A three-dimensional finite element analysis of stress distribution in maxillary central incisor with a horizontal mid root fracture after various management protocols.

Context: The incidence of root fractures is about 1.2%-7% in permanent teeth and horizontal mid root fractures are most common in maxillary anteriors. Aims: This study aims to evaluate the stress distribution in a maxillary central incisor with mid root fracture after various management protocols using three-dimensional finite element (FE) analysis. Materials and
Methods: Four three dimensional FE models were constructed: Model 1-Normal tooth, Model 2-tooth with horizontal mid root fracture, Model 3-tooth with horizontal mid root fracture, coronal fragment filled with Biodentine, and access cavity sealed with composite resin cement and apical fragment left untreated and Model 4-tooth with horizontal mid root fracture restored with intraradicular fiber post as a splint and access cavity sealed with composite resin cement. The properties of materials were assigned and a force of 100 N was applied at 45° angle to the longitudinal axis of the tooth onto the palatal surface incisal to the cingulum. Statistical Analysis: Von-Mises stress along the length of the root analyzed and compared.
Results: The maximum stress distribution was observed at the palatal end of the coronal radicular fragment in both without treatment and with biodentine treatment. The stress distribution was concentrated more at the junction of the splinted area in the intraradicular fiber post splinted model. Conclusions: The model with intraradicular fiber post as a splint exhibited more stress concentration at the splinted area due to bending forces. These stresses may adversely affect the healing around the fracture site and affect the longevity. Copyright:

INTRODUCTION

Dental traumatic injuries are the most common occurrence in 7–12 years of age group mainly due to falls and accidents.[12] The incidence of root fractures is about 1.2%–7% in permanent teeth and 2%–4% in primary teeth.[34] The root fracture involves the periodontal ligament, cementum, dentin, pulp and it can be at any level (cervical, middle, or apical) of the root. Horizontal fractures occur mostly in the middle third of the root (57%) followed by apical (34%) and common in maxillary anteriors with 95% of occurrence in maxillary central incisors. The coronal third fractures are rare and have poor prognosis, the apical third fractures usually maintain the pulp vital and are left untreated.[456]

The management of horizontal root fractures as per the existing literature includes; in case the tooth is vital, repositioning of the coronal fragment and immobilization and fixation to the adjacent tooth with rigid or semi-rigid splint for 2–3 months and checking the status of vitality for at least 1 year.[36789] In case of pulpal necrosis, obturation of the coronal fragment only with either gutta-percha or any biomimetic materials and retaining or removal of the apical fragment,[691011] removal of the coronal fragment and orthodontic extrusion of the apical fragment, removal of the apical fragment and stabilization with endoimplants, and intraradicular splints using files, fiber posts, etc., to unite the fracture fragments.[1213]

The immediate and short-term response to horizontal root fracture can be either (i) healing with hard dental tissue or (ii) healing with connective tissue or (iii) healing with bone and connective tissue or (iv) no healing and interposition of granulation tissue.[3] The long-term response may be late pulp necrosis and infection of the coronal fragment which still has to be further studied.[9]

There is limited literature on the long-term clinical studies of horizontal root fractures and the stresses that are distributed along a treated fractured root. Hence, which treatment protocol would be able to provide long-lasting function has to be explored.

A three-dimensional finite element analysis (3D-FEA) is a mathematical method that virtually creates models and subjects them to various complex mechanical stresses. It helps in analyzing the stress pattern at any location of the tooth which is difficult to record clinically.

Hence, the study was designed to evaluate the stress distribution in a maxillary central incisor with mid root fracture after various management protocols like no treatment or the coronal fragment filled with biodentine and apical fragment left untreated or restored with intraradicular fiber post as a splint using 3D-FEA. The null hypothesis assumed that the stress distribution was unaffected in all the treatment protocols.

