Abstract :

Keywords

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 College

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

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.

Stress analysis, Loading, Orthodontic forces, finite element modelling.

FEM is defined as a techn ique of discrediting a continuum into simple geometric shapes elements, enforcing material propert ies 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 behavior of the continuum.

The finite element method is a highly precise technique used to analyze structural stress. FEM has many advantages over 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

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 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.

Isotropic material properties were applied for enamel, dentin, POL, alveolar bone in the model. The applied material properties are summarized in table

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.

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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 a 1.1 ,4,6

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.

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.

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 .

Using these functions and their actual geometry of the element, the equilibrium equations between the

externa l forces acting on the element and the displacements occurring on its nodes can be determined.

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 technology corporation, USA). After completion of the models the assembly was exported for analysis using a software ca lled ANSYS(ANSYS , Inc, USA ).

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.

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 2000, 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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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 computer simulations of orthodontic tooth movement.

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.

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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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