**6. Application of FEA in endodontics**

Endodontology/Endodontics is the branch of dental sciences concerned with the form, function, health, injuries to and the diseases of the dental pulp and periradicular region, and their relationship with systemic health and well-being. Endodontic

therapy involves either root canal filling techniques by conventional methods; or endodontic surgery with the use of biocompatible restorative materials, instruments, and techniques performed. The objective of endodontic instrumentation is to produce a tapered continuous preparation that should preserve the anatomy of root canal and maintain a good apical seal and foramen as small as possible, without any deviation from the original canal curvature [23].

During canal instrumentation, pressure is generated against the dentinal walls that may lead to inappropriate canal preparation or microcracks. These microcracks may lead to vertical fracture - one of the cause for tooth loss. During instrumentation, nickel-titanium (NiTi) are the commonly used for shaping the root canal. So, in order to perform well and avoid instrument breakage inside the canal, the material used and the technique performed should be followed meticulously. FEA helps to analyze and predict the treatment outcome [24].

Satappan et al*.,* in 2000 analyzed the type and frequency of defects in NiTi rotary endodontic files after routine clinical use and reasons for their failure. They found torsional failure by using too much apical force during instrumentation as the more frequent cause than flexural fatigue, which resulted from the use in curved canals [25].

Hong et al*.,* in 2003 analyzed the stress variations by vertical and lateral condensation on mandibular first molar mesio-buccal root canal by step-back technique. They found vertical condensation technique generating high stresses and the reason for vertical root fracture was due to over-force and improper operation [2].

Subramaniam et al*.,* in 2007 compared the torsional and bending stresses in two simulated models of Ni-Ti rotary instruments, ProTaper and ProFile. They found the distribution of stresses was uniform in ProTaper model and stiffer by 30% than ProFile model, which shows ProFile is more flexible than ProTaper [26].

Kim et al*.,* in 2008 compared the stress distribution during root canal shaping and estimated the residual stress in three brands of Ni-Ti rotary instruments: ProFile, ProTaper, and ProTaper Universal (Dentsply Maillefer). They found that the original ProTaper design showed greatest pull in the apical direction and highest reaction torque from the root canal wall while, ProFile showed the least. The residual stress was highest in ProTaper followed by ProTaper Universal and ProFile. In ProTaper, stresses were concentrated at the cutting edge [27].

Lee et al*.,* in 2011 investigated on cyclic fatigue resistance of various Ni-Ti rotary files in different root canal curvatures by correlating cyclic fatigue fracture tests. They concluded that stiffer instrument had the highest stress concentration and the least number of rotations until fracture in the cyclic fatigue test. Increased curvature of the root canal generated higher stresses and shortened the lifetime of Ni-Ti files [28].

Belli et al*.,* in 2011 evaluated the effect of interfaces on stress distribution in incisor models of primary, secondary, and tertiary monoblocks generated either by adhesive resin sealers in combination with a bondable root filling material or by different adhesive posts. The concept of creating mechanically homogenous units within the root dentine is theoretically excellent, but accomplishing in the canal space is challenging because bonding is compromised by volumetric changes in resin-based materials to dentine, debris on canal walls, configuration factors, and differences in bond strengths. They found stresses within roots increased with an increase in the number of the adhesive interfaces [29].

#### **6.1 Application of FEA in post and core**

A considerable amount of tooth structure lost due to caries, endodontic therapy, and placement of previous restorations will compromise the tooth structure to

#### *Finite Element Analysis and Its Applications in Dentistry DOI: http://dx.doi.org/10.5772/intechopen.94064*

resume its full function to serve satisfactorily. The type of the tooth restoring and the amount of remaining coronal tooth structure are the two factors that influence the choice of technique. The second factor is probably the key important indicator in determining the prognosis a tooth that is restored. If a substantial amount of coronal structure is missing, a cast post and core is indicated [30].

