizing finite element analysis, four tooth samples with specific cross-sections (circular, oval, sand clock, and kidney) were selected. The teeth's outer surfaces were cleaned of plaque and soft tissue using a scaler, and the samples were then scanned and processed further. The teeth were scanned with a 3D scanner (Imetric, Switzerland). Since different teeth in the jaw have various cross-sections, corresponding teeth were used to prepare the scans, resulting in variations in dentin thickness based on the type of tooth and its cross-sectional shape. Circular cross-sections with 1, 2, and 3 mm thicknesses, oval cross-sections with 1, 1.5, and 2 mm thicknesses, and sand clock and kidney cross-sections with 0.5, 1, and 1.5 mm thicknesses were examined to investigate the stress distribution within the teeth. To keep the sample stable for scanning, the tooth under study was first mounted and scanned, and then the output format was converted to *stl for importing the information into SolidWorks. The SOLIDWORKS Simulation suite offers accessible and versatile tools for structural analysis, employing Finite Element Analysis (FEA) to predict the physical performance of CAD models in real-world scenarios. Its capabilities include both linear and non-linear static as well as dynamic evaluations. During the preprocessing stage, tooth scan data was imported into SOLIDWORKS, and modifications were made by removing enamel layers along with the lower appendage of the tooth associated with the scan paste. These adjustments ensured that the model could accurately reflect the desired conditions for analysis. To create canals with the four cross-sections and three thicknesses, the access cavity and canal space in the crown and root canal was first created and then filled with the appropriate composite (coronal part) and gutta percha (radicular part) materials (Fig. 1 ). In the next stage, based on the study by Seo et al. ( 19 ), the periodontal ligament and cortical bone were reconstructed with a thickness of 0.25 mm. Following the study by Rundquist & Versluis ( 7 ), reconstruction was carried out using SolidWorks, regarding the elasticity modulus of gingival tissue, periodontal ligament, trabecular and cortical bone, enamel, dentin, gutta percha, and composite (Table 1 ). Table 1 Modulus of elasticity of each tooth component and surrounding tissues Component Modulus of Elasticity (GPa) Enamel 84 Dentin 18 Gingival Tissue 0.06 Periodontal Ligament 0.07 Trabecular Bone 1.5 Cortical Bone 13.7 Composite 17.4 Gutta Percha 0.00069 Following these steps, the modeled tooth was mounted with three thicknesses for each cross-section. The initial volume of the tooth was meshed using the scanner to identify the object and assess stress distribution. To create a solid and integrated representation of the tooth structure, particularly in cases of caries and defects in the crown and root, and to more accurately analyze stress distribution, the default meshes were removed. The various tooth components were then re-meshed in Abaqus software (AbaqusCAE2017, Dassault Systèmes, France) based on the performed analysis and the selected element type. Abaqus is a software suite for finite element analysis and computer-aided engineering, Subsequently, the properties of each material were imported into the software in linear elastic form. As the tooth dimensions are in millimeters, the values were imported into the software in MPa. To model a homogeneous solid, the elements defined for each part of the tooth have uniform properties without cavities or gaps, using a method called solid homogeneous sectioning. Among the various methods for applying forces to a finite element, the 'static general' method was used in this study. The tooth, composed of multiple components such as dentin, gutta, composite, and enamel in the crown and root areas, required defined interactions and contact points for force loading. The components were connected using the Tie type of contact, ensuring that they adhered together without relative movement when force was applied. Next, to address the stress concentration at the force application point, the loading was distributed widely. A solid body, designed to apply the force, was created to resemble a part of the tooth. Compressive loading was then applied to anterior teeth with circular and oval cross-sections at a force of 50 N and an angle of 60° to the horizon ( 19 )(Fig. 2 ). Premolar models with kidney and sand clock cross-sections were subjected to a load of 50 N at both a right angle and 45° to the horizon. This force was decomposed into two components, X and Y, and applied to the solid body reference point. For anterior teeth, the reference point was the composite restorative material within the access cavity; for posterior teeth, it was the central fossa for vertical force and the buccal slope of the palatal cusp for force applied at a 45° angle to the tooth's longitudinal axis. Once the finite element analysis was completed, the results were extracted, and all data analysis was conducted using the numerical methods available in Abaqus finite element analysis software (Fig. 1 ). Results Occlusal Stress Distribution in the Cervical Region of Root Dentin with Circular-Shaped Cross-Section The stress distribution results in the dentinal wall of the cervical region of the anterior tooth, which has a circular cross-section in three different dentinal wall thicknesses, are summarized in Fig. 3 . As the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In a circular canal with a residual dentinal wall thickness of 1 mm, the maximum force is approximately 3.3 MPa. This force decreases to around 2.7 MPa with a 2 mm thickness and approximately 2.6 MPa with a 3 mm thickness. In the sample with the minimal thickness, stress points (red points) were observed extensively in the buccal area of the dentinal wall, which was not the case in the 2 mm and 3 mm thickness samples. Stress-free or minimal stress points (blue points) were absent in the 1 mm thickness; however, these areas significantly expanded in the 2 mm and 3 mm thickness samples. The least stress points were more prevalent on the palatal side of the cervical dentin. The stress distribution results in gutta-percha in the cervical region of anterior teeth demonstrated that with increasing dentin thickness, the stress distribution on gutta-percha became more uniform, eliminating stress areas as dentin thickness increased. In dentin with low thickness, areas of higher stress were observed at the junction of gutta-percha with dentinal walls, while areas with zero or minimal stress were found in the center of gutta-percha. Occlusal Stress Distribution in the Cervical Region of Root Dentin with an Oval-Shaped Cross-Section The results of stress distribution in the dentinal wall of the cervical region of an anterior tooth with an oval cross-section, evaluated at three different dentinal wall thicknesses, are summarized in Fig. 4 . As the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In an oval canal, the maximum force is approximately 15.7 MPa with a residual dentinal wall thickness of 1 mm, approximately 15.3 MPa with a thickness of 1.5 mm, and around 15.2 MPa with a thickness of 2 mm. Unlike the circular cross-section, the maximum stress points (red points) were not eliminated with an increasing amount of residual dentin. In the sample with the lowest thickness, stress points were observed in the buccal area of the dentinal wall. The low-stress areas (blue points) expanded significantly at thicknesses of 1.5 mm and 2 mm, with minimum stress points more prevalent on the palatal side of the cervical dentin. The asymmetrical shape of the root canal led to stress concentration, resulting in the maximum stress value being almost 5 times higher compared to the circular cross-section. Therefore, it can be concluded that the shape of the root canal has a greater effect than the thickness of the residual dentin. Occlusal Stress Distribution in the Cervical Region of Root Dentin with a Sand clock -Shaped Cross-Section As the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In an oval canal with a residual dentinal wall thickness of 0.5 mm, the maximum force is approximately 57.5 MPa. This force decreases to around 52.7 MPa with a thickness of 1 mm and approximately 38.3 MPa with a thickness of 1.5 mm. Generally, the maximum stresses increased compared to the circular and oval cross-sections. In the sample with the lowest thickness, stress points (red points) were observed in the mesiobuccal region of the dentinal wall, whereas these points were not observed in the canal with a thickness of 1 mm. The extent of the low-stress areas (blue points) expanded significantly at thicknesses of 1 mm and 1.5 mm, with minimum stress points more prevalent on the palatal side of the cervical dentin. The stress distribution results in the gutta-percha of the cervical region of premolar teeth showed that with increasing dentin thickness, the stress distribution on gutta-percha became more uniform, eliminating stress areas as dentin thickness increased. In dentin with low thickness, areas of higher stress were observed at the junction of gutta-percha with dentinal walls, while areas with the lowest stress were found in the center of gutta-percha. Occlusal Stress Distribution in the Cervical Region of Root Dentin with a Kidney-Shaped Cross-Section The results of stress distribution in the dentinal wall of the cervical region of a premolar tooth with a kidney-shaped cross-section, evaluated at three different dentinal wall thicknesses, are summarized in Fig. 6 . As the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In an oval canal with a residual dentinal wall thickness of 0.5 mm, the maximum force is approximately 72 MPa. This force decreases to around 60.3 MPa with a 1 mm thickness and approximately 55 MPa with a 1.5 mm thickness. In the sample with the lowest thickness, stress points (red points) were observed in the distobuccal region of the dentinal wall. The low-stress areas (blue points) expanded significantly at thicknesses of 1 mm and 1.5 mm, with the lowest stress points more prevalent on the palatal side of the cervical dentin. Based on the study results, as the canal cross-section shape changed from symmetrical (oval, circular) to asymmetrical, the maximum stress increased, but the area of regions with maximum stress (red points) decreased. Additionally, areas with minimum stress increased with the increasing thickness of the residual dentinal wall. The values of von Mises stress (mvM) in the dentinal wall of the cervical region of the tooth with different cross-sectional areas at three dentinal wall thicknesses are given in Table 2 . Table 2 Numerical values ​​of stress (MPa) in the studied groups Group Stress distribution Residual dentinal thickness Minimum Maximum Circular 1 mm 0.60 3.38 2 mm 0.30 2.77 3 mm ~ 0* 2.62 Oval 1 mm 1.31 15.68 1.5 mm 1.28 15.32 2 mm 1.27 15.22 Sand clock 0.5 mm 4.80 57.49 1 mm ~ 0 52.76 1.5 mm ~ 0 38.32 Kidney 0.5 mm 6.00 72.00 1 mm ~ 0 60.34 1.5 mm ~ 0 55.00 * Due to the use of MPa units, the stress value has been approximated and zero has been entered. Discussion Finite element analysis (FEA) is a valuable tool for investigating complex systems that are challenging to standardize both in vitro and in vivo. It