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Year : 2022  |  Volume : 14  |  Issue : 1  |  Page : 6-12

FEAr no more! Finite element analysis in orthodontics

Department of Orthodontics and Dentofacial Orthopaedics, BYPDU Dental College, Pune, Maharashtra, India

Date of Submission11-Nov-2021
Date of Acceptance15-Jan-2022
Date of Web Publication4-Jul-2022

Correspondence Address:
Dr. Shilpa Chawla
6 Venu Madhav Apartments, 104/7 Off Income Tax Lane, Lane No. 14, Prabhat Road, Pune - 411 004, Maharashtra
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jicdro.jicdro_79_21

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Finite element analysis (FEA) incorporates the principles of erudite engineering to scrutinize stresses that cause deformation in structural units. This technique uses computer-assisted design software and FEA analysis software for modeling structural units established on their geometry, loading, boundaries, and converts the data into algebraic equations to find solutions for different applications. In dentistry, this computer-based simulation method is deemed revolutionary in forecasting and quantifying stress in investigational biological tissues, dental prostheses, and restorations. This review is designed to explicate the significance of FEA in diverse facets of dentistry with special consideration to orthodontics.

Keywords: Dentistry, finite element analysis, orthodontics

How to cite this article:
Chawla S, Deshmukh S. FEAr no more! Finite element analysis in orthodontics. J Int Clin Dent Res Organ 2022;14:6-12

How to cite this URL:
Chawla S, Deshmukh S. FEAr no more! Finite element analysis in orthodontics. J Int Clin Dent Res Organ [serial online] 2022 [cited 2022 Dec 5];14:6-12. Available from: https://www.jicdro.org/text.asp?2022/14/1/6/349758

   Introduction Top

Finite element analysis (FEA) is a system for analyzing deformation and stresses in a structural unit which may be solid or fluid using the specific computer programs. It uses numerical methods which take into consideration the material properties; boundaries; load; geometry, etc., of the structural unit and predicts how a unit or a part will behave under certain conditions.[1]

Historically, this concept is known since the 16th century and it was utilized in the civil engineering and aerospace industries. FEA has its early beginnings in the 1950s by Rolls Royce (UK) and the airline industry in the US, such as Boeing and Bell. Wilson a professor at Berkley produced the first free FEA software programs.[2] The advantage of this method is that it can quantify strain and stress throughout the three-dimensional (3D) structural unit and not just on the surface.[3] Currently, it is being used in other fields such as chemical; biomedical; dentistry; geotechnical; manufacturing; plastics; automotive; electronics; and energy.[1],[4]

The history of FEA in the dental field dates back to 1973 when 2D models in restorative dentistry were ridden with many mathematical errors as hoop configurations of dentin were difficult to construct. This was then corrected in 1990 which saw the arrival of 3D models using computed tomography (CT) imaging with many sections of the jaws which could be stored and reconstructed into 3D prototypes. In addition, the notion of meshing and Monte Carlo numerical prediction models were presented to discern white spot lesions; demonstration of chewing forces, etc.[3]

The era between 2000 and 2010 has seen further advancements in computer technology and artificial intelligence that has paved way for better visualization of the restorations like dental implants, veneers, etc., using fine meshing and high resolution computing to better envisage the strain arenas for functional treatment of the dentition. Computer-assisted design (CAD) software such as Geomagic, Pro-engineering, and Solidworks is developed for 3-D imaging and then converting it to FEA programs such as Mimics, Marc, Ansys, and Abaqus.[3]

FEA relies on the Finite Element Method (FEM) which has its roots in a solid mathematical base using computer software packages that transform partial differential equations into algebraic equations. This computer-aided modeling method helps to find solutions for different applications as different structural units have multifaceted boundaries and geometrical conditions.[5],[6]

Given the importance of FEA as narrated above, this review article has been aimed at: exploring the value of FEA in different aspects of dentistry, for example, to study stresses generated in implants; endodontically treated teeth; restorations, etc., along with special consideration towards its solicitation in orthodontics.