MATERIALS AND METHODS

A maxillary central incisor extracted for periodontal reasons was randomly collected and used for the study. The geometry was captured using CBCT scan (HDXWILL, Seoul) and STL (stereolithography) file format (OnDemand 3D software, KavoKerr, India) was used as an input to generate the CAD (Computer-aided design) model using ANSYS SpaceClaim 19.2 (SpaceClaim Corporation, Massachusetts). The FE model was generated using solid 185 and solid 186 higher-order tetrahedron and hexahedral elements. 68329 Nodes and 39089 Elements were used to generate the FE model. The alveolar bone (height 17 mm and width 12 mm) and 0.3 mm thick periodontal ligament around the root surface was modeled.[14]

Four 3D-FE models were constructed: Model 1-Normal tooth, Model 2-tooth with horizontal mid root fracture, no displacement and with 0.3 mm separation between root fragments, Model 3-tooth with horizontal mid root fracture as in Model 2, coronal fragment filled with Biodentine and access cavity sealed with composite resin cement and apical fragment left untreated and Model 4-tooth with horizontal mid root fracture as in Model 2 and restored with intraradicular fiber post (Coronal diameter 1.3 mm, apical diameter 0.7 mm) as a splint and access cavity sealed with composite resin cement. All the clinical situations in Model 2, 3, and 4 have been modeled presuming that the treatment was done without much delay based on the pulpal status and 0.3 mm separation between fragments was filled with tissues either related to pulpal injury or inflammation or granulation tissue. Mesh convergence study was performed to determine the model accuracy. All materials properties were assumed to be isotropic, homogenous, and linear elastic [Table 1].[15161718]

Table 1

Isotropic material properties[15161718]

Material/component	Elastic modulus (Mpa)	Poisson’s ratio	Reference
Enamel	84,100	0.33	[15]
Dentin	18,600	0.31	[15]
Periodontal ligament	6.9	0.45	[1617]
Alveolar bone	13,700	0.30	[1617]
Gutta percha	0.69	0.45	[1617]
Fiber post	45,000	0.25	[1617]
Composite resin	16,600	0.24	[1617]
Resin cement	18,600	0.28	[15]
Biodentine	22,000	0.30	[18]

Boundary conditions and loading: The cortical bone was fixed and virtual loading force of 100N was applied with a 3 mm cylinder at 45° angulation to the long axis of the tooth incisal to the cingulum (middle third of the palatal fossa) which simulates the situation of the maxillary incisors receiving the loads from the mandibular incisors.[17] Linear elastic FEA was performed to evaluate the structural integrity of the tooth and stress distribution pattern was studied. The maximum stresses generated in the tooth and the experimental materials were calculated as von-Mises stress.

RESULTS

The pattern of stress distribution in Model 1 (normal healthy tooth) was taken as a baseline to compare the stresses in horizontal mid root fracture managed with no treatment, Biodentine filling, and intraradicular fiber post as a splint. Results are shown in terms of colored contour patterns, red indicates the maximum range of stress and dark blue the minimum [Figure 1].

Figure 1

Model 1 – Distribution of von Mises stresses in normal healthy tooth

In Model 2, maximum von-Mises stress of 0.48 MPa was observed at the palatal aspect of the coronal fragment of the fractured root end. The apical fragment showed minimum stresses when compared to the normal tooth [Figure 2a]. Model 3 showed a similar stress pattern like that of an untreated mid root fracture with maximum von-Mises stress of 0.47 MPa [Figure 2b]. Model 4 showed the maximum von-Mises stress (5.6 MPa) concentration at the junction where the coronal and apical fragment were splinted with fiber post and also at the palatal surface of the fracture end of coronal fragment but less when compared to other models discussed [Figure 2c].

Figure 2

(a) Model 2 – Distribution of von Mises stresses in horizontal mid root fracture tooth. (b) Model 3 – Distribution of von Mises stresses in coronal fragment filled with Biodentine and apical fragment left untreated. (c) Model 4 – Distribution of von Mises stresses in the coronal and radicular fragments splinted with fiber post

DISCUSSION

Horizontal root fractures are most common, with maxillary anteriors affected 95% of the time.[4] Middle third fractures are more common than coronal and apical third.[5] The management of horizontal root fracture depends on the mobility of the tooth fragment, location of fracture, and vitality of the tooth. The present study has chosen maxillary central incisor and fracture at the middle third with three commonly practiced treatment options to analyze the stress distribution along with the fractured fragments which indirectly helps to predict the longevity of the selected treatment option. The horizontal root fractures are difficult to be simulated in an experimental in vitro set up hence, 3D-FEA would be a better option.

