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EVALUATION OF APICAL FORCE DISTRIBUTION FOR
ORTHODONTIC TOOTH MOVEMENTS
- A FINITE ELEMENT ANALYSIS
Authors:
Dr. S. Rex
Post Graduate Student,
SRM Dental Col lege
T S 8464, Ayyanar Koil Street,
Pudukottai , Tamil Nadu - 622 001.
Phone: +91 99940 61942
Dr. Balasubramanian, M.D.S.
Dean, SRM Dental Coll ege
Dr. K. Ravi, M.D.S.
Vice Principal, SRM Dental Co llege
Dr. P. Krishna Raj, M.D.S.
Professor, SRM Dental College
Dr. S. Dilip, M.D.S.
Professor, SRM Dental Co llege
Abstract :
FEM is defined as a technique of discrediting a continuum into simple geometric shapes elements,
enforcing material properties and governing relationships on these elements giving due
consideration to loading and boundary conditions which results in a set of equation, solution
which gives the approximate behaviour of the continuum. This study was undertaken to determine
the types of orthodontic forces that cause high stress at the root apex. A 3-dimensional finite
lement model of a maxillary central incisor, its periodontal ligament (POL), and alveolar bone
was constructed on the basis of average anatomic morphology. The maxillary central incisor was
chosen for study because it is one of the teeth at greatest risk for apical root resorption . The
material properties of enamel, dentin, POL, and bone and 5 different load systems (tipping,
intrusion, extrusion, bodily movement, and rotational force) were tested. The finite element analysis
showed that purely intrusive, extrusive, and rotational forces had stresses concentrated at the
ap x of the root. The principal stress from a tipping force was located at the alveolar crest. For
bodily movement, stress was distributed throughout the POL; however, it was concentrated more
at the alveolar crest. We conclude that intrusive, extrusive, and rotational forces produce more
stress at the apex. Bodily movement and tipping forces concentrate forces at the alveolar crest,
not at the apex.
Keywords
Stress analysis, Loading, Orthodontic forces, finite element modelling.
FEM is defined as a techn iqu e of discrediting a
continuum into simple geometric shapes elements,
enforcing material propert i es and governing
relationships on these el ements giving due
consideration to loading and boundary conditions
which results in a set of equation, solution which gives
the approximate behavior of the continuum.
The finite element method is a highly precise technique
used to analyze structural stress. FEM has many
advantages ove r other methods highlighted by the
abi lity to include heterogeneity of tooth material and
irregularities of tooth contour. FEM has been used in
dentistry in a wide range of topics such as structure of
tooth, dental implants and root canals.
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Earlier studies utilized two dimensional FEM method
and later as technology improved, researchers created
three dimensional finite element model of tooth and
supporting tissue4,6,11,21 ,25
DISCUSSION
During tooth movement, changes in the periodontium
occur, depending on the magnitude, direction, and
duration of force applied. The knowledge of the
reactions of the supporting structures in orthodontic
treatment is still incomplete because histologic
techniques used today can provide only limited
information. The forces delivered by an orthodontic
appliance can be determined by direct measurement
with suitable instruments or, by mathematical
calculation. Most orthodontic appliances deliver a
relatively complicated set of forces and moments. The
problems inherent in studying the response of a tooth
subjected to a force system are much more complex
and difficult to solve than those of simple measurement
of the forces. Observations can be made on three levels
to describe a tooth's response to forces : the clinical
level, the cellular and biochemical level, and lastly the
stress-strain level . Theoretical methods using
engineering principles eliminate the need for direct
experimental measurements. Photoelastic stress
analysis is one of the methods and it can provide visua I
evidence of stress concentration areas within the model.
Photo elastic method involves construction of a model
of the structure to be investigated from a photoelastic
materi a1.1 ,4,6
The aim of the study was to determine the apical force
distribution from different types of orthodontic tooth
movement tipping, intrusion, extrusion, bodily
movement, rotation as using the finite element method.
AIMS & OBJECTIVES
To determine the apical force distribution produced
by tipping, bodily movement, intrusion, extrusion and
rotational movement using FEM.
Methodology
Modelling of the tooth:
The first step in finite element analysis is modelling.
The quality of the analysis depends on the accuracy of
the model. The maxillary central incisor was selected
to simulate an outer morphology for finite element
model. Scann i ng procedure of the tooth was completed
using computer tomography w ith a sliced thickness of
O.Smm .
The model preparation for this method is arduous, since
it is critical that the model is of uniform thickness. Stress
concentration area and magnitude of 3- dimensional
geometric shapes, which are subjected to mechanical
load, can be calculated using mathematica l methods.
This calculation method cannot apply to complex
structures, which are usually found in nature.