has been extensively employed to analyze stress distribution in tooth roots. Understanding stress distribution is crucial for comprehending fatigue extension in a structure. FEA provides a suitable method for conducting explicit and objective experiments on biological systems ( 20 ). Hence, this method was employed in this study to analyze the distribution of occlusal stresses in the cervical part of the root dentin with different thicknesses and cross-sections. Various thicknesses in circular, sand clock, oval, and kidney cross-sections were chosen because scans of real teeth were used in the study, making it impossible to reconstruct in the same thicknesses. For instance, in sand clock cross-sectional samples, if a thickness of 3 mm was used, the canal area would practically disappear. After designing the samples, a compressive force of 50 Newton was applied to anterior teeth with circular and oval cross-sections to simulate chewing force ( 21 ) at an angle of 60° to the horizon ( 19 ). The results revealed that in circular and oval cross-sections, the highest stress was observed in the buccal area of the dentinal wall for the sample with the lowest thickness (1 mm). This area was not observed in the circular cross-sections with thicknesses of 2 mm and 3 mm and did not expand significantly in the oval cross-section. A force of 50 Newtons was applied to premolars with kidney and sand clock cross-sections at right angles and 45° to the horizon with compression. In the sand clock cross-section of the sample with the lowest thickness (0.5 mm), stress was extensively observed in the mesiobuccal region of the dentinal wall, while in the kidney cross-section sample at this thickness, the highest stress was observed in the distobuccal region of the dentinal wall. The extent of low-stress areas showed significant expansion at thicknesses of 1 mm and 1.5 mm. In all four cross-sections studied, the minimum stress points were more prevalent on the palatal side of the cervical dentin. Based on the study's results, the highest stress was observed in the kidney, sand clock, oval, and circular cross-sections, respectively, for all three thicknesses of cervical dentin. Stresses are closely related to structural failure, which typically occurs when the applied load creates a stress that exceeds the material's ultimate strength. External root morphology has been identified as a potential factor affecting fracture susceptibility ( 15 ). Models based on real root fractures have demonstrated a strong similarity between fracture patterns and tensile stress distribution. Research has indicated that roots with a narrow mesiodistal diameter relative to the buccal dimension (such as oval, triangular, kidney-shaped, and ribbon-shaped roots) are more susceptible to fractures. This group includes maxillary and mandibular premolars, mesial roots of mandibular molars, mandibular incisors, and mesiobuccal roots of maxillary molars ( 11 , 22 ). Based on the results of this study, canals with sand clock and kidney cross-sections show an increase in stress concentration points as the dentin thickness in the cervical region decreases. These stress concentration points, when subjected to repeated loads from chewing, can lead to the development and spread of vertical root fractures over time. Findings by Lertchirakarn et al. ( 10 , 23 ) and Sathorn et al. ( 15 ) using finite element analysis (FEM/FEA) modeling showed that factors that potentially affect the sensitivity of roots to VRF are root canal shape, root morphology, and dentin thickness. Studies have shown that when the root canal shape or external root morphology is oval (such as in premolars) rather than circular, the stress distribution within the canal becomes asymmetric. This tends to create the highest stresses in the buccal-lingual direction on the inner wall of the canal, which may cause fractures to initiate at the point of greatest curvature and spread to the outer surface of the root. These models indicate that decreasing proximal dentin thickness increases fracture magnitude but does not affect the direction of maximum tensile stress within the canal. In these studies, including the present one, finite element analysis (FEA) was used. However, FEA has several limitations. The accuracy of a 3D FEA relies on the accuracy of the simulation model. The physical properties of biological structures are only approximate, as all materials are considered homogeneous and have a linear response to stress. In reality, the response of these structures to stress is more complex in a living organism. Additionally, the simulated stress distribution patterns may vary depending on the materials and properties assigned to each layer of the model and the specific model used in the experiments. In this technique, the numerical model should behave similarly to the structure under study. In the case of a tooth, this numerical model should mimic the clinical behavior of a real tooth in terms of pressure, tension, and displacement. Therefore, the inherent limitations of such studies must be considered ( 12 ). Validation of the results of such finite element models with direct experimental methods that relate root canal morphometric parameters and susceptibility to VRF is needed. von Arx & Bosshardt ( 24 ) showed in a histological analysis of 30 posteriorly extracted root-treated teeth that in 56.3% of the teeth with VRF, the root cross-section was shaped like a sand clock. Similarly, in an ex vivo study, Chai and Tamse ( 9 ) determined that roots with two canals connected by a strait were more vulnerable to VRF than roots with a single canal. This may partly explain why VRF is more prevalent in the mesiobuccal roots of maxillary molars and the mesial roots of mandibular molars ( 25 , 26 ). These roots typically have two or more canals, many of which are connected by an isthmus ( 27 – 29 ). Pilo et al. ( 12 ) stated that previous stress testing methods applied force unevenly to the root. Therefore, the related tests cannot truly evaluate the mechanical behavior of VRF. These researchers addressed this issue by employing a new bursting pressure method on maxillary central incisors and root-treated premolars. They found that when the root is more elliptical in cross-section (as in premolars), the bending moments in the buccal-lingual plane are at their maximum, resulting in the highest tangential stresses in this area. In the present study, four cross-sections were examined: circular, oval, sand clock, and kidney. The points with the least stress were consistently observed on the palatal side of the cervical dentin. In canals with circular and oval cross-sections, the samples with the least thickness showed stress points widely distributed in the buccal area of the dentinal wall. In roots with sand clock cross-sections, stress points were found in the mesiobuccal area, while in kidney cross-sections, they were located in the distobuccal area of the dentinal wall. Although previous studies have not reported stress distribution across the root cross-section of root-treated teeth, clinical and experimental studies have demonstrated that root fractures predominantly occur in the buccolingual direction ( 5 – 8 ). In many single-rooted incisors, the mesial and distal sides are more calcified and harder compared to the buccolingual sides, exhibiting a “butterfly effect.” This may also explain the high incidence of vertical root fractures that occur in the buccolingual direction ( 30 ). Small dentin cracks parallel or perpendicular to the root canal space have been reported in intact teeth ( 31 , 32 ). When dentin is removed, especially in the mesiodistal areas during canal preparation and shaping, these cracks may develop into incomplete fractures and later in the life of the tooth may progress buccally or lingually to form a complete fracture ( 32 ). The results of this study showed that in all four sections examined, increasing the thickness of the residual dentinal wall reduces both the maximum and minimum stress applied to the tooth structure. Additionally, as the thickness of the dentin in the cervical region increases, the stress distribution on the gutta-percha becomes more uniform, and the areas of stress decrease. Successful root canal therapy relies on adequate debridement and filling of the entire root canal system ( 33 ). For this purpose, dentists usually prepare a much larger root cavity for diagnosis and cleaning of the root canal. Increased tooth structure removal reduces dentin thickness and threatens the integrity of tooth structure (34). Maintaining the residual dentin thickness is a crucial challenge and requirement for successful root canal treatment. It is also an important factor that affects the longevity of root canal-treated teeth. Research has indicated that the minimum dentin thickness required to withstand the forces applied during canal filling is 0.3 mm( 35 ). A small residual dentin thickness may predispose the tooth to lateral perforation or root fracture( 36 ). It has been reported that using files with higher convergence, which result in greater root dentin loss, increases the likelihood of vertical root cracks in the tooth ( 35 ). Based on the results of the study by Kiliç et al.,( 5 ) the resistance to fracture against force decreases with increasing apical diameter and tapering in the mesial root. According to Qiu et al.( 37 ) and Yildiz-Doğanay et al.( 38 ), larger tapering is associated with a higher risk of root fracture. The results of the study by Sabeti et al. ( 39 ) also showed that access cavity preparation can reduce resistance. Prado et al. ( 40 ) also reported that different canal preparation techniques reduce fracture resistance compared to intact teeth. Although the aforementioned studies did not examine stress distribution in the residual dentin as done in the present study, it can be concluded that greater stress distribution in thin residual dentin thicknesses can reduce the dentin's resistance to functional forces, making the tooth more susceptible to root fractures. In addition to dentin thickness, specific biochemical properties of dentin are also predisposing factors in vertical root fractures (VRF). In a study on the stress-strain response in human dentin, Kishen et al. ( 41 ) found that the adaptation of dentin to functional strain-stress distribution leads to greater mineralization in the buccolingual regions. This may increase the likelihood of fracture propagation in this direction compared to the less mineralized and more collagenous areas in the mesiodistal region. Consequently, it is essential for dentists to have a thorough knowledge of dental anatomy and to consider the morphological characteristics of each specific case before treatment. This approach is the most appropriate for selecting the right instruments for cleaning and shaping the root canal, thereby minimizing unnecessary dentin removal ( 42 ). In the present study, Von Mises stress has been applied to evaluate the biomechanical behavior of the cervical dentin of the tooth structure in various dentinal thickness. Although Von Mises stress does not differentiate between compressive and tensile stresses, it is widely recognized for its ability to provide a comprehensive assessment of the overall stress state within materials ( 43 , 44 ). This criterion