Finite Element Analysis (FEA) was developed in the 1960s to solve aerospace structural problems. It has since been introduced to orthodontics and other dental fields. FEA involves dividing a complex problem into smaller, simpler elements and using shape functions to interpolate variables. Each element is assigned material properties. The computer program then calculates element stiffness, solves matrix equations, and outputs displacement, stress, and other results. FEA allows modeling of complex biological structures like teeth and bone. It has provided insights into stress distributions and tooth movement from various orthodontic appliances and mechanics.

1. Finite Element Analysis in
Orthodontics

2.  was developed in early 1960’s to solve the
structural problems of aerospace
 the term ‘ Finite Element’ was coined by Argyris
and Clough in1960.
 It was introduced in implant dentistry in 1976 by
Weinstein.

3.  FEM is a technique for obtaining a solution to a
complex mechanical problem by dividing the
problem domain into a collection of much
smaller and simpler domains (elements) in which
the field variables can be interpolated with the
use of shape function. These elements are
connected at specific (eg corner) locations called
nodal points
 Every element is assigned one or more
parameters (eg modulus of elasticity) that defines
its material (stiffness) behavior.

6.  The computer program calculates the stiffness
characteristics of each element and assembles
the element mesh through mutual forces and
displacements in each node.

7.  Components of Finite Element Method
Broadly divided into two parts:
A) Finite element modeling
B) Finite element analysis
 Finite element modeling
Geometric modeling is of three types:
1.Wire frame modeling
2.Surface modeling
3.Solid modeling
Once geometry is created it is transferred into a finite element model by
the processor. Mesh generation is used to describe this procedure

8.  Mesh generation
It forms the back bone of the finite element analysis. It
refers to the generation of nodal coordinates and
elements. It also includes the automatic numbering of
nodes and elements based on the minimal amount of
user supplied data.
 The ‘Element’ forms the basic constituent of the
finite element modeling.

9. The Element type defines the following:
Element Dimensionality
Element Shape
Element Order
Element Degree of Freedom
Physical Properties

10. Finite Element Analysis
There are 3 main components of Finite Element Analysis
package:
•Preprocessor
Generates nodes and elements
Generates element connectivity
Applies material properties
Applies boundary conditions
Applies load
•Processor
Generates element matrices
Computes nodal values and derivatives
Solves governing matrix equations
Compute parameters for memory / file management.
•Post processor
Analysis of results

11. Plots displacement contours
Plots stress contours
Plot contours of failure index
Plots deformed mesh over undeformed mesh
 Interpreting the Results and Analysis Display

12.  The output from the Finite Element Analysis is primarily in the
numerical form. It usually consists of nodal values of the field
variables and its derivatives. For example in solid mechanical
problems, the output is nodal displacement and element stresses.
In heat transfer problems, the output is nodal temperatures and
element heat fluxes. Graphic outputs and displays are usually
more informative. The curves and contours of the field variable
can be plotted and displayed. Also deformed shapes can be
displayed and superimposed on unreformed shapes. The output
is primarily in the form of color-coded maps. The quantitative
analysis is determined by interpreting these maps.
 The result involves calculation of stresses by Von Misses criteria
for each node.

13.  Physical Model- Constitutive Properties of Tissues
The tissues to be considered in the model are enamel, dentin, periodontal
ligament, pulp and bone. This last tissue can be classified in two categories:
cortical and cancellous. According to Anusavice (1998) most material
properties of human teeth have been measured, but their values vary from
author to author.
Enamel and Dentin
 Enamel is formed by parallel prisms of hydroxyapatite, oriented with its axis
normal to the surface of dentin. As a consequence, it exhibits an orthotropic
fragile mechanical behavior.

Dentin microstructure consists of tubules connected by organic material,
provoking anisotropy, as the organic material connecting the fibers is less
resistant than the hydroxyapatite. Both tissues exhibit fragile behavior under
tensile stress, especially enamel.

14.  Craig and Peyton, presented new values for dentin using a
compressive test. They found the limit of proportionality,
ultimate strength and Young’s modulus to be 167 MPa, 297 MPa
and 16 GPa. In a later work, Craig and co-workers verified, using
similar compression tests of enamel specimens, that no relevant
variation occurred when testing enamel samples from different
tooth locations, and obtained average values of 353MPa,
384MPa, 84.1 GPa for the limit of proportionality, ultimate
strength and Young’s modulus of the enamel.
 In 1959 Tyldesley reported 66.2 MPa (limit of proportionality)
and 267 MPa (ultimate strength) for the dentin and E to be 131
GPa for enamel, and 12.3 GPa for dentin.