[TAG:2]Description of the Planning the Model for Finite Element Analysis[3][/TAG:2]

  • Model construction - The objects are first isolated by identifying their different boundaries and then using CT, magnetic resonance imaging, micro-CT the images are constructed and stored as datasets and a solid model is created using 2D or 3D slices. For example, in the implant-bone interface, the common nodes between the diverse surfaces are itemized to study simulated dissemination of load within the item
  • The model created is loaded into the CAD programs like Geomagic which helps to smooth over irregularities with a meshing program installed in it and it makes up a solid image for the analysis as most un-touched CT images are polygonal slices with holes
  • The models are then validated using the principles of loading, conditions of the boundary, and properties of the material. Loading is studying the static biting forces in dental restorations and prostheses and FEA helps to define the direction and magnitudes of bite forces from the collected data. The next constraints of the model are delineated to minimize the errors while studying the bodily phenomena. The challenge in dentistry is the organic tissues, for example, the periodontal ligament (PDL) is difficult to distinguish on the CAD programs, and therefore, most dental research in FEA uses “linear elastic assumption” for analysis.

   Finite Element Analysis and Applications in Dentistry Top

FEA and its applications in dentistry can be enumerated as in [Table 1].
Table 1: Applications of FEA in dentistry

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Finite element analysis and implants

The solicitation of the FEM in dentistry is explained with an example from the placement of implants. The simulations generated by the FEA models elucidate the perfunctory features of the soft and hard tissues and the surrounding structures while positioning dental implants. Hence, if we need to measure stresses and strains, firstly, a virtual method has to be utilized with 3-D imaging like cone beam CT or CAD to study the geometrical boundaries. At that juncture a numerical-based model is generated, that needs to be tested. The next step is called discretization dividing the structure into simple finite elements connected at a single nodal point. The points are then assigned a Poisson's ratio or Young's modulus to measure the stresses and strains on the selected numerical model of teeth, bone, implants, etc.[6]

The outcomes of FEA is explained in a systematic review on dental implants[7] which states that the model generated and tested by FEM gives an idea of the bone geometry around the implant i.e., the implant-bone interface; the material, boundary, and loading situations; validation and convergence test. However, the hitch is that the model formulation based on knowledge on the mechanical behavior is important; as all the statistics and interpretation of the results rely on it otherwise the results can be flawed.

Finite element analysis and root canal treated teeth

Endodontics has helped to maintain the function and health of infected teeth. Even though the initial rate of survival of RC treated teeth is almost 90% but later on the pervasiveness of vertical root fracture, i.e., variable refrigerant flow which ranges from 11% to 20% becomes a reason for their extraction.[8] FEA is developed to learn about the dissemination of stress and resistance to fracture in endodontically treated teeth. This concept has been elucidated using von Mises stress criteria that include comprehensive, shear, and tensile stress to quantify the fracture resistance analysis.

This in vitro study[8] used an endodontically treated mandibular premolar tooth root filled with gutta-perch and core filled with composite resin and a 3-D FEA model was created. The results of the study showed that angular stress affects the root, cervical area, and the buccal cusp of the root canal treated tooth.

Finite element analysis and restorations

Investigations[9] on restorative materials and types of restorations, for example, CII Mesio-occlusal-distal cavities found that a 600 N static occlusal load simulating mastication of food had less stress distribution on indirect CAD/CAM restoration, especially with teeth having compromised remaining enamel and dentin as compared to direct restorations.

A recent study[10] on premolar model with five different Class II cavity preparations (vertical, tunnel, horizontal, direct access, etc.) restored with bulk filled flow composites or/conventional composites were evaluated using FEA for occlusal loading and shrinkage. The lowest shrinkage was found in bulk-filled flow composite indirect access (occlusal) cavities (36.12 Mpa) and the same cavity-conventional resin was 36.14 Mpa as compared to vertical slot (CL. II) with conventional resin (56.14 Mpa) and bulk filled flow resin 56.08 Mpa. Therefore, larger the cavity more polymerization shrinkage and more stress on the dentin and enamel structures.

