Evaluation of the mechanical stress on root from orthodontic tooth movement by sliding mechanics- a three-dimensional finite element analysis

INTRODUCTION

Force is the medicine in orthodontics as said by -

                                                                         Sheldon Freil.

Orthodontic space closure has always been a challenge for the orthodontist. Space closure using fixed appliances is usually accomplished using a variety of methods. Dental movement can be considered as one of the basic pillars of orthodontic tooth movement¹ .

Sliding mechanics, which causes bodily movement of the teeth along the arch wire ², is a basic method for an orthodontist to close space at an extraction site. Different types of orthodontic force may produce different mechanical stresses at varying locations within the root. There has not been sufficient mechanical stress investigation so far concerning this connection between the optimum forces of sliding mechanics and orthodontic tooth movement³ .

The finite element method is a numerical method of analysis that provides the orthodontist with the quantitative data that can extend the understanding of the physiologic reactions that occur and thus allows the study of stress distribution in biological system⁴ .

Thus the purpose of this study is to create a realistic finite element model to calculate the stress in the dental root from orthodontic tooth movement by sliding mechanics and integrate these simulations into the planning of the therapy.

MATERIALS AND METHODS

In this study a 3-dimensional finite element model of mandibular dental arch with brackets and arch wire without first premolar (due to extraction) was generated and used to calculate the stress in the dental root from orthodontic tooth movement by sliding mechanics and integrate these simulation into the planning of the therapy.

A PC workstation having an Intel Core Duo processor with 8GB RAM, 500 GB secondary storage and graphic accelerator were used. The software used for the geometric modeling in this study was ANSYS 12 .

STEPS INVOLVED IN THE GENERATION OF FINITE ELEMENT MODEL

1.Construction of a geometric model: In this study the analytical model incorporating all the layers of mandibular dental arch (without first premolar) with the brackets, wire and band was developed according to dimensions and morphology found in a standard text book of dental anatomy, physiology and occlusion by Wheeler's. Periodontal ligament was simulated as a 0.2mm thick ring around the model of the tooth (Fig.1) 

2.Conversion of the geometric model to a finite element model: The finite element model generation was achieved with the help of ANSYS 12 software. The finite element model approximately consisted of 50,923 nodes, 2, 34,268 elements and 3 degrees of freedom.

3.Material property data representation: These material properties were the average values reported in the literature (Table.1).In all the tissues the structures were assumed to be isotropic. (For an isotropic material the properties are same in all directions).

4.Defining the boundary condition: Boundary conditions were assigned to the nodes surrounding the outer most layers of the tooth roots and alveolar bone. The geometry of the tooth root and of the alveolus has to be kept constant during the movement. Simulated loads of 2 N at 0, 30 and 45 degrees from the horizontal axis were applied to the crown of the teeth.

5.Loading configuration: The loading configuration was designed to simulate sliding mechanics. Sliding force at 2N is ideal to ensure the bodily orthodontic tooth movement. (Table-2).

6.Solving the system of linear algebraic equation: The sequential application of the above steps leads to a system of algebraic equations where the nodal displacements are unknown. These equations are solved by frontal solver technique present in the ANSYS software.

RESULTS

Stress distribution on the roots of mandibular teeth on application of orthodontic force loadings was analyzed using FEM.

1. AT ZERO DEGREE OF HOROZONTAL LEVEL

In the case of linguo-labially directed force of 2 N at zero degree of horizontal level, the maximum level of stress was found at the cervical margin of the PDL of all the tooth root 2 which was 0.3088N/mm for cervical margin.(fig-2A&fig-2B). In the presence of the same load, the top of tooth crown showed the largest amount of displacement.(fig-3A&fig-3B)

2. AT 30 DEGREE OF HOROZONTAL LEVEL

In the case of linguo-labially directed force at 30 degree of horizontal level, the maximum stress on the root occurred 2 during tipping, 0.4744 N/mm for cervical margin (fig-4A&fig-4B). The top of tooth crown showed the largest amount of displacement 0.783 µm (fig-5A & fig-5B).The PDL underwent tensile stress along the root surface and the sub-apical level experienced compression.

3. AT 45 DEGREE OF HORIZONTAL LEVEL

In the case of linguo-labially directed forces at 45 degree of horizontal level, the stress was mainly concentrated at the neck of the tooth, decreasing uniformly to the apex and crown. The maximum stress on the root was 0.4133 N/mm2 for cervical margin (fig-6A & fig-6B). The top of tooth crown showed the largest amount of displacement 0.418 µm (fig-7A & fig-7B).The stress distribution on the mesial and distal sides showed almost symmetrical behaviors, the maximum compressive stress was localized mesially and the maximum tensile stress distally.

DISCUSSION

In clinical orthodontic practice, correction of malocclusion usually requires active movement of teeth by the application of forces. Over the years, it has been realized that the stresses generated in response to these orthodontic forces vary with different methods of force application and on different patients. Trying to understand or predict the complexities involved in the response of teeth to forces and moments has always been a challenge to orthodontists.

In this study, it was found that when the orthodontic forces used was 2 N, the maximum compressive stress was localized mesially, the maximum tensile stress distally and the stress distribution at the mesial and distal sides showed almost symmetrical behaviors, which is ideal to ensure the bodily orthodontic tooth movement by sliding mechanics.

