**8. Application of FEA in trauma and fractures**

Oral and maxillofacial surgery is one branch of dentistry, which has always been associated with biomechanics. Trauma surgery, orthognathic surgery, reconstructive surgery are the subdivisions where understanding the mechanism of fractures and its biological response to the biomechanical change are worth knowing for optimal treatment method and outcome [43].

When present technology was not available in the past, cadaveric studies were the only way of information and it is not possible to carry out designing and executing which at present times have ethical issues often challenging to have valid and reliable results. Furthermore, post mortem alterations and the age do not match in a typical facial trauma cadaver. One such example was René Le Fort, a French army surgeon, conducted a series of thorough experiments on the heads of cadavers. His work gave rise to a system of classifying facial fractures, now known as Le Fort types I, II and III [36, 43].

Since the maxillofacial region has vital anatomical structures, intervention in this region needs precise work to be carried out in restoring function and esthetics of the tissues in obtaining predictable and favorable long-term outcomes. In the field of trauma surgery, to identify the craniofacial region that are potential prone to fracture, FEA enables precise mapping of the maxillofacial region to know the biomechanics and stress pattern distribution of trauma that helps in evaluation of patient and optimizing the surgical protocol for treating the fractures [43].

Today, with the help of FEA mechanical properties of facial hard and soft tissues, osteosynthesis materials, implant components for fixing the fractured parts, and various biological and synthetic bone substitutes can be easily generated and determined due to the advancement in the computing and virtual analysis. It allows the testing of various fixation system to prevent the future failure due to its improper selection or inappropriate positioning. It made us possible to know the impact in biomechanical behaviour of testing materials on the biological responses

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

of the bone tested as well as adjacent anatomical structures more accurate, repeatable, time saving, and cost-effective way regardless of their complexity [43].

Isolated orbital floor fracture (IOFF), zygomatic bone fracture are the examples of more complex traumas occurring frequently in contact sports and their pathomechanism were also studied with the aid of FEA. In relatively rare facial traumas like in case of blast or gunshot wounds, FEA helps in exploring, analyzing and determining the mechanism of anatomical structures damaged and ways in reconstructing them. The pathomechanism underlying the type and method of fracture is exceptionally important as it may help in designing the helmets, other protecting devices. Rigid fixation is one of the key element in determining the long-term success for osseointegration. Inappropriate selection of an osteosynthesis component for the biological tissues can cause complication in fusion of bone. Therefore, FEA helps in determining and designing various fixation systems and methods [44, 45].

Osteosynthesis of condylar fracture and fixing the element is a challenging aspect for a maxillofacial surgeon due to its specific anatomy and surgical access. Through FEA, it has become possible for the researchers to find the better way and an exceptionally handy, easy mountable and durable element for optimal stabilizing and fixing the fractured fragments. A new type of "A-shape condylar plate" was designed for all levels of neck fractures and it can be used for stabilization of existed coronoid process fracture. FEA has proved to be a useful tool in investing and thorough evaluation of newer materials and solutions, which are more optimized, durable and light weight components before they can be used in the clinical situations [46].

Bujtár et al*.,* in 2010 analyzed the stress distribution in detailed models of human mandibles at 3 different stages of life (12, 20, and 67 years) with simulation of supra normal chewing forces at static conditions. They found higher elasticity in younger models in all regions of the mandible whereas higher levels of stress in a 67 year old at the mandibular neck region of edentulous mandible [47].

Huempfner-Hierl et al*.,* in 2014 showed a pattern of von Mises stresses beyond the yield point of bone that corresponded with fractures commonly seen clinically. They found Naso-orbitoethmoid fractures account for 5% of all facial fractures. They concluded that, FEM can be used to simulate the injuries occurring to the human skull that provides information about the pathogenesis of different types of fracture [48].

Murakami et al*.,* in 2014 evaluated the strength of mandible after removal of a lesion to illustrate the theoretical efficacy of preventive measures against pathologic fracture. They found plate application is effective to decrease the stress on the mandible after surgical removal of a cyst including third molar [43].

Santos et al*.,* in 2015 analyzed the stress distributions on the symphyseal, parasymphyseal, and mandibular body regions in the elderly edentulous mandible under applied traumatic loads, which enabled precise mapping of the stress distribution in a human elderly edentulous mandible (neck and mandibular angle) [49].

### **9. Application of FEA in orthodontics and dentofacial orthopedics**

Orthodontics is a specialty of dentistry, which deals with the diagnosis, prevention and correction of malpositioned teeth and jaws. It also focuses on determining and modifying the facial growth, known as dentofacial orthopedics. Abnormal alignment of the teeth and jaws is common. In the field of Orthodontics and Dentofacial Orthopedics, FEM has proved to be a reliable and valid procedure in evaluating the applied orthodontic forces.

