IP Indian Journal of Orthodontics and Dentofacial Research 2024;10(1):11–15

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IP Indian Journal of Orthodontics and Dentofacial Research

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Review Article
Finite element analysis-A biomechanical tool in orthodontics

Deepak Singh 1, Kaleem Fatima1 , Anshika Gandhi 1 *, Tulika Tripathi1 , Priyank Rai1
1 Dept. of Orthodontics, Maulana Azad Institute of Dental Sciences, New Delhi, India

ARTICLE INFO ABSTRACT

Article history: In orthodontic research, the finite element method (FEM) has been widely used as an engineering resource
Received 11-02-2024 for calculating the stress and deformation of complex structures. Applying the FEM can predict the graphic
Accepted 22-03-2024 representation of these tissue responses through the observation of areas of stress created by applied
Available online 04-04-2024 orthodontic mechanics. This method has the advantage of being non-invasive, accurate, and providing
quantitative and detailed data on the physiological reactions possible to occur in tissues. The purpose of
this article is to review and discuss the steps involved in applying the concept of finite elements and how
Keywords: they can be used in orthodontics. The stress distribution at the interface between the alveolar bone and
Digital Orthodontics the periodontal ligament, as well as the shifting trend in different tooth movement types while employing
computer software
different kinds of orthodontic devices, may both be assessed using FEM. For this reason, expertise with
orthodontic force
certain software is required. Despite the drawbacks of other experimental techniques, FEM is a crucial
bone remodelling technique for addressing inquiries regarding tooth movement.

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1. Introduction as they work on each patient. This is linked to rational

thinking, a fundamental understanding of biomechanics, as
One of the fundamental principles of orthodontics is the well as common sense. 3
systematic imposition of bone remodelling, which entails
applying particular force systems on the teeth in order
to cause progressive and permanent bone deformations. Finite element analysis (FEA) was initially introduced by
The process of bone remodelling causes the teeth to Turner et al. in 1956. Since then, it has been applied to a
move into new positions, and the alveolar bone and the variety of projects, including the construction of bridges,
periodontal ligament play a significant role in this process. dams, airplanes as well as in biomedical field. For a
The mechanical, biochemical, and physiological responses particular load, the distribution of stress inside the body
to the orthodontic forces are inextricably linked. 1,2 is determined by using computer software designed for
Orthodontic treatment can be carried out with an complex calculations. In addition, it illustrates the body’s
evidence-based approach, clinical experience, knowledge displacement both before and after the load is applied. 4,5
and experience gained from a postgraduate curriculum,
or even through specialised training and workshops. In
dentistry, orthodontics is a fascinating and challenging field, This review is intended to greatly simplify the idea of
an orthodontist’s work can be compared to solving a puzzle FEM and link it with orthodontics in order to provide
readers with an original take on the subject and to reinforce
* Corresponding author. existing knowledge for those who are already familiar with
E-mail address: deep14singh11@gmail.com (A. Gandhi). it.

https://doi.org/10.18231/j.ijodr.2024.003
2581-9356/© 2024 Author(s), Published by Innovative Publication. 11
 Singh et al. / IP Indian Journal of Orthodontics and Dentofacial Research 2024;10(1):11–15

Table 1: List of the materials with their physical properties

Materials Youngs modulus Poisson’s
(MPa) ratio
Tooth 20000 0.30
Periodontal 0.059 0.49
ligament
Alveolar bone 20000 0.30
Bracket 200000 0.33
Arch wire 200000 0.33
(Stainless steel)
Cancellous bone 1500 0.30
Cortical bone 15000 0.30
NiTi coil spring 83000 0.33
Buccal mucosa 8.33 0.30
Gingiva 37.63 0.30
Figure 3: Meshing of mandibular model showing nodes and
elements

1.1. Role of FEM in Orthodontics

In orthodontics, there are various analytical instruments
readily available. When contemplating a diagnosis and
treatment strategy, analysis is essential. Every approach has
advantages and disadvantages, which explains why more
advanced techniques for analysis are being devised. The
need for an enhanced analytical tool has gotten to the point
where traditional tools are no longer adequate. 6
A three-dimensional subject is depicted in two
dimensions in radiography. The overlapping of structures
makes it difficult for the clinician to understand. Although
there are other techniques, such as digital radiography,
Positron Emission Tomography, and Computer tomography
scanning, issues associated with radiation risk and three-
dimensional imaging remain to be addressed. Coned Beam
Computed Tomography provides a three-dimensional
Figure 1: Workflow to obtain results of finite element analysis image, but it also has disadvantages such as motion artifacts
and radiation danger. 7 In contrast to these, FEM is unique
in that it is radiation-free, non-invasive, supports three-
dimensional analysis, and can be used for both static and
dynamic biomechanical research. The first reconstruction
model on the computer can be created using any of the
traditional techniques; this model is then analysed and
simulated by FE using computer software. 8