A study[11] on mandibular molar teeth restored with PFM, Composite (Artglass), In-ceram (Zirconia–ICZ), Zirconia core with Ceramic (Lava) and Gold crown was evaluated using FEA. The crowns were loaded with two kinds of forces simulating normal axial and nonaxial masticatory forces of 225N and 600N axial bite force, respectively. The outcomes exhibited that all-ceramic crowns (ICZ and Lava) had the utmost von Mises values with chewing bite forces (123.74 Mpa) and less force dispersal to the adjacent tissues. The stress concentration is maximum on the middle one-third of the crown region for horizontal and angular masticatory forces but vertical maximum bite forces distribute stress mainly to the cervical portion of the root. This result indicates that all-ceramic crowns can be used effectively for damaged teeth.

   Finite Element Analysis in Orthodontics Top

FEA studies evaluating tooth movement[12] have studied stress distribution on the bone (apex and at the cervical area of the alveolar crest) and PDL thickness (0.24 mm and 0.15 mm) using FEM on different types of orthodontic tooth movement of central incisors, for example, tipping, extrusion, intrusion, and bodily tooth movement. The outcome elicited no change in the thickness of the PDL caused by stress but an extreme stress pattern was observed at the apical portion of the root as equated to the cervical alveolar crest, especially with extrusion, intrusion, bodily, and tipping movements. The consistent results by FEM are reliant on the precisely developed model where structurally the selection of appropriate material, geometry, and the boundary is very important.

   Orthodontic Mini-Implants Top

Among adult patients, i.e., rapid palatal expansion for transverse maxillary deficiency can be achieved effectively with mini-implants. This orthopedic skeletal expansion technique applies pressure to the basal bone. However, it is reported that loosening or loss of mini-implants is about 7%–28% due to the higher magnitude of forces applied to split the palatal suture. Palatal expansion (bone–borne) using bicortical versus monocortical mini-implant anchorage was studied using FEA used to identify these biomechanical issues.[13] Bicortical anchorage models showed greater transverse and parallel movement in the coronal plane with less peri-implant stress distribution as equated to the monocortical models. Bicortical implants had better stability, less deformation and fracture, and enhanced expansion.

FEA with its ability to study intricate structures with different materials has been established in this study[14] to illustrate the quantity of implant-bone osseointegration of the mini-implants with its adjacent structures. The study documented that orthodontic loading to the mini-implants should be done only after 15% osseointegration has taken place as by this stage the forces of the mini-screws are safely distributed to the cortical plate.

   Bone Screws in Orthognathic Surgeries Top

Surgical orthodontics is used to treat prognathism or retrognathic mandible with “two holes or four holes monocortical plate rigid fixation method and bilateral sagittal splitting osteotomy.” An in vitro study[15] was conducted on a saw-bone mandibular model and incorporated the principles of FEA by creating a 3-D image of the model with CT. The outcome of the research directed that the two-hole cortical plate was superior to the four-hole one as it transferred less von Mises pressure to the cortical bone (two-hole cortical 75.98 Mpa vs. four-hole 987.68 Mpa) and the plate/screw area (457.19 Mpa vs. 1781 Mp). In the two-hole cortical plate, the stress was focused on the distal area and the four-hole one to the central segment. Perfunctory failure of the four-hole was pronounced near the proximal portion of the osteotomy site (31.198N) and at the condyle area (32.198 N) but was not elicited by the two-hole cortical plate.

   Finite Element Analysis and Bone Resorption Top

An uncharacteristic side effect of orthodontics is the resorption of the root instigated by odontoclasts on applying heavy forces to the teeth due to increased hydrostatic force generation in the PDL.[16] A study[17] demonstrated that the heightened stress levels in the alveolar bone changed with increased destruction of the alveolar bone levels. For example, during tipping movement it has been observed that with increasing alveolar bone loss maximum stresses are concentrated at the cervical area as compared to normal bone height and intrusion movement the stress levels are concentrated at the apical and sub-apical areas; an 8 mm bone loss with vertically directed force results in four times more stress at the cervical area and 1.6 times at the apical and sub-apical areas.

   Finite Element Analysis and Cleft Lip and Palate Top

NAM or Naso-alveolar molding is a presurgical treatment that can be started at 2 weeks after birth in cleft lip and palate patients (CLP).[18] FEA models of CLP patients have established that at birth the stress patterns were highest in the regions of the naso-orbital ipsilateral area, anterior fossa, base of the skull, and frontal sinus at more than thirty-five thousand von Mises MPa and reduce in a month or 3½ months to <15,000.

