The Effect Of Force And Torsion On Orthodontic Tear Drop Loop - A Finite Element Analysis

INTRODUCTION

Closure of extraction spaces is an integral stage of many orthodontic treatment plans. In goal oriented orthodontics the closure of these spaces requires an understanding of the mechanical system utilized. Knowledge of the mechanics required to achieve specific treatment goals is necessary for efficient correction of the malocclusion.¹

An important aspect of orthodontic treatment is to understand tooth movement in response to mechanical loads and the associated adjacent tissue response at both clinical and histologic levels. To move teeth in a controlled fashion, correct mechanical principles and an ideal orthodontic appliance is necessary so as to better align the teeth to be moved. ²

Space closing mechanics can be broadly divided into two categories, which can be used to apply the force systems necessary to trigger the biologic phenomena that result in space-closing movement of individual teeth or groups of teeth ("en masse"). The first approach is the friction method which involves supplying the appropriate moments to the teeth via a continuous arch wire that passes through orthodontic brackets (delivering the moments via couples with equal and opposite non-collinear vertical forces at the mesial and distal bracket extremities.

The resulting instantaneous moment-to-force ratio (M/F) determines the initial displacement of the tooth (or teeth) within the periodontal ligament (PDL). Wire-bracket friction is a variable factor as the moving teeth displace along the arch wire with this approach, making it difficult to accurately predict M/F ratio.

The second approach involves bending arch wire loops of various configurations, sectionally (to deliver the desired M/F to an individual tooth) or segmentally or in a continuous arch wire (to deliver the desired M/F to several teeth). This approach is friction-free and does not depend on sliding the bracket along the archwire.³

Three basic properties can be considered for characterizing space closing loops: 1). The proportion moment /force ratio(M/F),which determines the centre of dental rotation and thus enables root control during the movement of the teeth, 2). The horizontal force produced during loop activation, and 3). The load/deflection ratio, which defines the amount and decrease in force at each millimeter of deactivation.⁴

Design alterations can be made in orthodontic appliances to increase the ability to direct and distribute the mechanical forces for tooth movement. The addition of helices or changes in alloy composition and processing are commonly used to allow clinicians to more accurately achieve desired forces for tooth movement. Therefore, accurate prediction of mechanical behavior as a function of shape and material properties is necessary in clinical practice.²

In orthodontics, FEM has been used successfully to model the application of forces and the mechanical behavior of orthodontic wires and different design of brackets. This would help in the development and improvement of orthodontic brackets and wire design.⁵

The null hypothesis of this study is that computer simulation accurately predicts the experimentally determined mechanical behavior of teardrop loops of different heights and can be considered an alternative for designing orthodontic appliances before treatment.

Thus the purpose of this study is to determine the force and the torsion obtained on activation of teardrop loops of 3 different heights (6mm, 7mm and 8mm) by universal testing machine and to evaluate the use of computer simulation to predict the force and the torsion obtained after the activation of teardrop loops of 3 heights.

METHODOLOGY

75 teardrop retraction loops of 0.019”× 0.025” (3M) stainless steel rectangular wire were bent and divided into 3 groups of 25 each based on the height of the loops( 6mm,7mm and 8mm). The same operator prepared the specimens using a glass slab and a light wire plier with medium tips. After preparation, each stainless steel wire extension measured 10.0 cm in length to allow its attachment to a universal testing machine (Instron-4667 England). All loops had a 2.5 mm internal arch circumference. A 15.0-cm wire segment of same cross-sectional dimension as the teardrop loops was connected on a straight hook (VERSA HOOK &BASE d-tech). This wire segment was connected by using a crimpable hook plier (d-tech) parallel to the loop at 4.0 mm from the base point of the loops (Fig.1)

For observation of the teardrop loop deformation during loading, a conventional protractor was scanned with 600 dpi resolution. The scanned image was then printed at a specific size so that its radius matched the length of the welded meter (Fig.2).

This setup was developed to investigate the torque angle produced after mechanical activation of the various teardrop loop groups. For computer simulation, the geometry of the springs used in the mechanical testing was obtained with a universal digital paquimeter (fig.3).  

The different loop models were created in Ansys version 10 which is the software used in the present study. According to the characteristics of the teardrop loop structures and also considering the specific movements imposed by the intended mechanical activation, BEAM 4 elements were used for the teardrop model. This (finite) uniaxial element can respond to tension, compression, traction, and torsion movements.

Testing apparatus

A Universal Testing Machine (Instron4667-England) (Fig.4) with a load cell carrying 20 N was attached to the machine. A crosshead speed of 1.0 mm/minute was used to activate the loops. Special care was taken to avoid torque incorporation while the loop was connected to the testing machine. For observation of the tear drop loop deformation during loading, a conventional protractor was scanned with 600 dpi resolution. 