The numerical method of analyzing stresses and deformations in structures is known as FEA. Its major advantage is the ability to solve complex biomechanical problems for which other study methods are inadequate and also helps in eliminating the need for large number of experimental teeth. Stress and strain can be calculated at every node and element throughout the structure any number of times and will yield identical results every time. In dentistry, FEA has been used to study internal stresses in teeth and different dental materials such as cements, posts, and full coverage restorations.[14151617]

The literature review showed decrease in von-Mises stress in root canal treated teeth and displacement was repeatedly found in the cervical area when compared to vital tooth,[19] and post and core restored intact tooth showed stress distribution on the inner side of the proximal radicular walls at the level of cervical region irrespective of post diameter and for metal posts it was observed on the inner side around the post apex.[151617] Therefore, to understand the stress distribution in horizontally fractured tooth, the baseline stress distribution pattern in an intact tooth was assessed to compare how the tooth behaves before, after fracture and after different treatment modalities.

The intact tooth (Model 1) showed minimum stress concentration in the internal crown part and along the pulp canal and maximum at the site of load. In Model 2 with mid root fracture there were minimum stresses in the apical fragment when compared to Model 1 as the load transfer was not occurring due to separated fragments. This may help the apical fragment maintain the vitality unless the pulp canal is infected or the blood supply to the apical fragment is lost. The literature also has shown that fractured roots which were left untreated maintained vitality for long.[789]

In Model 3, the coronal fragment after root fracture has a wide pulp canal at the apical end without apical constriction. So to seal the wide apical end, materials used for apexification can be used. Mineral trioxide aggregate (MTA) has been used in few case reports along with other materials such as gutta-percha, files, and posts in horizontal fracture management.[10112021] Biodentine, a bioactive dentin substitute having mechanical properties similar to dentin has been used in recent past for pulp capping, apexification, perforation repair and as a retrograde filling material. In the present study, biodentine was used to fill the root canal till the cement-enamel junction and the access cavity was sealed with composite resin cement. The studies have shown that when biodentine used as an obturating material, increased the fracture resistance of the tooth similar to MTA.[1822] The stress distribution in Model 3 showed a similar pattern as that of Model 2, which also helps in favorable healing at the fracture site.

In Model 4, the coronal and apical fragments of the root were splinted using fiber post and apical 5 mm was filled with gutta-percha, which was one of the management protocols in the past literature.[232425] The stress concentration was more at the fracture junction around the post with maximum value of 5.60 MPa and also at the palatal end of the coronal fragment but less when compared to Model 2 and 3 in that area. The stress distribution pattern was different from that observed in an intact tooth with fiber post and core.[151617] The fiber post bends on loading at the splinted area causing stress in the surrounding tissues which indirectly affects the healing of fracture site and the long term prognosis. The null hypothesis was rejected as the stress distribution was not the same in the models tested.

The limitations of the present study are it evaluated the stresses in the fractured root fragments on loading in mathematical models. The materials and structures used were considered to be isotropic, homogenous, and linearly elastic. A static loading in one particular angle (45°) was used and other simulations of protrusive and retrusive movements not considered. For better understanding, the behavior of the fragments and surrounding periodontium, in vitro models simulating the clinical structures should be devised. Role of immediate composite splinting to avoid coronal fragment movement if any, not considered. The findings of the present study need clinical correlation by reporting more number of cases with long-term follow-up.

CONCLUSIONS

Within the limitations of this study following conclusions can be derived:

The stress distribution is similar in both untreated and biodentine filled model. Hence, both the treatment options can be considered based on the pulp vitality status of the coronal fragment

The model with intraradicular fiber post as a splint exhibited more stress concentration at the splinted area due to bending forces in that area. These stresses may adversely affect the healing around the fracture site

When both coronal and apical fracture fragments lose the vitality, both should be obturated separately with any of the biocompatible obturating material (Guttapercha, MTA, Biodentin etc.,) and not splinted to avoid the stress concentration at the junction of fragments.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.