NAM helps to lessen the cleft lip width and alveolar gap; stretches the columella in bilateral CLP cases and decreases complications with scarring and improves nasal symmetry after surgery.

The downside of using FEA in newborns is that the bones are very thin and the consequences of the stress distributions in the FEA scans in this research are a bit overrated than the actual numbers.[18]

   Finite Element Analysis and Arch Expansion in Orthodontics Top

In orthodontics, rapid maxillary arch expansion is a common procedure to correct bilateral or unilateral cross-bites cases along the mid-palatal suture this also causes distraction at the base of the skull and other facial sutures.[19],[20],[21],[22] An in vitro study[19] where FEA models were created to study the projected degree of expansion and its anticipated forces by the rapid palatal expander using a strain gauge. For example, a total activation of two mm results in a 100 N force in the direction of expansion and almost 85% of the force directly acts on the palate and the teeth.[19]

A different research study[23] comparing mini-screws assisted, conventional and bone-borne rapid palatal expanders elucidated that the conventional expanders were the maximum stress generators especially in the regions of anchor teeth, suture segment, and frontal process of the maxilla; the bone-borne caused excessive pressure near the mini screw assisted expansion that was a favorable option with fewer chances of tipping of the anchoring teeth and on the buccal portion of the anchoring teeth.

   Finite Element Analysis and Mandibular Advancement Devices Top

Mandibular advancement device (MAD) is used for obstructive sleep apnoea i.e., OSA patients as they help to reposition the mandible in the forward direction to assist in breathing and to keep the airway patent.[24] But such devices are not free of side effects as they cause discomfort, pain, and even deviations in the occlusion. Therefore in appraisal to a conventional single piece, U/L comprising MAD a newly developed MAD made of separate U/L trays of a softer biocompatible material with an upper distal downward protrusive extension which functions as lock once the mandible moves forward is more comfortable and compliance-oriented. FEA examination revealed that most of the stress in this design was distributed to the gingiva of the upper teeth. As FE analysis helps to predict stress distribution when subjected to external forces it is more cost-effective than animal experiments to test dental appliances like orthodontic braces. The simulation program and the algorithms generated by FE analysis assist in coming up with new innovative MAD devices for skeletal deformities patients with constricted maxilla or mandible that is retrognathic.[25],[26],[27],[28],[29],[30]

   Finite Element Analysis and Aligners Top

Orthodontics has moved into a new realm of clear aligner technology from removable and fixed orthodontics as it uses polymer removable appliances that are more comfortable and this technology is equated to fixed appliances, as de-bonding the brackets can cause damage to the enamel. But the hitch is that it can provide much less orthodontic load and allows movement in the range of 0.25–0.33 mm only in the horizontal direction resulting in several changes of the appliances. It is mostly recommended for nonextraction cases and minor corrections in the alignment of upper and lower teeth. This technology makes use of the thickness of the aligner and its attachment to the tooth.[31],[32],[33],[34],[35],[36]

FEA is innovative in studying the effect of aligning technology that focuses on the PDL and the alveolar bone while tooth movement takes place.[31] The stresses on the PDL using aligner technology surges with increasing thickness of the aligner for example in a lingually inclined and axially rotated tooth, 0.75 mm thickness as contrasted to 0.5 mm thickness produces six percent more pressure in the PDL and changes the axis of rotation.

   Summary Top

  • FEA quantifies stress and strain in a solid model effectively with valid and reliable results
  • It can simulate biologic dynamic and static models in pre-, post-, and intraoperative stages with accurate results
  • For FEA to be successful-the geometry, type of material, boundaries have to be known precisely or it can give a flawed interpretation of the results
  • The results are a subjective interpretation of the operator due to the multifaceted anatomy of the biological structures
  • Lately, with the advent of more sophisticated software, it is possible to quantify stress and strain in a range of tooth movements and carry out nonlinear simulations of structures such as PDL (PDL of the tooth); ceramics; metal restorations; composites, and other soft tissues.[43]

   Conclusion Top

FEA is a resourceful contrivance that is not prescription-oriented but numerically adapted to give specific solutions to a host of problems. As the interpretations are subjective due to its experimental element, care has to be implemented while solving clinical issues with this method.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

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