2. Armamentarium for FEM analysis 9

A) CT (Computed Tomography) SCAN of required area and
its DICOM Files
B) Software available in market
• MIMICS, 3D Slicer, Invivo5, OsiriX MD etc.
• FUSION 360, Free CAD, Blender, Solve Space etc.
• Hyper Mesh CAE, Abaqus, MATLAB, Solid Edge and
ANSYS etc.
Figure 2: Geometric model of mandible
C) Workstation

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• i5 quad core or higher version processor 6.1. Assigning of Material Properties

• 16GB RAM 2.5 GHz or higher configuration
Poisson’s coefficient and the young modulus of elasticity
• 4GB or more Graphics
are set for the model. Young’s modulus depicts the
• 2TB or more HDD or SDD
inclination of the linear section of the stress-deformation
• 15" or higher dimension screen monitor
diagram, whereas Poisson’s coefficient relates to the
absolute value of the relationship between transverse and
3. Steps involved in the Finite Element Model longitudinal deformations in an axial traction axis. These
Preparation physical properties have to be introduced for teeth, gingiva,
Following the acquisition of the necessary DICOM (Digital cortical bone, cancellous bone, and periodontal ligament
Imaging and Communications in Medicine) files, the etc. according to the literature. 10 (Table 1)
following procedures must be taken in order to receive the
appropriate results (Flowchart Figure 1) 7. Simulations and Result Interpretation
Finding the areas of stress and, consequently, the places
4. Construction of the Geometric Model where tooth movement takes place is made possible by the
In order to create geometrically superior and correct models, FEM’s results, which allow for examination of the stress
it is fascinating to employ a resource with anatomical distribution caused by forces between the bone and the
records and adjustments in CAD software to carry out periodontal ligament. It also makes it possible for us to draw
this experimental approach. In order to achieve that, a conclusions regarding regions where root resorption is more
virtual model must be created using image processing likely. In order to show the direction of tooth displacement
and digital reconstruction tools like 3D Slicer and Mimics following force application, colours and arrows are used to
etc. For better resolution, computed tomography should be reveal these results.
produced using cross-sections that are at least 0.25 mm
apart. The segments will be captured in DICOM format and 8. Review of Literature and Discussion
then transferred into software for digital reconstruction and
To truly grasp the essence of this review, the reader must
image processing.
initially realise that the FEM is a theoretical concept
and that it cannot withstand arguments based solely on
5. Conversion of the Geometric Models to a Finite scientific evidence without the highest possible standard of
Element Model clinical trials. In addition to dealing with material qualities
We also discretized the model, or converted it from a and properties, FEM also takes geometrical considerations
solid state into a mesh of nodes and elements, using the into account. The entire system, including the body’s
previously stated software to facilitate analysis using dimensions, produced stress, and initial force, differs
FEM. The elements are space coordinates represented substantially from its final state. The conclusion that one
by tetrahedrons and hexahedrons, which are the most cannot compute or forecast the tooth’s final position from
common formats in which they can appear. Each element’s its beginning one without the use of mathematical formulas
extremities have points, or nodes, connecting them and precise numerical values seems reasonable.
to construct an ordered mesh between the elements. With experimental animal models, numerous
Information is transmitted between elements through investigations on orthodontic force-induced tooth
their bonds. The virtual model is exported from movement were carried out. These investigations offer
Solidworks software to Ansys Workbench V11 or other insights into the effects of using orthodontic stresses
similar programme for finite elements simulation after it on human tissues. Animal research ethics committees
has been completely rebuilt and converted into this mesh of frequently object to this kind of investigation since it uses
finite elements. (Figures 2 and 3) live animals in a lab setting. It is possible to predict the tissue
reactions to applied orthodontic mechanics using FEM.
Photoelastic models are an alternative set of experimental
6. Boundary Conditions and Sumptions
models that are used to study the biomechanics of tooth
Suppose an element is constructed on the computer and movement; however, they have the drawback of just
a force is applied to it, it will act like a free-floating studying the model’s outside, leaving internal structures
rigid body and will undergo a translatory or rotatory like the periodontal ligament unexplored. 11–16
motion or a combination of the two without experiencing In their research, Jafari et al. employed transverse
deformation. To study its deformation, some degrees of orthopaedic forces to analyse the stress distribution patterns
freedom (movement of the node in each direction x, y, and within the craniofacial complex during rapid maxillary
z) for some of the nodes must be restricted. Such constraints expansion using a 3D FE model of a dry human skull. This
are termed boundary conditions. study indicates that the expansion stresses are dispersed to