Tanne et al*.,* in 1995 did a 3-D FE study to investigate the location of nasomaxillary complex centre of resistance (CRe). 9·8 N of force directed anteriorly and inferiorly were applied at five different levels, parallel and perpendicular to the occlusal plane. When a horizontal force was applied at a point in the horizontal plane, passing through the superior ridge of the pterygomaxillary fissure, the complex exhibited a translatory displacement of 1·0 μm approximately in forward direction. Whereas, clockwise or counter clockwise rotation when the forces were applied at the remaining levels suggesting that CRe of the nasomaxillary complex is located on the postero-superior ridge of the pterygomaxillary fissure, registered on the median sagittal plane [2].

Many researchers have developed various FE models in order to understand the interaction between tooth mobility and periodontal ligament. Jones et al., in 2001 validated an FE model and found PDL as the main mediator for orthodontic tooth movement and the material properties of PDL are difficult to quantify [7].

The use of the lingual orthodontic technique has increased over time, as adults dislike the visibility of orthodontic appliances. Sung et al*.,* in 2003 evaluated the effect of compensating curves on canine retraction between the lingual and the labial orthodontic techniques. The compensating curve was increased on the .016-in stainless steel labial or lingual archwire, and a 150-g force was applied distally on the canine. The pattern of tooth movement (with or without a compensating curve) was found to be different between labial and lingual techniques. As the amount of compensating curve increased (0, 2, and 4 mm) in the archwire, the rotation and the distal tipping of the canine was reduced. The anti-tip and anti-rotation action of compensating curve on the canine retraction was greater in the labial archwire than in the lingual archwire [50].

Cattaneo et al., in 2009 studied on Orthodontic tooth movement (OTM) which occurs when an orthodontic force is applied to the brackets. The modeling and remodeling process of the supporting structures occurs by alteration in the distribution of stress/strain in the periodontium. As per the classical OTM theories, symmetric zones of compression and tension are present in the periodontium. However, they did not consider the complex mechanical properties of the PDL, the morphology of alveolar structures', and magnitude of the applied force. The authors could not confirm the classical ideal of symmetrical compressive and tensile areas in periodontium as per the OTM scenarios. They found light continuous orthodontics forces will be perceived as intermittent by the periodontium. They expressed that, as the roots and alveolar bone morphology are patient-specific, FEA should not be based on general models [51].

Lingual orthodontics has developed rapidly in recent years; however, research on torque control variance of the maxillary incisors in both lingual and labial orthodontics is still limited. Liang et al*.,* in 2009 generated maxilla and maxillary incisors models to evaluate the torque control during retraction in labial and lingual orthodontic technique for maxillary incisors. They found loads of the same magnitude produced translation of the maxillary incisor in labial orthodontics but lingual crown tipping in lingual orthodontics. This suggested the loss of torque control during retraction of the maxillary incisors in extraction patients is more likely in lingual orthodontic treatment [52].

Field et al*.,* in 2009 investigated the stress–strain responses of teeth to orthodontic loading. Two cases were analyzed, consisting of a single-tooth system with a mandibular canine, and a multi-tooth system with mandibular incisor, canine, and first premolar that are subjected to orthodontic tipping forces. They found stress levels greater in the multi-tooth system than in the single-tooth system also, elevated distortion strain energies at the alveolar crest area and tensile and compressive stresses at the apical sites clinically associated with root resorption [22].

## **9.1 Orthognathic surgery**

Orthognathic surgery also known as corrective jaw surgery or simply jaw surgery is aimed to correct the conditions of jaw and face. They relate to correct the structure, growth modification, disorders of TMJ, sleep apnea, malocclusion problems owing to skeletal disharmonies, or other orthodontic problems that cannot be treated with orthodontic braces. It involves the surgical manipulation of the structures of the facial skeleton in restoring the suitable anatomy and their functional relationship with dentofacial skeletal abnormalities for the patient's sense of self and well-being. Successful outcome depend on meticulous preoperative planning until finalization of occlusion. Virtual planning promotes a more accurate analysis of dentofacial deformity and preoperative planning with the help of computerbased technique like FEA, an invaluable tool in providing comprehensive patient education. Today's orthognathic treatment consists of standard orthognathic procedure in correcting jaw deformities like maxillary and mandibular prognathism, open bite, difficulty in chewing and swallowing, TMJ dysfunction pain, excessive wear of the teeth, and receding chins. It includes adjunctive procedures like genioplasty, septorhinoplasty, and lipectomy of the neck to improve hard and soft tissue contours [53].

Chabanas et al*.,* in 2002 presented their study on the treatment protocol – a computer aided maxillofacial sequence for orthognathic surgery in the patients with large gnathic defects because the treatment protocol is difficult and time consuming [43].

Erkmen et al*.,* in 2005 conducted a study and found that the use of 2.0 mm lag screws placed in a triangular configuration provided most sufficient stability and lesser stress fields at the osteotomy site compared to other rigid fixation methods [54].

For successful outcome in any orthognathic surgeries, selection of an appropriate bridging element is a key determinant, corrective mandibular surgery like bilateral sagittal split osteotomy (BSSO) is not an exception to stabilize the bony segments with different fixing elements and FEA is an important tool [43].

Stróżyk et al*.,* in 2011 compared three types of fixation during BSSO using 3-D FE model divided into 3 segments with 5 mm gap in between according to BSSO line. Three fixation systems were bridged to the osteotomized fragments, a 20 N and 80 N force applied at the incisor and molar area respectively. They concluded that the most stable bridging after BSSO can be obtained with bicortical screw fixation [55].