15. Periodontal ligament and pulp
 Rees and Jacobsen(1997) found values of E as 50 MPa,
using a finite element simulation and adjusting the
ligament modulus to get measured values of
displacements in two experimental systems. They found
in the literature a large dispersion in the values of
modulus of elasticity used in finite element models,
ranging from 0.07 to 1750 MPa. Ko et al(1992) and Ho et
al (1994) used a value of E=68.9MPa. and 0.45 for the
Poisson ratio ν.
 For pulp, Rubin and Capilouto (1983) used in their work
of an elasticity modulus for the pulp of 2.07 MPa and
Poisson’s ratio of 0.45.

16.  Due to its very small stiffness, the pulp can be
ignored when examining the mechanical
behavior of dental structures. In some works,
the periodontal ligament is not included in the
models, and the geometry of the pulp cavity is
not considered, with the section of the tooth
solid. Authors such as Darendeliler et al (1992)
Thresher and Saito(1973) point to the
importance of including the pulp cavity in
computational models for the tooth.

17.  Bone
In the region of interest, the bone is heterogeneous and
anisotropic, and is constituted of two different parts: the
cortical layer and the spongeous internal basis. The
former is a compact and stiff tissue with modulus of
elasticity of 13.7 GPa, and the Poisson’s ratio of 0.3.
The latter, named cancellous bone, is much more
flexible, with a Young modulus of only 1.37 GPa, and
0.3 for Poisson coefficient.. Many authors choose not to
consider the bone in their models, applying fixed
boundary conditions directly to the upper surface of the
dentin.

18. Occlusion
 the subject occlusion envelopes all factors that cause,
affect, influence or result from the mandibular
position, its function, parafunction or disfunction,
and not only the dental contact relationships
 Due to occlusal contact nature, horizontal and axial loads are
produced during mastication. This load combination leads to
tooth movement in all directions
 Contact angle is affected by occlusal morphology. In
humans, bite load was measured to be 500 N in the molar
region and 100 to 200 N in the incisor region. Maximum
axial loads are of 70 to 150 N. Occlusal load during
bruxism can reach values up to 1000 N according to Peters
et al.

19. Modeling
 Stress analysis is performed using the Finite Element
Method, which is particularly suitable to biological
structures since it allows easier modeling of
geometrically complex and multi-material domains. The
commercial code ANSYS is used as the FEM analysis
platform on this work.
Properties E v
Enamel 4.1x104 0.30
Dentin 1.86x 104 0.30
PDL 68.9 0.45
Cortical bone 1.37x 104 0.30
Cancellous bone 1.37x104 0.30
TABLE Tooth tissue material mechanical properties

20. Discretization
 Figure shows model
element discretization
used for the tooth
model, resulting in a total
of 4,996 elements of 8
nodes (15,117 nodes)
and a system with 30,234
degrees of freedom.
 Numerical Analysis

21. Application of FEM in orthodontics
 Stress related responses of molar to TPA
Bobak et al (1997)
FEM analysis was used to analyze the effects of the transpalatal arch on
periodontal stresses and displacements when subjected to
orthodontic forces. The forces simulated were analogous to those
used clinically when a transpalatal arch is used to "increase
anchorage" (e.g., mesially directed forces produced by an elastomeric
chain during canine retraction). To accomplish this analysis, an
appropriate finite element model first was constructed. Resultant
stresses and displacements in a model without a transpalatal arch
were compared qualitatively with stresses produced in a model with a
transpalatal arch to address the hypothesis that the TPA can indeed
modify periodontal stresses.

24. Results showed that
1. Fringe plots of intermediate principal stresses possessing a high
level of sensitivity failed to resolve any effects due to the
presence of a transpalatal arch on root surface, periodontal
ligament, or alveolar bone stress patterns;
2. Scatter graphs of stresses calculated at element centroids
distinguished differences in stress values due to the presence of a
transpalatal arch. When normalized, however, the values differed
by less than 1%; and
3. The results of analyses with altered physical bone properties that
allowed simulation of increased molar displacements suggest
that the transpalatal arch is effective in controlling molar
rotations.
The results of the finite element analysis therefore suggest that the
presence of a TPA induces only minor changes in the dental and
periodontal stress distributions.