The scanned image was then printed at a specific size so that its radius matched the length of the welded meter (Fig.3). Apositive sign was allocated to clockwise rotated specimens and a negative sign to those that were rotated anti clockwise. All specimens were measured for loop deformation (torque) after the activation steps (0.5 mm, 1.0 mm, 1.5 mm, and 2.0 mm)

RESULTS

The loops were designed in AutoCAD software, and finite element analysis was performed with Ansys 10 software. Statistical analysis of the mechanical experiment force results was obtained by ANOVA and the Tukey post-hoc test (P<0.01). Statistical analysis of the mechanical experiment torsion results was obtained by ANOVA and the Tukey post-hoc test (P<0.01).

Higher mean force (N) was recorded in 6mm specimen followed by 7mm and 8mm specimen respectively. The difference in mean force was found to be statistically significant between 6mm & 7mm (P<0.001), 6mm & 8mm (P<0.001) as well as between 7mm & 8mm (P<0.001). (Table-1) 

Higher mean torsion is recorded in 7mm specimen followed by 8mm and 6mm specimen respectively. The difference in mean force between the specimens are found to be statistically significant (P<0.001). (Table-2)

The correlation test and the paired t test (P <.05) were used to compare the computer simulation with the mechanical experiment. Paired t tests showed no significant differences (P>.05) between experimental and computer simulation results. (Table-3 & Table-4)

DISCUSSION

Biomechanical knowledge of orthodontic appliances allows better treatments and accuracy in dental movements. After mechanical testing, the 6- mm teardrop loop had the highest force results at all activation levels. This loop also showed proportional behavior regarding the force obtained and the activation displacement.

The correct spring height is proportional to the patient's anatomic limitation. These results are 6 comparable with those of Burstone and Koenig who observed the relationship between the addition of helicoids and the decreased force and moment for various activation procedures. When possible, springs that release low force levels are preferred.

The ideal force applied to achieve movement of the mandibular incisors is 7 approximately 2.60N . The springs that best approached this value were the teardrop loops of 6- mm height activated 0.5 mm, which provided 2.58 N force and the teardrop loop of 8-mm height activated 1.0 mm, which provided 2.69 N force. The teardrop loops with heights of 7 and 8 mm activated 0.5 mm had values less than 2.60 N: 1.92 and 1.29 N, respectively. The teardrop loops with heights of 7 and 8 mm activated 1.5, and 2.0 mm had higher forces than the ideal values for mandibular incisor movement. For the maxillary 7 incisors, the ideal force level is 3.10 N. When activated 1.0 mm, the teardrop loops with heights of 7 and 8 mm induced forces that were close to the ideal levels: 3.56 and 2.69 N, respectively. Activations greater than 1.0 mm showed forces that were higher than the ideal value for all springs tested. Considering the torsion angle incorporated after activation, the torque observed ranged from 0° to 3°. The 7mm teardrop loop had the highest values on all the activations tested: 0.5°, 1.0°, 1.2°, and 1.5° for activations of 0.5, 1.0, 1.5, and 2.0 mm, respectively.

The spring that incorporated less torque was the 6-mm teardrop, which had values of 0.2°, 0.8°, 1.0°, and 1.3° for activations of 0.5, 1.0, 1.5, and 2.0 mm, respectively. On the other hand, the FEA simulation did not show torque incorporation during or after activation. The torque observed in the experimental study can be explained by the absence of dimensional symmetry, even though a template was used during specimen preparation. The discrepancy observed between experimental and computer simulation could be due to the symmetry designed into the software. Between groups, comparisons of mean force values showed significant differences between groups (Table 1&Table-2), suggesting that circumferences and lengths for the spring to be used should be considered in clinical practice.

Considering torque angle, the only case when a significant difference was observed was between the 7mm and 8 mm teardrop loop .In spite of a significant difference, the values were small and can be ignored in clinical practice. The computer simulation showed remarkably close results compared with mechanical experimen tation.

The small variations observed between experimental and simulation results might be because, in the computational simulation, the teardrop loop was symmetric with respect to its geometric form. According to Thurow⁸ the computational simulations identified the highest stress concentrations of the tear drop loop at the curvature of the loop.

Additionally, computer simulation software has gained interfaces that are more user friendly and, thus, has become more popular recently. These 2 factors might result in the development of customized software for orthodontic applications and the choice of appliances used in clinical practice.

Limitations of the study

Finite element method is an approximation study. The limitation of this study involves approximation in the material behavior and geometry of the tissue which may affect the stress values and the pattern of distribution. In this study the stress strain relationship of the tissues were assumed to be linear, elastic and isotropic and the variation of density and trabecular pattern of the alveolar bone were not considered.

CONCLUSION

Height of the loop is a very important factor in the amount of force produced by all types of loops. Amount of force produced by teardrop loops of different heights decreased with increase in the height of the loop. It means that for reaching a definitive amount of force with a longer loop, clinician needs to incorporate more amount of activation.

The correct spring height is proportional to the patient's anatomic limitation (depth of the sulcus). When possible, springs that release low force levels (longer size) are preferred.

The ideal force applied to achieve movement of the mandibular incisors is approximately 2.60 N.

For the maxillary incisors, the ideal force required for movement is 3.10 N

The computer simulation accurately predicted the experimentally determined mechanical behavior of teardrop loops of different heights and should be considered an alternative while designing orthodontic appliances before treatment. Thus the null hypothesis of this study is accepted.