is particularly advantageous in dental biomechanics, where complex interactions occur between different tissues and loading scenarios. Several studies in the field of dental finite element analysis have employed Von Mises stress to effectively analyze stress distribution and mechanical performance( 7 , 45 – 47 ). By using this measure, the present study aimed to capture the overall stress distribution patterns within the tooth, which aligns with the study's objectives of understanding structural integrity rather than focusing solely on fracture initiation sites. This approach ensures consistency with established methodologies and enhances the comparability of our results with prior research in the domain. The findings of the present study have significant clinical implications, particularly in the context of preserving cervical dentin during restorative and endodontic treatments. By analyzing occlusal stress distribution in varying dentinal thickness and cross-sectional designs, the study highlights the importance of tailoring treatment strategies to specific tooth groups and anatomical variations. This knowledge aids clinicians in optimizing restorative procedures to minimize stress concentration and reduce the risk of cervical fractures. Moreover, understanding stress distribution patterns in relation to dentinal thickness offers valuable insights for designing biomaterials and restorative techniques that better mimic natural tooth structure, thereby enhancing long-term clinical outcomes. Conclusion Considering the limitations of software studies, our findings suggest that the highest stress in the residual dentin of the cervical region is observed in the following cross-sections, from highest to lowest: kidney, sand clock, oval, and circular. In all the sections studied, as the thickness of the residual dentinal wall increases, both the maximum and minimum stresses applied to the tooth structure decrease. Additionally, with increasing thickness of the dentin in the cervical region, the stress distribution on the gutta-percha becomes more uniform, and the stress areas decrease with increasing dentin thickness. In all four cross-sections, the points with minimum stress were observed more on the palatal side of the cervical dentin. In the canal with circular and oval cross-sections in the sample with the least thickness, stress points were observed broadly in the buccal area of the dentinal wall. In the sand clock-shaped root, they were most prevalent in the mesiobuccal area, and in the kidney-shaped cross-section, they were found in the distobuccal area of the dentinal wall. To confirm the results of the present study, it is recommended to conduct further studies using different forces and directions similar to clinical conditions. Declarations Ethical approval This article was distilled from a student thesis with research code: 1247, approved by the Research Council of the School of Dentistry, Yazd. This study received the ethics code: IR.SSU.DENTISTRY.REC.1401.079 from the Committee of Ethics in Human Research at Shahid Sadoughi University of Medical Sciences, Yazd. Author Contribution MK and NSK designed the study, wrote the manuscript and submitted it. NSK gathered data. MS and MMJ cooperated in finite element analysis, manuscript writing and revising the manuscript. All authors reviewed the manuscript. Acknowledgement This study has been supported financially by the Vice Chancellor for Research and Technology of Yazd Shahid Sadoughi University of Medical Sciences. References Sousa-Neto MD, Silva-Sousa YC, Mazzi-Chaves JF, Carvalho KKT, Barbosa AFS, Versiani MA, et al. Root canal preparation using micro-computed tomography analysis: a literature review. Braz Oral Res. 2018;32(suppl 1):e66. Siqueira Junior JF, Rôças IDN, Marceliano-Alves MF, Pérez AR, Ricucci D. Unprepared root canal surface areas: causes, clinical implications, and therapeutic strategies. Braz Oral Res. 2018;32(suppl 1):e65. Shay B, Moshonov J. [Single file endodontic treatment: a new era?]. Refuat Hapeh Vehashinayim (1993) 2013;30(2):6–9, 76. Buchanan LS. The standardized-taper root canal preparation–Part 1. Concepts for variably tapered shaping instruments. Int Endod J. 2000;33(6):516–29. Kılıç Y, Karataşlıoğlu E, Kaval ME. The Effect of Root Canal Preparation Size and Taper of Middle Mesial Canals on Fracture Resistance of the Mandibular Molar Teeth: An In Vitro Study. J Endod. 2021;47(9):1467–71. Torabinejad M, Fouad A, Shabahang S, Endodontics. Principles and Practice. 6th ed. St.Louis: Elsevier Health Sciences; 2020. Rundquist BD, Versluis A. How does canal taper affect root stresses? Int Endod J. 2006;39(3):226–37. Holcomb JQ, Pitts DL, Nicholls JI. Further investigation of spreader loads required to cause vertical root fracture during lateral condensation. J Endod. 1987;13(6):277–84. Chai H, Tamse A. The Effect of Isthmus on Vertical Root Fracture in Endodontically Treated Teeth. J Endod. 2015;41(9):1515–9. Lertchirakarn V, Palamara JE, Messer HH. Patterns of vertical root fracture: factors affecting stress distribution in the root canal. J Endod. 2003;29(8):523–8. Tamse A. Vertical root fractures in endodontically treated teeth: diagnostic signs and clinical management. Endodontic Top. 2006;13(1):84–94. Pilo R, Metzger Z, Brosh T. Effect of root morphology on the susceptibility of endodontically treated teeth to vertical root fracture: An ex-vivo model. J Mech Behav Biomed Mater. 2017;69:267–74. Kumari G, Sarangi S, Panda B, Aruna V, Kasana J, Sinha P, et al. Comparison of CBCT examined root thickness and fracture resistance. Bioinformation. 2024;20(9):1012–6. Silva LR, de Lima KL, Santos AA, Leles CR, Estrela C, de Freitas Silva BS, et al. Dentin thickness as a risk factor for vertical root fracture in endodontically treated teeth: a case-control study. Clin Oral Investig. 2021;25(3):1099–105. Sathorn C, Palamara JE, Palamara D, Messer HH. Effect of root canal size and external root surface morphology on fracture susceptibility and pattern: a finite element analysis. J Endod. 2005;31(4):288–92. Erdemir A, Guess TM, Halloran J, Tadepalli SC, Morrison TM. Considerations for reporting finite element analysis studies in biomechanics. J Biomech. 2012;45(4):625–33. Mathur VP, Atif M, Duggal I, Tewari N, Duggal R, Chawla A. Reporting guidelines for in-silico studies using finite element analysis in medicine (RIFEM). Comput Methods Programs Biomed. 2022;216:106675. Welch-Phillips A, Gibbons D, Ahern DP, Butler JS. What Is Finite Elem Analysis? Clin Spine Surg. 2020;33(8):323–4. Seo DG, Yi YA, Shin SJ, Park JW. Analysis of factors associated with cracked teeth. J Endod. 2012;38(3):288–92. Jiang Q, Huang Y, Tu X, Li Z, He Y, Yang X. Biomechanical Properties of First Maxillary Molars with Different Endodontic Cavities: A Finite Element Analysis. J Endod. 2018;44(8):1283–8. Steiner M, Mitsias ME, Ludwig K, Kern M. In vitro evaluation of a mechanical testing chewing simulator. Dent Mater. 2009;25(4):494–9. Gutmann JL. The dentin-root complex: anatomic and biologic considerations in restoring endodontically treated teeth. J Prosthet Dent. 1992;67(4):458–67. Lertchirakarn V, Palamara JE, Messer HH. Finite element analysis and strain-gauge studies of vertical root fracture. J Endod. 2003;29(8):529–34. von Arx T, Bosshardt D. Vertical root fractures of endodontically treated posterior teeth: A histologic analysis with clinical and radiographic correlates. Swiss Dent J. 2017;127(1):14–23. PradeepKumar AR, Shemesh H, Jothilatha S, Vijayabharathi R, Jayalakshmi S, Kishen A. Diagnosis of Vertical Root Fractures in Restored Endodontically Treated Teeth: A Time-dependent Retrospective Cohort Study. J Endod. 2016;42(8):1175–80. von Arx T, Maldonado P, Bornstein MM. Occurrence of Vertical Root Fractures after Apical Surgery: A Retrospective Analysis. J Endod. 2021;47(2):239–46. Teixeira FB, Sano CL, Gomes BP, Zaia AA, Ferraz CC, Souza-Filho FJ. A preliminary in vitro study of the incidence and position of the root canal isthmus in maxillary and mandibular first molars. Int Endod J. 2003;36(4):276–80. von Arx T. Frequency and type of canal isthmuses in first molars detected by endoscopic inspection during periradicular surgery. Int Endod J. 2005;38(3):160–8. von Arx T, Steiner RG, Tay FR. Apical surgery: endoscopic findings at the resection level of 168 consecutively treated roots. Int Endod J. 2011;44(4):290–302. Russell AA, Chris He LH, Chandler NP. Investigation of dentin hardness in roots exhibiting the butterfly effect. J Endod. 2014;40(6):842–4. Boyarsky H, Davis R. Root fracture with dentin-retained posts. Am J Dent. 1992;5(1):11–4. Onnink PA, Davis RD, Wayman BE. An in vitro comparison of incomplete root fractures associated with three obturation techniques. J Endod. 1994;20(1):32–7. Al-Fouzan KS, Ounis HF, Merdad K, Al-Hezaimi K. Incidence of canal systems in the mesio-buccal roots of maxillary first and second molars in Saudi Arabian population. Australian Endodontic J. 2013;39(3):98–101. Tang W, Wu Y, Smales RJ. Identifying and Reducing Risks for Potential Fractures in Endodontically Treated Teeth. J Endod. 2010;36(4):609–17. Peters OA. Current challenges and concepts in the preparation of root canal systems: a review. J Endod. 2004;30(8):559–67. Fuss Z, Lustig J, Katz A, Tamse A. An evaluation of endodontically treated vertical root fractured teeth: impact of operative procedures. J Endod. 2001;27(1):46–8. Qiu S, Chen Y, Tsauo C, Wu W, Huang D, Zhou X et al. Microcomputed tomography analysis of the radicular residual dentin thickness in mandibular second molars after virtual fiber post placement: Identification of danger zones. J Prosthet Dent. 2023;130(1):109.e1-109.e10. Doğanay-Yıldız E, Fidan ME, Sakarya RE, Dinçer B. The effect of taper and apical preparation size on fracture resistance of roots. Aust Endod J. 2021;47(1):67–72. Sabeti M, Kazem M, Dianat O, Bahrololumi N, Beglou A, Rahimipour K, et al. Impact of Access Cavity Design and Root Canal Taper on Fracture Resistance of Endodontically Treated Teeth: An Ex Vivo Investigation. J Endod. 2018;44(9):1402–6. Prado M, de Lima NRB, de Lima CO, Gusman H, Simão RA. Resistance to vertical root fracture of root filled teeth using different conceptual approaches to canal preparation. Int Endod J. 2016;49(9):898–904. Kishen A, Kumar GV, Chen NN. Stress-strain response in human dentine: rethinking fracture predilection in postcore restored teeth. Dent Traumatol. 2004;20(2):90–100. Patel S, Rhodes J. A practical guide to endodontic access cavity preparation in molar teeth. Br Dent J. 2007;203(3):133. Moga RA, Olteanu CD, Daniel BM, Buru SM. Finite Elements Analysis of Tooth-A Comparative Analysis of Multiple Failure Criteria. Int J Environ Res Public Health 2023;20(5). Atif M, Tewari N, Reshikesh M, Chanda A, Mathur VP, Morankar R. Methods and applications of finite element analysis in dental trauma research: A scoping review. Dent Traumatol. 2024;40(4):366–88. Maravić T, Comba A, Mazzitelli C, Bartoletti L, Balla I, di Pietro E, et al. Finite element and in vitro study on biomechanical behavior of endodontically treated premolars restored with direct or indirect composite restorations. Sci Rep. 2022;12(1):12671. Pérez-González A, Iserte-Vilar JL, González-Lluch C. Interpreting finite element results for brittle materials in endodontic restorations. Biomed Eng Online. 