25. Stresses induced in the periodontal ligament
 Mc Guiness et al (1992) examined initial stresses
within the periodontal ligament of a tooth when
subjected to an orthodontic force when using an
edgewise appliance. To achieve this, a finite element
model of a human maxillary canine tooth was
constructed and subjected to load.
 The Finite element analysis revealed that stress in
the periodontal ligament due to most orthodontic
forces, including those produced by edgewise
appliances, is largely concentrated at the cervical
margin and at the apex.

26. Stress in PDL of molar due to simulated bone loss

27. Minimum principal stress in
PDL of maxillary first molar
without bone loss under
mesializing
force (300 g)

28. Minimum principal stress in PDL of maxillary first molar with 3.5-mm
bone loss under mesializing force (300 g)

29. Finite Element based Cephalometric Analysis
 Sameshima, Melnick (1994)
 The finite element method has proven to be a useful tool for
morphometric analysis in craniofacial biology. However, few
attempts have been made to adapt this method for routine use
by clinicians. The CEFEA program incorporates the advanced
features of the finite element method but bypasses the
detailed understanding of the engineering and mathematics
previously required to interpret results. The program uses the
color graphics display of common personal computers to
show size change, shape change, and angle of maximum
change. These are pictured as colored triangles of clinically
relevant regions between pre- and mid- or posttreatment
lateral headfilms. The program is designed to have features of
interest in both clinical practice and research.

30.  The user first selects SIZE to visualize where major size
change occurred and to determine if the change was nearly
the same for groups of related elements, e.g., body of the
mandible. Next, the user assesses SHAPE to determine the
pattern of craniofacial development (shape change) in the
same way. Finally, the user accesses ANGLE to observe
common direction with respect to known gradients, e.g.,
growth parallel to the body of the mandible. A control panel
allows the user to switch back and forth among the three
screens, or to select a different case at will to make a swift
and meaningful assessment of the effects of treatment,
either during treatment or at its completion

33. Mandibular changes in Class II Div 1 patients
treated with twin block appliance
) Singh, Clark (2001)
 Comparing male pubertal configurations, finite element
scaling analysis revealed marked positive allometry(=27%) in
the condylar neck and negative allometry (=16%) at the apex
of the coronoid process. For the female pubertal
configurations, local increases in size were noticeable at the
condylar neck (=15%), with negative allometry (=9%) in the
coronoid process. For shape change, all configurations were
highly isotropic over the entire mandibular nodal mesh.
Therefore, in growing patients treated for Class II Division
1malocclusions with Twin-block appliances, condylar growth,
coronoid process remodeling, and osteogenesin corpus and
dentoalveolar regions may reflect the correction of the
underlying skeletal dysmorphology.

34. A)Pubertal male configuration. Note white/purple area of condylar neck
region, indicating increase in size of up to ≈28%. Green coronoid process
shows decrease in size of ≈16%. Reddish coloration of angle, ramus,
corpus, and symphyseal regions indicates ≈1%-5% increase in size in those
regions. B) Pubertal female configuration. Note white/purple coloration in
condylar neck region, indicating ≈15% increase in local size. Green
coloration of coronoid process, angle, and symphyseal regions indicates
decrease in local size of ≈9%. Red regions of ramus show little change in
size, whereas purple coloration of corpus indicates ≈2% increase in size.

35. Bond strength offered by various bracket base
design
 Knox et al (2001) determined the effect of altering the
geometry of the bracket base mesh on the quality of
orthodontic attachment employing a three-
dimensional finite element computer model

37.  They showed that in the double-mesh design,
the relatively coarse outer mesh is shielded from
the applied load by the increased stiffness of the
deeper mesh layer. In addition, there is more of
a gradient in stiffness from the bracket base to
the fine mesh and ultimately the coarse mesh
resulting in a less abrupt change in physical
properties, and this reduces stress concentration
at the adhesive interface.

38. FEM Analysis of distal en masse movement of
maxillary dentition with multiloop edgewise
archwire
Chang et al(2004)
 The authors compared the effects of multiloop
edgewise archwire on distal en masse movement
with a continuous plain ideal archwire. The
stress a distribution and displacement of
maxillary dentition was analysed when Class II
intermaxillary elastics(300 gm/ side) and 5
degree tip back bends were applied to the ideal
archwire and multiloop edgewise archwire

40.  The results showed that compared with ideal archwire
the multiloop edgewise a archwire showed less
discrepancy in the amount of tooth movement and
individual tooth movements were more uniform and
balanced. There was minimal vertical displacement or
rotation of teeth with multiloop edgewise archwire.