Surgically Assisted Palatal Expansion (SARPE) is an orthognathic surgical procedure that is performed frequently in the patients with narrower maxilla. De Assis et al*.,* in 2014 investigated the stress distribution in maxillae that underwent SARPE. They constructed five maxillary models with no osteotomy, Le Fort I osteotomy with a step in the zygomaticomaxillary buttress, Le Fort I osteotomy with a step in the zygomaticomaxillary buttress and the pterygomaxillary disjunction, Le Fort I osteotomy without a step, and Le Fort I osteotomy with pterygomaxillary disjunction and no step. The distribution of tensions in maxillae that underwent SARPE was simulated by the FEM and they revealed that the steps in the zygomaticomaxillary buttress and the pterygomaxillary disjunction seems to be important in decreasing the harmful dissipation of tensions during SARPE [56].

A more complex surgery involving correction of deformation of both the jaws simulating the maxillary and mandibular jaw osteotomy using FEA was also executed. Fujii et al*.,* in 2017 conducted a study to determine whether non-linear 3D-FEA can be applied to simulate pterygomaxillary dysjunction during Le Fort I osteotomy (LFI) not involving a curved osteotome (LFI-non COSep), and to predict potential changes in the fracture pattern associated with extending the cutting line. In their study, the

rate of agreement between the predicted pterygomaxillary dysjunction patterns and those observed in the postoperative 3D-CT images was 87.0%. The predicted incidence of pterygoid process fracture was higher for cutting lines that extended to the pterygomaxillary junction than for conventional cutting lines. They also added that, 3-D FEA can be a useful tool in predicting pterygomaxillary dysjunction patterns and provides useful information in selecting safe procedures during LFI-non-COSep [57].

Knoops et al*.,* in 2019 conducted a study to compare the soft tissue prediction accuracy of several available computer programmes like Dolphin, ProPlan CMF, and Probabilistic Finite Element Method (PFEM) in patients with Le Fort I osteotomy. They concluded that patient or population-specific material properties can be defined in PFEM, while no soft tissue parameters are adjustable in ProPlan. Therefore, PFEM provides accurate soft tissue prediction and can be a useful tool in preoperative patient communication [58].

### **10. Application of FEA in reconstructive surgery**

The FEM technique can also be used in oncosurgeries and reconstructive surgery where an extensive resection is needed and reconstruction of jawbones are done. The crucial parameter form the postoperative point of view is the amount of bone segment removed from the surgical site, which includes size, shape, and location. The aim of reconstructing the bone defect should result in restoration of the integrity, its anatomy and the functionality of stomatognathic system. With the aid of digital technology; modeling, simulation and analysis, it is possible to know and compare the stress levels and distribution on and at the bone-graft interface and predictable behaviour of the reconstructed site to identify the most suitable transplant for a given clinical situation and to find the appropriate bone fusion under favorable conditions in the reconstructed area [43].

Moiduddin et al*.,* in 2017 studied to present an integrated framework model in designing and analyzing customized porous reconstruction plate based on the selection of implant design techniques. Reconstruction of large mandibular defects often leads to complications while using reconstruction plates. Studies proved that implants with porous structures can effectively enhances the biological fixation to the bone but, no study reported on the design and analysis of the customized porous mandibular reconstruction. In their study, two customized implant design techniques; mirroring and anatomical were compared. They recommended the use of mirror design reconstruction technique in mandibular bone repair, which not only improves the stability but also the flexibility of mandibular reconstruction under chewing conditions [59].

Hu et al*.,* in 2019 performed a study to characterize the mechanical behaviour of 3-D printed anisotropic scaffolds as bone analogs by fused deposition modeling (FDM). Using topological optimization and 3-D printing technology, designing and manufacturing of a customized graft with porous scaffold structure is necessary in repairing large mandibular defects. They used CBCT images of an edentulous 50-year-old patient. The topological optimized graft provided the best mechanical properties. They highlighted the use of numerical simulations and 3-D printing technology in designing and manufacturing the artificial porous graft [60].

#### **11. Application of FEA in periodontics**

PDL is a highly specialized soft connective tissue that is present between the tooth root and the alveolar bone. The primary function is to support the tooth and *Finite Element Analysis and Its Applications in Dentistry DOI: http://dx.doi.org/10.5772/intechopen.94064*

is the most important component of periodontium. Various studies included and investigated on its biomechanics and stress distribution under normal, masticatory, and traumatic loads. PDL is the crucial aspect in designing as it influences the properties of a 3-D model, though it is difficult in modeling and not a concern for the study. Ignoring the PDL may result in inaccurate values of stress and strain distribution [36].

Tuna et al*.,* in 2014 conducted a study and pointed out the advantage of simulating as a contact model at the interface of tooth root and alveolar process instead of a solid meshed FE model with poor geometric morphology or very dense mesh to save the time. They reinforced the use of PDL in designing the tooth model and its associated structures that increases the accuracy and contribution to the smoothness of interface stress distributions [61].