The Finite Element model of the mandibular dental arch with sliding mechanics consists of 2,34,268 elements, 50,923 nodes and 3 degrees of freedom. This new model allows a much more detailed depiction of the dental roots and orthodontic appliance and can be used for the analysis of the stress distribution of sliding mechanics in space-closing under different loading conditions. With the development of implant anchorage, orthodontic force at 30 and 45 degrees from the horizontal axis became more and more common in space-closing by sliding mechanics.

Clinically, orthodontic forces at 30 and 45 degrees have been traditionally suspected in some cases of root resorption. Analysis of the mechanical stress on roots after horizontal loading at 0, 30 and 45 degrees in our study showed that the cervical third of the mandibular teeth root supported greater part of loadings of stress magnitude and distribution. The highest stress concentration in the roots was localized at the cervical margin in all the three conditions and the stress distribution was less concentrated at the apical region, which are in agreement with some previous studies.

Our findings coincide with a study done by Ping et al⁵ , which is a 3-dimensional finite element model incorporating all layers of a human mandibular dental arch. Simulated orthodontic force of 2 N at 0, 30 and 45 degrees from the horizontal axis was applied to the crown of the teeth. The finite element analysis showed that the stress was mainly concentrated at the neck of the tooth decreasing uniformly to the apex and crown. When compared to our study the stress pattern was found to be similar but the maximum stress was found to be less. This may be due to the difference in finite element tooth model.

In a 3-dimensional finite element study done on the mandibular canine the stresses during tooth movement with diverse degrees of bone loss were determined with a labiolingual force of 100 gms. The result showed that the distribution of stresses is seen at the cervical margin which is similar with our study⁶ .

David.J et al.⁷ did a 3-dimensional finite element model of a maxillary central incisor, its periodontal ligament (PDL), and alveolar bone which was constructed on the basis of average anatomic morphology. The finite element analysis showed that the principal stress from a tipping force was located at the alveolar crest. So the bodily movement and tipping forces concentrate at the alveolar crest, not at the apex, which is similar to our study.

In the study done by Allahyar Geramy⁸ with a 3-D finite element model of a human maxillary central incisor of the same configuration except for the alveolar bone height showed that the alveolar bone loss caused increased stress production under the same load compared with healthy bone support (without alveolar bone resorption). The result showed that the stress concentration was at cervical margin of the periodontal ligament which is similar to our study.

The finite element method, which has been applied in the mechanical analysis of stress and strain in the field of engineering, makes it practical to elucidate the biomechanical state variables such as displacements, strains & stresses induced in living structures by various external forces. However, one should be aware that the structural and spatial relationships of various dentofacial components vary among the individuals⁹ . It is important to realize that these factors may contribute to varied responses of the dentoskeletal components on loading, thus affecting the locations of the centre of resistance¹⁰ . Analytical results of the FEM are highly dependent on the models developed; therefore, they have to be constructed to be equivalent to real objects in various aspects.

From a structural engineering point of view, geometry idealization, material data selection, and assignment of boundary conditions of the present analysis were sound.

Limitations of the study

The three-dimensional model created in this experiment is an idealized model of a mandibular arch, in reality no tooth has the ideal shape and proportion.

The results of the finite element method analysis must be interpreted with care. The accuracy of the analysis is dependent on modelling structures as closely as possible to the actual. However, a certain amount of approximation manifested chiefly in terms of type and number of arrangement of elements is inevitable in complex designs. Apart from this, one must be aware of the assumption used in the formulation, material characterization, nature of boundary conditions and the representations of loads. All these factors affect the validity of the results.

Finite element method is an approximation study. The limitation of this study involves approximation in the material behaviour and geometry of the tissue which may affect the stress values and pattern of distribution.

In this study the stress-strain relationships of the tissue were assumed to be linear, elastic and isotropic and the variation of density and trabecular pattern of alveolar bone were not considered.

CONCLUSION

The present study was done to analyze the mechanical stress on root from orthodontic tooth movement by sliding mechanics, using 3 dimensional FEM.

It is clear from this analysis that

The 3-dimentional FEM model is useful in analyzing the mechanical stress on root surfaces in response to orthodontic forces.

At 0 degree of horizontal level, the greatest amount or the maximum level of stress was found at the cervical margin of the PDL at all tooth roots. The maximum stress at the subapical level was approximately 45 percent of the cervical stress.

At 30 degree of horizontal level, the maximum stresses occurred at the root crest region of the canine, the highest stress on the root occurred during tipping. The maximum stress at the sub-apical level was approximately 20 percent of the cervical stress.

At 45 degree of horizontal level, the stress was mainly concentrated at the neck of the tooth, decreasing uniformly to the apex and crown. The highest stress on the root was at the cervical margin of the canine.

Clinical implications of this study suggested that if the clinician is concerned about placing an implant as anchorage by sliding mechanics to close dental arch space, there was the same risk of root resorption after loading of 2N at 0, 30 and 45 degrees from the horizontal level. However the link between external forces and apical root resorption is not very clear cut. Because of lack of reliable animal model, we simply do not know why similar mechanical forces affect one person so differently from others. It is likely that root resorption is a complex, multifactorial system with bio-chemical thresholds that vary significantly among individuals.

Finally it can be concluded that this tri-dimensional model is a useful example to investigate the biomechanism of dental movement, keeping in mind that it is more valid as a qualitative study.

The future direction of FEM studies should involve more accurate simulation of loading and approximation of material behaviors as well as variations in geometries of PDL, bone and tooth in 3-dimensional finite element analysis.