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the sphenoid and zygomatic bones as well as other related degree twist angle, and clinicians should stay within these
structures, not just the intermaxillary suture. 16 torque limitations to prevent plastic deformation that could
Using a FEM model, Chaturvedi et al. assessed the result in incorrect tooth positioning. 24
impact of orthodontic retraction force on thick and thin A Finite Element (FE) model for clear thermoplastic
gingival biotypes of anterior teeth with grade I and teeth aligners was successfully designed and validated by
II gingival recession. They discovered that orthodontic Ye et al. As a result, we can accurately capitalise on
treatment significantly altered the gingival tissue and helped the model to anticipate the stresses and moments that the
to correct periodontal defects; however, bone density was aligners will apply to teeth, enhancing our knowledge of the
found to be a significant factor in improving gingival biomechanics of these devices and the movement of teeth
recession. 17,18 they cause. 25
Because PDL is crucial for tooth movement, there is
a clear correlation between PDL stress and orthodontic 9. Limitations of Finite Element Analysis
tooth movement. Using the three-dimensional finite element
method, Tanne K et al. examined the stress levels caused by 1. Like every theoretical model of a biological system,
orthodontic forces in the periodontal tissue. They discovered this one has certain limitations such as mistakes
that, depending on the tooth’s centre of rotation, the pattern made in the modelling, material property assignment,
and amount of stresses in the periodontium caused by a boundary condition application, or even the application
given force magnitude varied significantly. 19 of inaccurate forces to an incorrect formulation may
Aesthetics is a primary consideration in orthognathic lead to improper results.
surgery because individuals are extremely concerned about 2. This is a complex analysis that depends on computers
their post-operative facial morphology. Virtual orthognathic and programmes, much care must be given both during
surgery and the development of facial 3D simulation models the modelling phase and in the steps that precede the
have opened up new avenues of communication between the final run of the results to ensure that the right input data
surgeon and the patient. In their work, Obaidellah et al. use is sent in for the desired results.
FEM on three-dimensional face models to present a surgical 3. It is also difficult, if not impossible, to recreate
planning, simulation, and prediction of facial soft tissue biological tissue exactly like it exists in mechanical
appearance with relation to mandibular advancement using models.
the osteotomy planning system. Using a 3D FE model of 4. The expense of the FEM study is another main
the soft tissues of the face, Chabanas et al. predicted the soft constraint. The fact that the FEM is mostly utilised for
tissue deformations in the face that arise from repositioning research and does not now have an appropriate cost in
bones during maxillofacial surgery. 20,21 several countries should be emphasised.
In order to assess continuous and simultaneous
alterations in orthodontic mini-implant diameter and length 10. Conclusion
and to determine their ideal ranges in the maxillary posterior The Finite Element Method (FEM) is a valuable tool in
region, Jiang et al. performed a finite element analysis. orthodontic research because it highlights a number of
They discovered that the best biomechanical option was important points, including the following: the direction of
a diameter larger than 1.5 mm combined with the longest tooth displacement; the optimal location of orthodontic
length within the safety limit. 22 appliances during a particular mechanics; the areas most
sing a three-dimensional finite element computer model, likely to exhibit root resorption; and the distribution
Shyagali et al. evaluated the variations in stresses produced of stresses on the archwires. Because FEM is precise,
in the bracket-cement-tooth system by means of a peel noninvasive, controls the research variables, and yields
load in single and double-mesh bracket bases. The findings quantitative data about the internal structures of the
indicate that altering the bracket’s shape can enhance nasomaxillary and mandibular complex, including the
bonding capabilities and lessen enamel damage as it periodontal ligament, it can overcome the shortcomings
debonds. These details could help develop new, creative of other experimental methods. The method, however,
bracket designs intended for therapeutic application. 23 uses extremely specific software, therefore it demands
In order to assess the torque-induced bracket slot understanding of computer engineering.
deformation in the widely used 0.018-inch (") and
0.022" conventional Stainless Steel (SS) brackets with 11. Source of Funding
clinically relevant archwires during various angles of twist,
Harikrishnan et al. conducted an in-silico study. They found None.
that the slot deformation in both the 0.018" and 0.022"
brackets increased with the angle of twist. Therefore, it can 12. Conflict of Interest
be said that bracket slots only bend elastically up to a 30- None.

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