41. Stress differences between sliding and
sectional mechanics
 Vasquez et al(2001
 A 3D mathematical model was constructed
which simulated an endosseous implant upper
canine with its PDL and cortical and cancellous
bone. Levels of initial stress were measured 2
types of canine retraction mechanics

43.  The results showed that the area with the
highest stress was the cervical margin of the
osseointegrated implant and its cortical bone but
they were of such low magnitude that were
unable to produce any permanent failure of the
implant. Stress distribution was similar in the
PDL and in the cortical bone around the canine,
with a larger magnitude and more irregular stress
distribution in the cortical bone. The zero stress
area is associated with the centre of rotation of
tooth.

44. Stress distribution and displacement of various
craniofacial structures following application of
transverse orthopedic forces
 Jafari, Sadashiv Shetty, Kumar M(2003)
 The study was to evaluate the pattern of stress
accumulation, dissipation, and displacement of
various craniofacial structures after RME, using a
three-dimensional FEM study.

46.  The results of the study using the three-
dimensional FEM of a human skull indicted that
the transverse orthopedic forces not only
produced an expansive force at the
intermaxillary suture but also high forces on
various structures on the craniofacial complex,
particularly the sphenoid and zygomatic bones.
The confining effect of the pterygoid plates of
the sphenoid minimizes dramatically the ability
of the palatine bones to separate at the
midsagittal plane.

47.  Further posteriorly, the pterygoid plates can
bend only to a limited extent because pressure is
applied to them, and their resistance to bending
increases significantly in the parts closer to the
cranial base where the plates are much more
rigid.
 Therefore, the clinician should realize that with
activation of the RME appliance he/she is
producing not only an expansion force at the
intermaxillary suture but also forces on other
structures within the craniofacial complex that
may or may not be beneficial for the patient.

48. Optimization of unilateral overjet
management by FEM
 Geramy (2002)
 The main goal of this research was to introduce,
evaluate, and mathematically optimize the
treatment procedure of unilateral overjet cases.
Patients with Class II subdivision malocclusions
usually reach a point with canines in a Class I
position, and a unilateral overjet remains to be
treated at the next stage of treatment.

49.  This study tried to prepare an archwire design
that combines the midline-shift correction and
the unilateral overjet reduction simultaneously.
The analyses of displacements were carried out
by the finite element method. The upper dental
arch was designed three-dimensionally. Three
archwire designs that were thought to be useful
in these cases were modeled and engaged the
dental-arch model separately

50.  The use of an archwire containing a closed vertical
loop with a helix distal to the lateral incisor on the
affected (excess overjet) side and an open vertical loop
without a helix distal to the lateral incisor on the
normal side (normal overjet) while lacing the four
incisors can be suggested as an optimum procedure to
treat a unilateral overjet that is combined with a midline
shift. The archwire cross-section depends on the initial
position of the incisors. This mechanotherapy can be
prescribed for both dental arches

52. Transfer of occlusal forces through maxillary
molars
 Cattaneo, Dallastra, Melsen B (2003)
 The morphology of the skeleton is known to
reflect functional demand. A change in the
intramaxillary position of molars can be expected
to influence the transfer of occlusal forces to the
facial skeleton. A finite element analysis was used
to simulate the displacement of a molar in relation
to the well-defined morphology of the maxilla.

53.  Three 3-dimensional unilateral models of a
maxilla from a skull with skeletal Class I and
neutral molar relationships were produced based
on CT-scan data. The maxillary first molar was
localized so that the contour of the mesial root
continued into the infrazygomatic crest.

55.  When the molar was loaded with occlusal forces,
the stresses were transferred predominantly
through the infrazygomatic crest. This changed
when mesial and distal displacements of the
molars were simulated. In the model with mesial
molar displacement, a larger part of the bite
forces were transferred through the anterior part
of the maxilla, resulting in the buccal bone
being loaded in compression.

56. Fig 3. Lateral view of deformed plots (actual deformations are magnified
by factor of 60) of 3 maxilla models (mesial, left; neutral, middle; distal, right)
with distribution of superior-inferior displacements (positive values denote
superior movement). Units given in millimeters.

