3-D finite element analysis of the effects of post location and loading location on stress distribution in root canals of the mandibular 1st molar

Abstract Objective The purpose of this study was to evaluate, by using finite element analysis, the influence of post location and occlusal loading location on the stress distribution pattern inside the root canals of the mandibular 1st molar. Material and Methods Three different 3-D models of the mandibular 1st molar were established: no post (NP) – a model of endodontic and prosthodontic treatments; mesiobuccal post (MP) – a model of endodontic and prosthodontic treatments with a post in the mesiobuccal canal; and distal post (DP) – a model of endodontic and prosthodontic treatments with a post in the distal canal. A vertical force of 300 N, perpendicular to the occlusal plane, was applied to one of five 1 mm2 areas on the occlusal surface; mesial marginal ridge, distal marginal ridge, mesiobuccal cusp, distobuccal cusp, and central fossa. Finite element analysis was used to calculate the equivalent von Mises stresses on each root canal. Results The DP model showed similar maximum stress values to the NP model, while the MP model showed markedly greater maximum stress values. The post procedure increased stress concentration inside the canals, although this was significantly affected by the site of the force. Conclusions In the mandibular 1st molar, the distal canal is the better place to insert the post than the mesiobuccal canal. However, if insertion into the mesiobuccal canal is unavoidable, there should be consideration on the occlusal contact, making central fossa and distal marginal ridge the main functioning areas.


Introduction
The tooth is a complex structure mainly composed of pulp, dentin, cementum, and enamel, which is surrounded by periodontal tissues including the periodontal ligament and alveolar bone 19 . It deals with the most important function of grinding and chewing of foods, which subsequently results in force generation and transmission from the crown to the alveolar bone.
The natural biomechanical balance of the tooth is well suited to this purpose, with the material properties of its aforementioned components functioning together to achieve this end. Therefore, the tooth must withstand the stress exerted during the chewing process; if it does not, it will fracture, especially in the root, resulting in permanent loss of function 12 .
It is commonly accepted that severely damaged tooth, whether by dental caries or fracture, must undergo the root canal therapy. When an extensive amount of coronal structure is lost, the post would be the first choice of treatment to prevent the core material from being detached 6, 8,18,26 . It is in agreement that the post, if needed in the posterior region, should be inserted in the largest and straightest canal; namely, the distal canal in the mandibular molars, and the palatal canal in the maxillary molars 26 .
Root canal treatment, which is intended to save the tooth, may adversely cause iatrogenic damage, particularly during canal preparation, canal filling, and post preparation 2,23,28 . It is obvious that endodontic treatment, whether with the post or not, changes the balance of the tooth structure, so the different phenomenon would happen as a force transmission system. of the distal or mesiobuccal root canal, with a 0.1 mm layer of cement around the post, and the empty space inside the teeth was filled with core material. To mimic a tooth with severe loss of coronal dentin, most of the coronal component was removed so that only 2.0 mm of the coronal portion above the cementoenamel junction was left; the removed portions were replaced with the restorative material. Finally, a 1.0 mm axial reduction and a 1.5 mm occlusal reduction were conducted, and the crown was added to the prepared coronal portion (Figure 2).

Finite element analysis
The models were transferred to the static structural analysis system in ANSYS for finite element analysis.
Zirconium oxide was chosen as the material for the prosthetic crown, and glass fiber for the post. The canal was filled using gutta-percha, and the post was cemented into the canal using Panavia. The core and coronal portion were constructed using resin-based composite material. All materials, other than the glass fiber post, were assumed to be homogeneous, isotropic, and linear elastic; the glass fiber post was considered as orthotropic, linear elastic material. The elastic moduli and Poisson's ratio of the materials used in this study are shown in Figure 3 4 Buccolingual at apex 2.5

Results
The root canals were divided into three portions: the coronal third, middle third, and apical third.         vary as much as that of the mandibular 2 nd molar 20 .
Moreover, the external and internal root shapes of the mandibular 1 st molar have been investigated and analyzed by many authors 5,10,11,20 . With such accumulated data, the "standard morphology" of the mandibular 1 st molar for finite element analysis was created.
Most authors in this field have designed their models by scanning a real tooth and adding the inner shape of the root canals to the outer shape obtained 4,6,15,16,24,27 . In this study, however, both outer and inner shapes of the tooth were designed using information accumulated from many previous authors 5, 10,11,20 . In this way, it is possible to use the