2011;10:44. Huang L, Nemoto R, Okada D, Shin C, Saleh O, Oishi Y, et al. Investigation of stress distribution within an endodontically treated tooth restored with different restorations. J Dent Sci. 2022;17(3):1115–24. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Jun, 2025 Read the published version in BMC Oral Health → Version 1 posted Editorial decision: Revision requested 02 May, 2025 Editor assigned by journal 02 May, 2025 Reviewers agreed at journal 20 Apr, 2025 Reviews received at journal 20 Apr, 2025 Reviews received at journal 19 Apr, 2025 Reviewers agreed at journal 19 Apr, 2025 Reviewers agreed at journal 18 Apr, 2025 Reviewers invited by journal 16 Apr, 2025 Submission checks completed at journal 16 Apr, 2025 First submitted to journal 11 Apr, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6009419","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":443911565,"identity":"6a44f1dc-b70d-4722-9f68-9ee1a27233e3","order_by":0,"name":"Niloofar Sadat Kashfi","email":"","orcid":"","institution":"Shahid Sadoughi University of Medical Sciences and Health Services","correspondingAuthor":false,"prefix":"","firstName":"Niloofar","middleName":"Sadat","lastName":"Kashfi","suffix":""},{"id":443911567,"identity":"f7368c5e-d9e4-446f-93d1-5c15e5451a0a","order_by":1,"name":"Mohammad Mahdi Jalili","email":"","orcid":"","institution":"Yazd University","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"Mahdi","lastName":"Jalili","suffix":""},{"id":443911569,"identity":"2ff92bbf-c509-4e07-81aa-c8757f35dd4a","order_by":2,"name":"Mina Soltanianzadeh","email":"","orcid":"","institution":"Shahid Sadoughi University of Medical Sciences and Health Services","correspondingAuthor":false,"prefix":"","firstName":"Mina","middleName":"","lastName":"Soltanianzadeh","suffix":""},{"id":443911571,"identity":"ee3c2197-d016-4c37-b816-daaee49d98c8","order_by":3,"name":"Maryam Kazemipoor","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYDCCAwzMYJoNTFYAMTNzAylazoC0MBKpBQwY28Akfi18tw8wG/z4YxPNJ9188HHlvNpo/naglh8V23BqkTyXwJzYw5OW2yZzLNnw7LbjuTMOMzYw9py5jVOLwRkG5gM8Eodz2yRyzCQbtx3LbQBqYWZsw6/l4B+D/1Atc47lzidGSzJPwgGoloaa3A2EtEieYWw2ljmQDPFLw7EDuRuBWg7i8wvfGebDkm/+2OXOn9188GFDTV3uvPOHDz74UYFbCyIWJMDkYTB5AI96JADRUkec4lEwCkbBKBhRAABE/1tHkLVc3AAAAABJRU5ErkJggg==","orcid":"","institution":"Shahid Sadoughi University of Medical Sciences and Health Services","correspondingAuthor":true,"prefix":"","firstName":"Maryam","middleName":"","lastName":"Kazemipoor","suffix":""}],"badges":[],"createdAt":"2025-02-11 17:23:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6009419/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6009419/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12903-025-06184-y","type":"published","date":"2025-06-05T15:57:53+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":80855428,"identity":"c73daf63-a661-4baa-aefb-e029a0f807dd","added_by":"auto","created_at":"2025-04-17 20:57:26","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":46355,"visible":true,"origin":"","legend":"\u003cp\u003ea. Sagittal section of the reconstructed tooth, b. finite element mesh representation of tooth sample.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6009419/v1/7a93340fa88d45773f2d6f03.jpg"},{"id":80855543,"identity":"a19cc88d-2177-4819-8ff8-14e78420cfc0","added_by":"auto","created_at":"2025-04-17 21:05:26","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":263404,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic representation of the tooth model illustrating the direction and application of forces.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6009419/v1/f7f39dd0c797cfbe88048879.jpeg"},{"id":80855436,"identity":"1f9e8404-1de5-4f94-802b-b24f4d0e3f62","added_by":"auto","created_at":"2025-04-17 20:57:26","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":458542,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution in the dentinal wall of the cervical region of an anterior tooth with a circular cross-section, shown at three different dentinal wall thicknesses: A) 1 mm, B) 2 mm, and C) 3 mm.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6009419/v1/8dae65c5a58db822a0e33c58.jpeg"},{"id":80855546,"identity":"dd99bf75-c543-4307-b252-0d6a2866a74e","added_by":"auto","created_at":"2025-04-17 21:05:26","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":434115,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution in the dentinal wall of the cervical region of an anterior tooth with an oval cross-section, shown at three different dentinal wall thicknesses: A) 1 mm, B) 1.5 mm, and C) 2 mm.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6009419/v1/874b8c4aa40ca8bc2a2d2317.jpeg"},{"id":80855440,"identity":"97861ce7-3b48-4712-b1ec-53ba85b21be2","added_by":"auto","created_at":"2025-04-17 20:57:26","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":756295,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution in the dentinal wall of the cervical region of an anterior tooth with a sand clock cross-section, shown at three different dentinal wall thicknesses: A) 0.5 mm, B) 1 mm, and C) 1.5 mm.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6009419/v1/e26c23f487dab10cf690c3f8.jpeg"},{"id":80855430,"identity":"77560f74-3ddf-4119-80e1-3efcbbcf1b41","added_by":"auto","created_at":"2025-04-17 20:57:26","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":590024,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution in the dentinal wall of the cervical region of an anterior tooth with a kidney-shaped cross-section, shown at three different dentinal wall thicknesses: A) 0.5 mm, B) 1 mm, and C) 1.5 mm.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6009419/v1/2f6386b43a5c96d000867e10.jpeg"},{"id":84242628,"identity":"8e142911-823b-4bd7-bf2e-324f618a4548","added_by":"auto","created_at":"2025-06-09 16:10:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3270469,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6009419/v1/ea089be3-ad78-45bb-9aae-e94fed442b4e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Finite Element Analysis of Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section Running title:Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section","fulltext":[{"header":"Introduction","content":"\u003cp\u003eRoot canal therapy (RCT) is conducted to thoroughly clean and shape the root canal, eliminate existing microorganisms, fill the canal, ensure a proper seal, and prevent the re-entry of microbes into the periapical bone space (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e). Mechanical-chemical preparation is essential for cleaning, disinfecting, and shaping the root canal. This step is crucial in treating a tooth with pulpitis, as successful treatment relies on the thorough removal of bacteria, their by-products, and necrotic tissues, which could otherwise support bacterial regrowth (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e). Root canal shaping is another critical and predictive step in root canal treatment, particularly during the final stages. It plays a crucial role in ensuring proper root canal disinfection (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e). Numerous clinical experiences and studies have highlighted the benefits of conical canal preparation during shaping, including enhanced cleaning efficiency, improved control of root apical instrumentation, reduced reliance on precise working length measurement, and more consistent apical resistance form (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e).The use of highly tapered rotary instruments can cause changes in the volume and geometry of the root canal, hence increasing the risk of vertical root fracture due to excessive dentin removal from the middle and cervical third of the canal (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e). In general, the canal tapering should be adequate to enable deep penetration of the sealer and filling material, while avoiding excessive tapering that could lead to procedural errors and unnecessary weakening of the root (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). Canal preparation, particularly the tapering rate, involves the removal of dentin from the canal wall. This process can compromise the root's structural integrity, significantly weakening the tooth root and potentially causing the formation of microcracks and fractures in the root dentin (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e). Studies suggest that the shape of the root canal cross-section and the dentin thickness may influence the susceptibility of roots to vertical root fractures. It has been observed that an oval-shaped cross-section, as opposed to a circular one, results in asymmetric stress distribution within the canal, with a greater tendency for stresses to occur in the buccal-lingual direction on the canal's inner wall (\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e). The role of root cross-section in stress distribution within the cervical dentin is a critical factor in understanding mechanical behavior under occlusal forces. Variations in root cross-sectional shape influence how stress is concentrated and dispersed across the cervical region. Studies employing finite element analysis (FEA) have demonstrated that elliptical or irregular root cross-sections tend to exhibit higher stress concentrations compared to circular cross-sections, due to uneven geometry that may amplify localized stress (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e). Additionally, the thickness of dentin in different cross-sectional regions impacts its ability to endure mechanical stress; thinner sections are more prone to deformation and failure under load (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e). These insights underscore the importance of root morphology and dentin thickness in assessing the biomechanical performance and susceptibility to structural compromise under physiological conditions. Enhancing the understanding of these factors may contribute to improved clinical strategies for dental restorations and preventive care.\u003c/p\u003e \u003cp\u003eAttempts have been made to explore the correlation between simulated morphometric parameters of root segments and susceptibility to root fracture using finite element modeling/finite element analysis (FEM/FEA)(\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e). Finite element analysis is a computational technique that predicts the response of different materials to a range of forces (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e). This technique has been used in dentistry primarily for implant design and testing (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e). Using FEA, a direct relationship has been demonstrated between the amount of stress applied to the radicular region and the diameter of the simulated canals (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e). The cervical region of dentin is crucial for the distribution of masticatory forces. Studies have shown that vertical root fractures due to these forces typically initiate and spread from this area (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e). Therefore, this study examined the distribution of occlusal stresses in the cervical region of root dentin with varying thicknesses and cross-sections using the Finite Element Analysis (FEA) method.