The method of restoring a structurally weakened tooth is post and core system, which is most common and widely used. This system can be categorized into two; custom cast metal posts and cores that are single piece, and a two component design comprising a prefabricated post to which other core materials is subsequently adapted. While fabricating a custom post and core, the difference in the elastic modulus of dentine and post material may be a source for root structure because of stress and debonding of posts due to stress contraction of the cement. Design of the post also effects the stress distribution, which was found as the most common mode of failure. Ferrule preparation creates a positive effect in reducing the stress concentration in an endodontically treated tooth. FEM can be used in various types of materials like carbon, metal, glass fiber, and zirconia ceramic and different configurations of dowel like smooth and serrated on the stress distribution of the teeth [6, 7].

Studies have showed that the increase in elastic modulus of post material cause decrease in the stress in dentin. However, Boschian et al., in 2006 have reported that higher the elastic modulus of post material than dentin can cause a dangerous, non-homogenous stress in root dentin. Also Silva et al., in 2009 reported that the stress distribution is more related to endodontically treated teeth restored with a post than the post's external configuration. Therefore, whenever the clinician is planning to use a post he has to choose a post material, which has the stiffness similar to dentin. They evaluated the stress distribution in maxillary central incisor, which is endodontically treated and restored with fiberglass and metallic prefabricated posts [7].

Necchi et al*.,* in 2008 conducted a study on rotary endodontic instruments to demonstrate the usefulness of the FEM in improving the knowledge of the mechanical behaviour of Ni-Ti and stainless steel ProTaper F1 instrument during root canal preparation. The results found the radius and position of the canal curvature as the most critical parameters in determining the stress whilst high stress levels are produced by decrease in the radius and instrumenting apical to the mid root position. They advised to discard the instrument after its use in those type of root canals [31].

The use of glass fiber dowels showed less stress than the metal, carbon, and ceramic posts which few researchers found. However, there are some differences in the material properties, boundaries and loading conditions. A study by Eraslan et al., in 2009 showed a reduction in VM stress in an endodontically treated tooth restored with all-ceramic post and core than with zirconium oxide ceramic post and fiber post at the dentin wall and within the post [32].

In a study by Zhou et al*.,* in 2009 a mandibular second premolar was used to evaluate the stress distribution restored with fiber post and core with various shapes and diameter in axial and non-axial loads. They found no significant change with the increase in post diameter irrespective of the shape. They recommended trapezium and cone fiber posts as the ideal design for restoring the crown and root portion as they produced least maximum stress in non-axial loads than in axial load [33].

For fixation of post and core to the remaining tooth structure cements like zinc-phosphate, glass ionomer, resin-modified glass ionomer, and resin cement are used. The difference in elastic modulus of these cements, post materials and dentin results in stress concentration under function. In 2010, Soares et al., found zinc-phosphate and conventional glass ionomer cement producing high stress

concentrations at dentin-cement interface. They also demonstrated that resin cement recorded higher fracture resistance values than other cements, which was in accordance with the study done by Suzuki et al., in 2008 [7].

A systematic review in 2010 by Al-Omiri et al*.,* discussed the importance of ferrule and emphasized the use of adhesive resin-fiber posts and composite cores as the best luting technique with respect to the biomechanical behaviour and tooth fracture resistance [34].

Al-Omiri et al*.,* in 2011 conducted a study on 3-D FEM of maxillary second premolar restored with an all-ceramic crown supported by a titanium post and a resin-based composite core to analyze the stress concentration areas. They found higher incidence of deep root fractures in teeth restored with post-retained crowns below the level of crestal bone due to the increase in intracanal stresses with horizontal loads generating more dentinal stress than vertical loads. Though endodontic posts provide retention for coronal restoration, the dentinal stress value was higher than those without posts were. Smaller diameter posts with modulus of elasticity similar to dentine were associated with better stress distribution. More the amount of radicular dentin around the post better/reduced dentinal stress concentration within the root [35].