57.  In the model with distal molar displacement, the
posterior part of the maxilla was deformed
through compression; this resulted in higher
compensatory tensile stresses in the anterior part
of the maxilla and at the zygomatic arch. This
distribution of the occlusal forces might
contribute to the posterior rotation often
described as the orthopedic effect of extraoral
traction.

58. Comparative evaluation of different
compensating curves in labial and lingual
techniques (Sung et al 2003)
 In this study, human mandibular left teeth were aligned, and a
3-dimensional finite element model was made (consisting of
19382 nodes and 12150 elements). To compare 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 relative direction and the amount of tooth displacement
of the finite element model were compared on a schematic
displacement graph (magnified 10,000 times), and the
compressive stress distributed on the root surface was
observed.

59.  The pattern of tooth movement (with or
without a compensating curve) was different
between the labial and the 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
antitip and antirotation action of compensating
curve on the canine retraction was greater in the
labial archwire than in the lingual archwire.

61. Anchorage effects of various shape palatal
osseointegrated implants
 Chen et al (2005)
 Anchorage effects of three types of cylinder
osseointegrated implants (simple implant, step
implant, screw implant) were investigated. Three
finite element models were constructed. Each
consisted of two maxillary second premolars,
their associated periodontal ligament (PDL) and
alveolar bones, palatal bone, palatal implant, and
a transpalatal arch. Another model without an
implant was used for comparison.

63.  The results showed that the palatal implant could
significantly reduce von Mises stress in the PDL
(maximum von Mises stress was reduced 24.3–27.7%).
The von Mises stress magnitude in the PDL was almost
same in the three models with implants. The stress in
the implant surrounding bone was very low.
 These results suggested that the implant is a useful tool
for increasing anchorage. Adding a step is useful to
lower the stress in the implant and surrounding bone,
but adding a screw to a cylinder implant had little
advantage in increasing the anchorage effect.

64. References
 Tanne et al. Three dimensional FEM analysis for stress in the
periodontal tissue by orthodontics forces AJODO 1987; 92; 499
 Cobo et al. Initial stress induced in periodontal tissuewith diverge
degree of bone loss by an orthodontic force: 3D FEM analysis
AJODO 1993; 104; 448
 McGuiness NJP, Wilson A, Jones ML, Middleton J, et al. Stress
induced by edgewise appliances in the periodontal ligament—a finite
element study. Angle Orthod. 1991;62:15–21.
 Vasquez et al.Initial Stress Differences Between Sliding and Sectional
Mechanics with an Endosseous Implant as Anchorage: A 3-
Dimensional Finite Element Analysis(Angle Orthod 2001;71:247–256.)
 Geramy A. Initial stress produced in the periodontal membrane by
orthodontic loads in the presence of varying loss of alveolar bone: a
three-dimensional finite element analysis. Eur J Orthod.
2002;24(1):21–33.

65.  Jeon et al Analysis of stress in the periodontium of maxillary first
molar with a 3D FEM model AJODO 1999;115;267
 Knox et alAn Evaluation of the Quality of Orthodontic
Attachment Offered by Single- and Double-Mesh Bracket Bases
Using the Finite Element Method of Stress Analysis. Angle orthod
2001 ;71; 149
 Sameshima,Melnik. Finite element based cephalometric analysis
Angle orthod 1994; 5 ; 343
 Fotos et al Orthodontic forces generated by simulated archwire
applince evaluated by FEM Angle Orthod 1990, 4 ; 277
 Transverse Jafari, Sadashiv Shetty, Kumar : Study of Stress
Distribution and Displacement of VariousCraniofacial Structures
Following Application of Orthopedic Forces—A Three-dimensional

66.  Sung et al.A comparative evaluation of different
compensating curves in the lingual and labial techniques
using 3D FEM (Am J Orthod Dentofacial Orthop
2003;123:441-50)
 Chang et al. 3D FEM Analysis in distal en masse
movement of the maxillary dentition with multiloop
edgewise archwire. Europ Journ of orthod 2004;26; 339
 Bobak et al.Stress related molar responses to TPA: an
FEM analysis AJODO 1997; 112;512
 Chen et al. Anchorge effects of various shape palatal
osseointegrated implant. Angle Orthod 2005; 75; 378