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cp\u003eIn this descriptive study utilizing finite element analysis, four tooth samples with specific cross-sections (circular, oval, sand clock, and kidney) were selected. The teeth's outer surfaces were cleaned of plaque and soft tissue using a scaler, and the samples were then scanned and processed further.\u003c/p\u003e \u003cp\u003eThe teeth were scanned with a 3D scanner (Imetric, Switzerland). Since different teeth in the jaw have various cross-sections, corresponding teeth were used to prepare the scans, resulting in variations in dentin thickness based on the type of tooth and its cross-sectional shape. Circular cross-sections with 1, 2, and 3 mm thicknesses, oval cross-sections with 1, 1.5, and 2 mm thicknesses, and sand clock and kidney cross-sections with 0.5, 1, and 1.5 mm thicknesses were examined to investigate the stress distribution within the teeth.\u003c/p\u003e \u003cp\u003eTo keep the sample stable for scanning, the tooth under study was first mounted and scanned, and then the output format was converted to *stl for importing the information into SolidWorks. The SOLIDWORKS Simulation suite offers accessible and versatile tools for structural analysis, employing Finite Element Analysis (FEA) to predict the physical performance of CAD models in real-world scenarios. Its capabilities include both linear and non-linear static as well as dynamic evaluations. During the preprocessing stage, tooth scan data was imported into SOLIDWORKS, and modifications were made by removing enamel layers along with the lower appendage of the tooth associated with the scan paste. These adjustments ensured that the model could accurately reflect the desired conditions for analysis. To create canals with the four cross-sections and three thicknesses, the access cavity and canal space in the crown and root canal was first created and then filled with the appropriate composite (coronal part) and gutta percha (radicular part) materials (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the next stage, based on the study by Seo et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e), the periodontal ligament and cortical bone were reconstructed with a thickness of 0.25 mm. Following the study by Rundquist \u0026amp; Versluis (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e), reconstruction was carried out using SolidWorks, regarding the elasticity modulus of gingival tissue, periodontal ligament, trabecular and cortical bone, enamel, dentin, gutta percha, and composite (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModulus of elasticity of each tooth component and surrounding tissues\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComponent\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModulus of Elasticity (GPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnamel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDentin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGingival Tissue\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePeriodontal Ligament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTrabecular Bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCortical Bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComposite\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGutta Percha\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00069\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFollowing these steps, the modeled tooth was mounted with three thicknesses for each cross-section. The initial volume of the tooth was meshed using the scanner to identify the object and assess stress distribution. To create a solid and integrated representation of the tooth structure, particularly in cases of caries and defects in the crown and root, and to more accurately analyze stress distribution, the default meshes were removed. The various tooth components were then re-meshed in Abaqus software (AbaqusCAE2017, Dassault Syst\u0026egrave;mes, France) based on the performed analysis and the selected element type. Abaqus is a software suite for finite element analysis and computer-aided engineering, Subsequently, the properties of each material were imported into the software in linear elastic form. As the tooth dimensions are in millimeters, the values were imported into the software in MPa.\u003c/p\u003e \u003cp\u003eTo model a homogeneous solid, the elements defined for each part of the tooth have uniform properties without cavities or gaps, using a method called solid homogeneous sectioning. Among the various methods for applying forces to a finite element, the 'static general' method was used in this study. The tooth, composed of multiple components such as dentin, gutta, composite, and enamel in the crown and root areas, required defined interactions and contact points for force loading. The components were connected using the Tie type of contact, ensuring that they adhered together without relative movement when force was applied.\u003c/p\u003e \u003cp\u003eNext, to address the stress concentration at the force application point, the loading was distributed widely. A solid body, designed to apply the force, was created to resemble a part of the tooth. Compressive loading was then applied to anterior teeth with circular and oval cross-sections at a force of 50 N and an angle of 60\u0026deg; to the horizon (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e)(Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Premolar models with kidney and sand clock cross-sections were subjected to a load of 50 N at both a right angle and 45\u0026deg; to the horizon. This force was decomposed into two components, X and Y, and applied to the solid body reference point. For anterior teeth, the reference point was the composite restorative material within the access cavity; for posterior teeth, it was the central fossa for vertical force and the buccal slope of the palatal cusp for force applied at a 45\u0026deg; angle to the tooth's longitudinal axis. Once the finite element analysis was completed, the results were extracted, and all data analysis was conducted using the numerical methods available in Abaqus finite element analysis software (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eOcclusal Stress Distribution in the Cervical Region of Root Dentin with Circular-Shaped Cross-Section\u003c/h2\u003e \u003cp\u003eThe stress distribution results in the dentinal wall of the cervical region of the anterior tooth, which has a circular cross-section in three different dentinal wall thicknesses, are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In a circular canal with a residual dentinal wall thickness of 1 mm, the maximum force is approximately 3.3 MPa. This force decreases to around 2.7 MPa with a 2 mm thickness and approximately 2.6 MPa with a 3 mm thickness. In the sample with the minimal thickness, stress points (red points) were observed extensively in the buccal area of the dentinal wall, which was not the case in the 2 mm and 3 mm thickness samples. Stress-free or minimal stress points (blue points) were absent in the 1 mm thickness; however, these areas significantly expanded in the 2 mm and 3 mm thickness samples. The least stress points were more prevalent on the palatal side of the cervical dentin.\u003c/p\u003e \u003cp\u003eThe stress distribution results in gutta-percha in the cervical region of anterior teeth demonstrated that with increasing dentin thickness, the stress distribution on gutta-percha became more uniform, eliminating stress areas as dentin thickness increased. In dentin with low thickness, areas of higher stress were observed at the junction of gutta-percha with dentinal walls, while areas with zero or minimal stress were found in the center of gutta-percha.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eOcclusal Stress Distribution in the Cervical Region of Root Dentin with an Oval-Shaped Cross-Section\u003c/h3\u003e\n\u003cp\u003eThe results of stress distribution in the dentinal wall of the cervical region of an anterior tooth with an oval cross-section, evaluated at three different dentinal wall thicknesses, are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In an oval canal, the maximum force is approximately 15.7 MPa with a residual dentinal wall thickness of 1 mm, approximately 15.3 MPa with a thickness of 1.5 mm, and around 15.2 MPa with a thickness of 2 mm. Unlike the circular cross-section, the maximum stress points (red points) were not eliminated with an increasing amount of residual dentin. In the sample with the lowest thickness, stress points were observed in the buccal area of the dentinal wall. The low-stress areas (blue points) expanded significantly at thicknesses of 1.5 mm and 2 mm, with minimum stress points more prevalent on the palatal side of the cervical dentin. The asymmetrical shape of the root canal led to stress concentration, resulting in the maximum stress value being almost 5 times higher compared to the circular cross-section. Therefore, it can be concluded that the shape of the root canal has a greater effect than the thickness of the residual dentin.\u003c/p\u003e \u003cp\u003e \u003cb\u003eOcclusal Stress Distribution in the Cervical Region of Root Dentin with a Sand clock -Shaped Cross-Section\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In an oval canal with a residual dentinal wall thickness of 0.5 mm, the maximum force is approximately 57.5 MPa. This force decreases to around 52.7 MPa with a thickness of 1 mm and approximately 38.3 MPa with a thickness of 1.5 mm. Generally, the maximum stresses increased compared to the circular and oval cross-sections. In the sample with the lowest thickness, stress points (red points) were observed in the mesiobuccal region of the dentinal wall, whereas these points were not observed in the canal with a thickness of 1 mm. The extent of the low-stress areas (blue points) expanded significantly at thicknesses of 1 mm and 1.5 mm, with minimum stress points more prevalent on the palatal side of the cervical dentin.\u003c/p\u003e \u003cp\u003eThe stress distribution results in the gutta-percha of the cervical region of premolar teeth showed that with increasing dentin thickness, the stress distribution on gutta-percha became more uniform, eliminating stress areas as dentin thickness increased. In dentin with low thickness, areas of higher stress were observed at the junction of gutta-percha with dentinal walls, while areas with the lowest stress were found in the center of gutta-percha.\u003c/p\u003e\n\u003ch3\u003eOcclusal Stress Distribution in the Cervical Region of Root Dentin with a Kidney-Shaped Cross-Section\u003c/h3\u003e\n\u003cp\u003eThe results of stress distribution in the dentinal wall of the cervical region of a premolar tooth with a kidney-shaped cross-section, evaluated at three different dentinal wall thicknesses, are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs the thickness of the residual dentinal wall increases, the maximum and minimum stresses applied to the tooth structure decrease. In an oval canal with a residual dentinal wall thickness of 0.5 mm, the maximum force is approximately 72 MPa. This force decreases to around 60.3 MPa with a 1 mm thickness and approximately 55 MPa with a 1.5 mm thickness. In the sample with the lowest thickness, stress points (red points) were observed in the distobuccal region of the dentinal wall. The low-stress areas (blue points) expanded significantly at thicknesses of 1 mm and 1.5 mm, with the lowest stress points more prevalent on the palatal side of the cervical dentin.