The image section in CT are obtained in DICOM
(Digital imaging and communication of medicine). This
obtained two dimensional data was reconstructed to
give a three dimensional model using a software called
Pro/Engineer (parametric technology corporation,
USA).Thefinal model was completed by superimposing
the prepared tooth model. Boundary conditions,
material properties and applied 10ad.After completion
of the models the assembly was then exported for
analysis using ANSYS Workbench (ANSYS, Inc, USA)
through a bidirectional understandable translator
system called IGES. Once imported the software can
do an automatic meshing and establish contacts with
defined material properties.
Finite element analysis (FEA) is a computerized
numerical method for solving complex problems by
dividing complex structures into many small
interconnected simple structures which are called finite
elements. It was first developed in 1943 by Richard
Courant, to obtain approximate solutions in vibration
systems. Finite element method analysis have been
widely used in engineering since 1960s. However in
dentistry this kind of analysis is rather recent. Although
the first article published by Farah et al on the subject
dates back to 1973, this technique is still used.
Isotropic material properties were applied for enamel,
dentin, POL, alveolar bone in the model. The applied
material properties are summarized in table
The first step is to subdivide the complex geometry into
a suitable set of smaller "e lements " of "finite "
dimensions when combined from the "mesh" model
of the investigated structures. Each element can adapt
a specific geometric shape (i.e. triangle, square,
tetrahedron etc) with a specific internal strain function .
Results
Von Mises equivalent stress distributions in the root
and the alveolar bone was analyzed in the study.
Figure shows the distributions of equivalent stresses
according to a liner colour scale, where red indicate
areas with the highest stresses, and blue the lowest.
Using these functions and their actual geometry of the
element, the equilibrium equations between the
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externa l forces acting on the element and the
displacements occurring on its nodes can be
determined.
simu lation. Although the mechanical behaviour of the
PDL is understood to be non-linearly elastic, many
investigators assigned linear mechanical properties
because of lack of scientific quantitative data. This lack
of information is a source of error in co mputer
simu lations of orthodontic tooth movement.
The Maxillary central incisor has been chosen for the
study because during orthodontic treatment they are
subjected to orthodontic forces for prolonged period
of time and also most of the studies stated that apical
root resorption occurs mainly in the maxillary anterior
teeth. In our study, the three dimensional finite element
model of a maxillary central incisor was created by
various steps.First step was the modelling. CT scan of
a patient of central incisor was taken along with alveolar
bone. The scanned images was viewed with the
software DICOM. The obtained two dimensional data
was reconstructed to give a three dimensional model
using a software called pro/Engineer (parametric
techno logy corporation, USA). After completion of the
models the assembly was exported for analysis using a
software ca lled ANSYS(ANSYS , Inc, USA ).
CONCLUSION
The FEM study showed that for intrusion stress
concentration was more in the root apex. For extrusion
stress concentration was in the mid root and the apex.
Stress was distributed over a wider area and was thus
in lesser magnitude. For rotation maximum stress was
towards the mid root. For tipping stress concentration
was towards the alveolar crest and the apical third of
the alveolar bone. For bodily movement maximum
stress was on the alveolar crest and not at the apex.
The clinical implication of the evaluation of stress
pattern is to keep the orthodontic forces as light as
possible especially for tooth movements like intrusion
to prevent damage to the root. The future improvements
in software and updated versions could help in
refinement of meshing process and creating a more
accurate 3 D FE model.
The maxillary central incisor model was created to
represent the exact geometry of the root apex with
morphology along with PDL. In the present study, the
three dimensional finite element model had 22393 four
noded linear tetrahedral type and 87988 elements for
enamel, dentin, and alveolar bone. In a FEM study for
tooth movement, Young's modulus and Poisson's ratio
are the essential parameters which are required as
mathematica l inputs for generating the finite element
model. The results are based on these inputs and any
alteration would affect the outcome of results.
REFERENCES:
This study shows that intrusive, extrusive and rotational
forces produce stress patterns in the apex. But the stress
patterns for extrusive and rotational tooth movement
was distributed over a wider area. Bodily movement
and tipp ing forces concentrate forces at the alveolar
crest ,not at the afex. In a study conducted by David
J.Rudolph et al 1 in 2 000, a similar result was
evidenced.
Early investigators indicated that multiple factors are
involved for root resorption such as genetic and
systemic factors, sex, tooth movement type, orthodontic
force magnitude, duration and type of forces. They
also categorized that these risk factors are patient related
or treatment related.
The present study showed that the Von Mises stress
(hydrostatic pressure) seen at the root apex was very
much less than the normal capillary blood pressure ,
when recommended optimal orthodontic forces were
used ,except for intrusion . For intrusion it may require
even less force levels. The limitations of the study
include some basic assumptions for the purpose of
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Fig.l : STRESS PATTERN FOR INTRUSION
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Fig.2 : STRESS PATTERN FOR EXTRUSION
Fig.3 : STRESS PATIERN FOR ROTATION
Fig.4 : STRESS PATIERN FOR TIPPING
Fig 5: STRESS PATIERN FOR BODILY MOVEMENT
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