\u003c/p\u003e \u003cp\u003eBased on the study results, as the canal cross-section shape changed from symmetrical (oval, circular) to asymmetrical, the maximum stress increased, but the area of regions with maximum stress (red points) decreased. Additionally, areas with minimum stress increased with the increasing thickness of the residual dentinal wall. The values of von Mises stress (mvM) in the dentinal wall of the cervical region of the tooth with different cross-sectional areas at three dentinal wall thicknesses are given in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNumerical values ​​of stress (MPa) in the studied groups\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStress distribution\u003c/p\u003e \u003cp\u003eResidual dentinal thickness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eCircular\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e~\u003c/b\u003e\u0026thinsp;0*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eOval\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSand clock\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e57.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e52.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e38.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eKidney\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e72.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e60.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e55.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e* Due to the use of MPa units, the stress value has been approximated and zero has been entered.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eFinite element analysis (FEA) is a valuable tool for investigating complex systems that are challenging to standardize both in vitro and in vivo. It has been extensively employed to analyze stress distribution in tooth roots. Understanding stress distribution is crucial for comprehending fatigue extension in a structure. FEA provides a suitable method for conducting explicit and objective experiments on biological systems (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e). Hence, this method was employed in this study to analyze the distribution of occlusal stresses in the cervical part of the root dentin with different thicknesses and cross-sections. Various thicknesses in circular, sand clock, oval, and kidney cross-sections were chosen because scans of real teeth were used in the study, making it impossible to reconstruct in the same thicknesses. For instance, in sand clock cross-sectional samples, if a thickness of 3 mm was used, the canal area would practically disappear. After designing the samples, a compressive force of 50 Newton was applied to anterior teeth with circular and oval cross-sections to simulate chewing force (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e) at an angle of 60\u0026deg; to the horizon (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e). The results revealed that in circular and oval cross-sections, the highest stress was observed in the buccal area of the dentinal wall for the sample with the lowest thickness (1 mm). This area was not observed in the circular cross-sections with thicknesses of 2 mm and 3 mm and did not expand significantly in the oval cross-section. A force of 50 Newtons was applied to premolars with kidney and sand clock cross-sections at right angles and 45\u0026deg; to the horizon with compression. In the sand clock cross-section of the sample with the lowest thickness (0.5 mm), stress was extensively observed in the mesiobuccal region of the dentinal wall, while in the kidney cross-section sample at this thickness, the highest stress was observed in the distobuccal region of the dentinal wall.\u003c/p\u003e \u003cp\u003eThe extent of low-stress areas showed significant expansion at thicknesses of 1 mm and 1.5 mm. In all four cross-sections studied, the minimum stress points were more prevalent on the palatal side of the cervical dentin. Based on the study's results, the highest stress was observed in the kidney, sand clock, oval, and circular cross-sections, respectively, for all three thicknesses of cervical dentin. Stresses are closely related to structural failure, which typically occurs when the applied load creates a stress that exceeds the material's ultimate strength. External root morphology has been identified as a potential factor affecting fracture susceptibility (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eModels based on real root fractures have demonstrated a strong similarity between fracture patterns and tensile stress distribution. Research has indicated that roots with a narrow mesiodistal diameter relative to the buccal dimension (such as oval, triangular, kidney-shaped, and ribbon-shaped roots) are more susceptible to fractures. This group includes maxillary and mandibular premolars, mesial roots of mandibular molars, mandibular incisors, and mesiobuccal roots of maxillary molars (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e). Based on the results of this study, canals with sand clock and kidney cross-sections show an increase in stress concentration points as the dentin thickness in the cervical region decreases. These stress concentration points, when subjected to repeated loads from chewing, can lead to the development and spread of vertical root fractures over time.\u003c/p\u003e \u003cp\u003eFindings by Lertchirakarn et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e) and Sathorn et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e) using finite element analysis (FEM/FEA) modeling showed that factors that potentially affect the sensitivity of roots to VRF are root canal shape, root morphology, and dentin thickness. Studies have shown that when the root canal shape or external root morphology is oval (such as in premolars) rather than circular, the stress distribution within the canal becomes asymmetric. This tends to create the highest stresses in the buccal-lingual direction on the inner wall of the canal, which may cause fractures to initiate at the point of greatest curvature and spread to the outer surface of the root. These models indicate that decreasing proximal dentin thickness increases fracture magnitude but does not affect the direction of maximum tensile stress within the canal.\u003c/p\u003e \u003cp\u003eIn these studies, including the present one, finite element analysis (FEA) was used. However, FEA has several limitations. The accuracy of a 3D FEA relies on the accuracy of the simulation model. The physical properties of biological structures are only approximate, as all materials are considered homogeneous and have a linear response to stress. In reality, the response of these structures to stress is more complex in a living organism. Additionally, the simulated stress distribution patterns may vary depending on the materials and properties assigned to each layer of the model and the specific model used in the experiments. In this technique, the numerical model should behave similarly to the structure under study. In the case of a tooth, this numerical model should mimic the clinical behavior of a real tooth in terms of pressure, tension, and displacement. Therefore, the inherent limitations of such studies must be considered (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eValidation of the results of such finite element models with direct experimental methods that relate root canal morphometric parameters and susceptibility to VRF is needed. von Arx \u0026amp; Bosshardt (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e) showed in a histological analysis of 30 posteriorly extracted root-treated teeth that in 56.3% of the teeth with VRF, the root cross-section was shaped like a sand clock. Similarly, in an \u003cem\u003eex vivo\u003c/em\u003e study, Chai and Tamse (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e) determined that roots with two canals connected by a strait were more vulnerable to VRF than roots with a single canal. This may partly explain why VRF is more prevalent in the mesiobuccal roots of maxillary molars and the mesial roots of mandibular molars (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e). These roots typically have two or more canals, many of which are connected by an isthmus (\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e). Pilo et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e) stated that previous stress testing methods applied force unevenly to the root. Therefore, the related tests cannot truly evaluate the mechanical behavior of VRF. These researchers addressed this issue by employing a new bursting pressure method on maxillary central incisors and root-treated premolars. They found that when the root is more elliptical in cross-section (as in premolars), the bending moments in the buccal-lingual plane are at their maximum, resulting in the highest tangential stresses in this area.\u003c/p\u003e \u003cp\u003eIn the present study, four cross-sections were examined: circular, oval, sand clock, and kidney. The points with the least stress were consistently observed on the palatal side of the cervical dentin. In canals with circular and oval cross-sections, the samples with the least thickness showed stress points widely distributed in the buccal area of the dentinal wall. In roots with sand clock cross-sections, stress points were found in the mesiobuccal area, while in kidney cross-sections, they were located in the distobuccal area of the dentinal wall.\u003c/p\u003e \u003cp\u003eAlthough previous studies have not reported stress distribution across the root cross-section of root-treated teeth, clinical and experimental studies have demonstrated that root fractures predominantly occur in the buccolingual direction (\u003cspan additionalcitationids=\"CR6 CR7\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn many single-rooted incisors, the mesial and distal sides are more calcified and harder compared to the buccolingual sides, exhibiting a \u0026ldquo;butterfly effect.\u0026rdquo; This may also explain the high incidence of vertical root fractures that occur in the buccolingual direction (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e). Small dentin cracks parallel or perpendicular to the root canal space have been reported in intact teeth (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e). When dentin is removed, especially in the mesiodistal areas during canal preparation and shaping, these cracks may develop into incomplete fractures and later in the life of the tooth may progress buccally or lingually to form a complete fracture (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e). The results of this study showed that in all four sections examined, increasing the thickness of the residual dentinal wall reduces both the maximum and minimum stress applied to the tooth structure. Additionally, as the thickness of the dentin in the cervical region increases, the stress distribution on the gutta-percha becomes more uniform, and the areas of stress decrease. Successful root canal therapy relies on adequate debridement and filling of the entire root canal system (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e). For this purpose, dentists usually prepare a much larger root cavity for diagnosis and cleaning of the root canal. Increased tooth structure removal reduces dentin thickness and threatens the integrity of tooth structure (34). Maintaining the residual dentin thickness is a crucial challenge and requirement for successful root canal treatment. It is also an important factor that affects the longevity of root canal-treated teeth. Research has indicated that the minimum dentin thickness required to withstand the forces applied during canal filling is 0.3 mm(\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e). A small residual dentin thickness may predispose the tooth to lateral perforation or root fracture(\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e). It has been reported that using files with higher convergence, which result in greater root dentin loss, increases the likelihood of vertical root cracks in the tooth (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e). Based on the results of the study by Kili\u0026ccedil; et al.,(\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e) the resistance to fracture against force decreases with increasing apical diameter and tapering in the mesial root. According to Qiu et al.(\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e) and Yildiz-Doğanay et al.(\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e), larger tapering is associated with a higher risk of root fracture. The results of the study by Sabeti et al. (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e) also showed that access cavity preparation can reduce resistance. Prado et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e) also reported that different canal preparation techniques reduce fracture resistance compared to intact teeth. Although the aforementioned studies did not examine stress distribution in the residual dentin as done in the present study, it can be concluded that greater stress distribution in thin residual dentin thicknesses can reduce the dentin's resistance to functional forces, making the tooth more susceptible to root fractures. In addition to dentin thickness, specific biochemical properties of dentin are also predisposing factors in vertical root fractures (VRF). In a study on the stress-strain response in human dentin, Kishen et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e) found that the adaptation of dentin to functional strain-stress distribution leads to greater mineralization in the buccolingual regions. This may increase the likelihood of fracture propagation in this direction compared to the less mineralized and more collagenous areas in the mesiodistal region. Consequently, it is essential for dentists to have a thorough knowledge of dental anatomy and to consider the morphological characteristics of each specific case before treatment. This approach is the most appropriate for selecting the right instruments for cleaning and shaping the root canal, thereby minimizing unnecessary dentin removal (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e). In the present study, Von Mises stress has been applied to evaluate the biomechanical behavior of the cervical dentin of the tooth structure in various dentinal thickness. Although Von Mises stress does not differentiate between compressive and tensile stresses, it is widely recognized for its ability to provide a comprehensive assessment of the overall stress state within materials (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e). This criterion is particularly advantageous in dental biomechanics, where complex interactions occur between different tissues and loading scenarios. Several studies in the field of dental finite element analysis have employed Von Mises stress to effectively analyze stress distribution and mechanical performance(\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan additionalcitationids=\"CR46\" citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e). By using this measure, the present study aimed to capture the overall stress distribution patterns within the tooth, which aligns with the study's objectives of understanding structural integrity rather than focusing solely on fracture initiation sites. This approach ensures consistency with established methodologies and enhances the comparability of our results with prior research in the domain. The findings of the present study have significant clinical implications, particularly in the context of preserving cervical dentin during restorative and endodontic treatments. By analyzing occlusal stress distribution in varying dentinal thickness and cross-sectional designs, the study highlights the importance of tailoring treatment strategies to specific tooth groups and anatomical variations. This knowledge aids clinicians in optimizing restorative procedures to minimize stress concentration and reduce the risk of cervical fractures. Moreover, understanding stress distribution patterns in relation to dentinal thickness offers valuable insights for designing biomaterials and restorative techniques that better mimic natural tooth structure, thereby enhancing long-term clinical outcomes.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eConsidering the limitations of software studies, our findings suggest that the highest stress in the residual dentin of the cervical region is observed in the following cross-sections, from highest to lowest: kidney, sand clock, oval, and circular. In all the sections studied, as the thickness of the residual dentinal wall increases, both the maximum and minimum stresses applied to the tooth structure decrease. Additionally, with increasing thickness of the dentin in the cervical region, the stress distribution on the gutta-percha becomes more uniform, and the stress areas decrease with increasing dentin thickness. In all four cross-sections, the points with minimum stress were observed more on the palatal side of the cervical dentin. In the canal with circular and oval cross-sections in the sample with the least thickness, stress points were observed broadly in the buccal area of the dentinal wall. In the sand clock-shaped root, they were most prevalent in the mesiobuccal area, and in the kidney-shaped cross-section, they were found in the distobuccal area of the dentinal wall. To confirm the results of the present study, it is recommended to conduct further studies using different forces and directions similar to clinical conditions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eEthical approval\u003c/h2\u003e \u003cp\u003eThis article was distilled from a student thesis with research code: 1247, approved by the Research Council of the School of Dentistry, Yazd. This study received the ethics code: IR.SSU.DENTISTRY.REC.1401.079 from the Committee of Ethics in Human Research at Shahid Sadoughi University of Medical Sciences, Yazd.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eMK and NSK designed the study, wrote the manuscript and submitted it. NSK gathered data. MS and MMJ cooperated in finite element analysis, manuscript writing and revising the manuscript. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis study has been supported financially by the Vice Chancellor for Research and Technology of Yazd Shahid Sadoughi University of Medical Sciences.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSousa-Neto MD, Silva-Sousa YC, Mazzi-Chaves JF, Carvalho KKT, Barbosa AFS, Versiani MA, et al. Root canal preparation using micro-computed tomography analysis: a literature review. Braz Oral Res. 2018;32(suppl 1):e66.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSiqueira Junior JF, R\u0026ocirc;\u0026ccedil;as IDN, Marceliano-Alves MF, P\u0026eacute;rez AR, Ricucci D. Unprepared root canal surface areas: causes, clinical implications, and therapeutic strategies. Braz Oral Res. 2018;32(suppl 1):e65.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShay B, Moshonov J. [Single file endodontic treatment: a new era?]. Refuat Hapeh Vehashinayim (1993) 2013;30(2):6\u0026ndash;9, 76.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBuchanan LS. The standardized-taper root canal preparation\u0026ndash;Part 1. Concepts for variably tapered shaping instruments. Int Endod J. 2000;33(6):516\u0026ndash;29.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKılı\u0026ccedil; Y, Karataşlıoğlu E, Kaval ME. The Effect of Root Canal Preparation Size and Taper of Middle Mesial Canals on Fracture Resistance of the Mandibular Molar Teeth: An In Vitro Study. J Endod. 2021;47(9):1467\u0026ndash;71.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTorabinejad M, Fouad A, Shabahang S, Endodontics. Principles and Practice. 6th ed. St.Louis: Elsevier Health Sciences; 2020.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRundquist BD, Versluis A. How does canal taper affect root stresses? Int Endod J. 2006;39(3):226\u0026ndash;37.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHolcomb JQ, Pitts DL, Nicholls JI. Further investigation of spreader loads required to cause vertical root fracture during lateral condensation. J Endod. 1987;13(6):277\u0026ndash;84.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChai H, Tamse A. The Effect of Isthmus on Vertical Root Fracture in Endodontically Treated Teeth. J Endod. 2015;41(9):1515\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLertchirakarn V, Palamara JE, Messer HH. Patterns of vertical root fracture: factors affecting stress distribution in the root canal. J Endod. 2003;29(8):523\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTamse A. Vertical root fractures in endodontically treated teeth: diagnostic signs and clinical management. Endodontic Top. 2006;13(1):84\u0026ndash;94.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePilo R, Metzger Z, Brosh T. Effect of root morphology on the susceptibility of endodontically treated teeth to vertical root fracture: An ex-vivo model. J Mech Behav Biomed Mater. 2017;69:267\u0026ndash;74.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumari G, Sarangi S, Panda B, Aruna V, Kasana J, Sinha P, et al. Comparison of CBCT examined root thickness and fracture resistance. Bioinformation. 2024;20(9):1012\u0026ndash;6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSilva LR, de Lima KL, Santos AA, Leles CR, Estrela C, de Freitas Silva BS, et al. Dentin thickness as a risk factor for vertical root fracture in endodontically treated teeth: a case-control study. Clin Oral Investig. 2021;25(3):1099\u0026ndash;105.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSathorn C, Palamara JE, Palamara D, Messer HH. Effect of root canal size and external root surface morphology on fracture susceptibility and pattern: a finite element analysis. J Endod. 2005;31(4):288\u0026ndash;92.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eErdemir A, Guess TM, Halloran J, Tadepalli SC, Morrison TM. Considerations for reporting finite element analysis studies in biomechanics. J Biomech. 2012;45(4):625\u0026ndash;33.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMathur VP, Atif M, Duggal I, Tewari N, Duggal R, Chawla A. Reporting guidelines for in-silico studies using finite element analysis in medicine (RIFEM). Comput Methods Programs Biomed. 2022;216:106675.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWelch-Phillips A, Gibbons D, Ahern DP, Butler JS. What Is Finite Elem Analysis? Clin Spine Surg. 2020;33(8):323\u0026ndash;4.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSeo DG, Yi YA, Shin SJ, Park JW. Analysis of factors associated with cracked teeth. J Endod. 2012;38(3):288\u0026ndash;92.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJiang Q, Huang Y, Tu X, Li Z, He Y, Yang X. Biomechanical Properties of First Maxillary Molars with Different Endodontic Cavities: A Finite Element Analysis. J Endod. 2018;44(8):1283\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSteiner M, Mitsias ME, Ludwig K, Kern M. In vitro evaluation of a mechanical testing chewing simulator. Dent Mater. 2009;25(4):494\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGutmann JL. The dentin-root complex: anatomic and biologic considerations in restoring endodontically treated teeth. J Prosthet Dent. 1992;67(4):458\u0026ndash;67.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLertchirakarn V, Palamara JE, Messer HH. Finite element analysis and strain-gauge studies of vertical root fracture. J Endod. 2003;29(8):529\u0026ndash;34.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003evon Arx T, Bosshardt D. Vertical root fractures of endodontically treated posterior teeth: A histologic analysis with clinical and radiographic correlates. Swiss Dent J. 2017;127(1):14\u0026ndash;23.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePradeepKumar AR, Shemesh H, Jothilatha S, Vijayabharathi R, Jayalakshmi S, Kishen A. Diagnosis of Vertical Root Fractures in Restored Endodontically Treated Teeth: A Time-dependent Retrospective Cohort Study. J Endod. 2016;42(8):1175\u0026ndash;80.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003evon Arx T, Maldonado P, Bornstein MM. Occurrence of Vertical Root Fractures after Apical Surgery: A Retrospective Analysis. J Endod. 2021;47(2):239\u0026ndash;46.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTeixeira FB, Sano CL, Gomes BP, Zaia AA, Ferraz CC, Souza-Filho FJ. A preliminary in vitro study of the incidence and position of the root canal isthmus in maxillary and mandibular first molars. Int Endod J. 2003;36(4):276\u0026ndash;80.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003evon Arx T. Frequency and type of canal isthmuses in first molars detected by endoscopic inspection during periradicular surgery. Int Endod J. 2005;38(3):160\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003evon Arx T, Steiner RG, Tay FR. Apical surgery: endoscopic findings at the resection level of 168 consecutively treated roots. Int Endod J. 2011;44(4):290\u0026ndash;302.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRussell AA, Chris He LH, Chandler NP. Investigation of dentin hardness in roots exhibiting the butterfly effect. J Endod. 2014;40(6):842\u0026ndash;4.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBoyarsky H, Davis R. Root fracture with dentin-retained posts. Am J Dent. 1992;5(1):11\u0026ndash;4.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOnnink PA, Davis RD, Wayman BE. An in vitro comparison of incomplete root fractures associated with three obturation techniques. J Endod. 1994;20(1):32\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAl-Fouzan KS, Ounis HF, Merdad K, Al-Hezaimi K. Incidence of canal systems in the mesio-buccal roots of maxillary first and second molars in Saudi Arabian population. Australian Endodontic J. 2013;39(3):98\u0026ndash;101.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTang W, Wu Y, Smales RJ. Identifying and Reducing Risks for Potential Fractures in Endodontically Treated Teeth. J Endod. 2010;36(4):609\u0026ndash;17.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePeters OA. Current challenges and concepts in the preparation of root canal systems: a review. J Endod. 2004;30(8):559\u0026ndash;67.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFuss Z, Lustig J, Katz A, Tamse A. An evaluation of endodontically treated vertical root fractured teeth: impact of operative procedures. J Endod. 2001;27(1):46\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQiu S, Chen Y, Tsauo C, Wu W, Huang D, Zhou X et al. Microcomputed tomography analysis of the radicular residual dentin thickness in mandibular second molars after virtual fiber post placement: Identification of danger zones. J Prosthet Dent. 2023;130(1):109.e1-109.e10.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDoğanay-Yıldız E, Fidan ME, Sakarya RE, Din\u0026ccedil;er B. The effect of taper and apical preparation size on fracture resistance of roots. Aust Endod J. 2021;47(1):67\u0026ndash;72.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSabeti M, Kazem M, Dianat O, Bahrololumi N, Beglou A, Rahimipour K, et al. Impact of Access Cavity Design and Root Canal Taper on Fracture Resistance of Endodontically Treated Teeth: An Ex Vivo Investigation. J Endod. 2018;44(9):1402\u0026ndash;6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePrado M, de Lima NRB, de Lima CO, Gusman H, Sim\u0026atilde;o RA. Resistance to vertical root fracture of root filled teeth using different conceptual approaches to canal preparation. Int Endod J. 2016;49(9):898\u0026ndash;904.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKishen A, Kumar GV, Chen NN. Stress-strain response in human dentine: rethinking fracture predilection in postcore restored teeth. Dent Traumatol. 2004;20(2):90\u0026ndash;100.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePatel S, Rhodes J. A practical guide to endodontic access cavity preparation in molar teeth. Br Dent J. 2007;203(3):133.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoga RA, Olteanu CD, Daniel BM, Buru SM. Finite Elements Analysis of Tooth-A Comparative Analysis of Multiple Failure Criteria. Int J Environ Res Public Health 2023;20(5).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAtif M, Tewari N, Reshikesh M, Chanda A, Mathur VP, Morankar R. Methods and applications of finite element analysis in dental trauma research: A scoping review. Dent Traumatol. 2024;40(4):366\u0026ndash;88.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMaravić T, Comba A, Mazzitelli C, Bartoletti L, Balla I, di Pietro E, et al. Finite element and in vitro study on biomechanical behavior of endodontically treated premolars restored with direct or indirect composite restorations. Sci Rep. 2022;12(1):12671.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eP\u0026eacute;rez-Gonz\u0026aacute;lez A, Iserte-Vilar JL, Gonz\u0026aacute;lez-Lluch C. Interpreting finite element results for brittle materials in endodontic restorations. Biomed Eng Online. 2011;10:44.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang L, Nemoto R, Okada D, Shin C, Saleh O, Oishi Y, et al. Investigation of stress distribution within an endodontically treated tooth restored with different restorations. J Dent Sci. 2022;17(3):1115\u0026ndash;24.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Dental stress analysis, finite element analysis, root canal therapy (RCT), dental pulp cavity, dentin","lastPublishedDoi":"10.21203/rs.3.rs-6009419/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6009419/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground \u0026amp; Objective:\u003c/strong\u003e The cervical region of dentin plays a crucial role in the distribution of masticatory forces, with vertical root fractures often initiating and spreading from this area. This study investigates the distribution of occlusal stresses in the cervical region of root dentin, considering varying thicknesses and cross-sections, using Finite Element Analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMaterials \u0026amp; Methods:\u003c/strong\u003e Sections from central and premolar teeth were imported into CAD to create 3D models. The tooth structure and surrounding tissues were modeled using mechanical properties such as Young's modulus and Poisson's ratio. Four cross-sectional shapes—circular, oval, sand clock, and kidney—were designed. A force of 50 Newtons, representing the occlusal force of the opposing tooth, was applied to the palatal surface of the models at a 60° angle for anterior teeth and a 45° angle for premolars. The stress distribution in the cervical dentin was then analyzed.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e Von Mises stress values indicated that stress points were highest in the kidney, sand clock, oval, and circular cross-sections, respectively. Increased thickness of the residual dentinal wall resulted in reduced maximum and minimum stress and a smaller area of stress regions. In all cross-sections, the minimum and maximum stress points were predominantly on the palatal and buccal sides of the cervical dentin, respectively.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusion:\u003c/strong\u003e The study demonstrated that stress distribution in teeth varies with different root cross-sections, with higher stress observed in the sand clock and kidney cross-sections. Thinner dentin in the cervical region leads to greater stress concentration, especially in the buccal area of the tooth.\u003c/p\u003e","manuscriptTitle":"Finite Element Analysis of Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section Running title:Occlusal Stress in Cervical Dentin: Effects of Thickness and Cross-Section","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-17 20:57:22","doi":"10.21203/rs.3.rs-6009419/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-05-02T18:00:14+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-02T17:58:06+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"81409230947771677841644164195568699265","date":"2025-04-21T02:33:47+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-20T11:06:44+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-19T19:59:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"199257581646780738027843297215101019118","date":"2025-04-19T19:48:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"241917159650036384547480826795341628041","date":"2025-04-18T14:56:06+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-16T14:35:30+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-16T14:28:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Oral Health","date":"2025-04-11T13:07:28+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6b7e945a-a138-4250-bcd7-50e54f9a0f9a","owner":[],"postedDate":"April 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-06-09T16:04:43+00:00","versionOfRecord":{"articleIdentity":"rs-6009419","link":"https://doi.org/10.1186/s12903-025-06184-y","journal":{"identity":"bmc-oral-health","isVorOnly":false,"title":"BMC Oral Health"},"publishedOn":"2025-06-05 15:57:53","publishedOnDateReadable":"June 5th, 2025"},"versionCreatedAt":"2025-04-17 20:57:22","video":"","vorDoi":"10.1186/s12903-025-06184-y","vorDoiUrl":"https://doi.org/10.1186/s12903-025-06184-y","workflowStages":[]},"version":"v1","identity":"rs-6009419","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6009419","identity":"rs-6009419","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}