Scientific Innovation · Scientific Innovation 318 ORTHODONTICS The Art and Practice of Dentofacial Enhancement 1Senior Professor, Department of Orthodontics, Yenepoya Dental College,

Scientific Innovation

318 ORTHODONTICS The Art and Practice of Dentofacial Enhancement

1 Senior Professor, Department of Orthodontics, Yenepoya Dental College, Yenepoya University, Mangalore, India.

2 Assistant Professor, Department of Orthodontics, Yenepoya Dental College, Yenepoya University, Mangalore, India.

3 Former Postgraduate Student, Department of Orthodontics, Yenepoya Dental College, Yenepoya University, Mangalore, India.

4 Senior Professor and Head, Department of Orthodontics, Yenepoya Dental College, Yenepoya University, Mangalore, India.

CORRESPONDENCE Dr Tariq Ajaz Ansari Department of Orthodontics and Dentofacial Orthopedics Yenepoya University Nithyanandanagar Mangalore 575018 India Email: [email protected]

Evaluation of the power arm in bringing about bodily movement using finite element analysis

Tariq Ajaz Ansari, BDS, MDS1

Rohan Mascarenhas, BDS, MDS2

Akhter Husain, BDS, MDS3

Mohammed Salim, BDS, MDS4

Aim: To evaluate the effectiveness of the power arm in bringing about bodily movement and to determine the ideal length and location of the power arm. Methods: A geometric model of the maxillary right canine was constructed and subsequently converted to a finite element model. Material property data were represented, boundary conditions were defined, and force was applied. Different situations were simulated in which a power arm of varying vertical lengths were attached at different locations on the tooth—namely, the incisal, middle, and cervical thirds. Results: The amount of bodily movement is maximum when the force is delivered directly at the cervical third. It decreases at the middle third and is least when attached at incisal third. The varying lengths of the power arm for a particular site of attachment does not bring about any change in the movement. Conclusion: The attachment of the power arm at the cervical third brought about maximum bodily movement, followed by the middle and incisal thirds. Variations in length of the power arm at different sites of attachment did not bring any change in the outcome. Thus, the point of attachment is critical in bringing about bodily movement. ORTHODONTICS (CHIC) 2011;12:318–329.

Key words: bodily movement, finite element analysis, power arm

Orthodontic tooth movement takes place when force systems are de-livered to the teeth, resulting in different types of displacement in the periodontium. The stress in the periodontal ligament initiates cellu-

lar reaction, which results in resorption and apposition of alveolar bone and leads to tooth displacement.

Several studies have described the reactions of teeth and their support-ing tissues when loaded with an orthodontic force. However, each method of study has its own shortcomings.

The most advanced and reliable study is finite element analysis. This is a nu-meric form of analysis that allows stresses and displacements to be identified. It involves discretization of the continuum (dividing the structure of interest) into a number of elements. This method has proven effective in many dental

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fields, such as simulation of tooth movement and optimum orthodontic me-chanics. Finite element analysis has been used in dentistry to investigate the skeletal and dental responses to mechanical forces in orthodontic research. This method also has the potential for equivalent mathematic modeling of a real object of complicated shape and different materials. Thus, finite element analysis offers an ideal method for accurate modeling of the teeth and peri-odontium with its complicated three-dimensional (3D) geometry.

The force systems used on an orthodontic patient can be complicated. Ex-perimental techniques on patients or animals are usually limited in applying known complex force systems. Finite element analysis makes it possible to analytically apply various force systems at any point and in any direction.

It is important to keep in mind that finite element analysis will give results based on the nature of the modeling system, and for that reason, the proce-dure for modeling is most important.

According to Caputo,1 bodily movement of the canine was more likely to occur when the force activation did not exceed 300 g and the gable angle was 45 to 60 degrees. According to Smith and Burstone,2 forces applied to a tooth produce translation (bodily movement), rotation, or a combination of translation and rotation, depending on the relationship of the line of action of the force to the center of resistance of the tooth. In an experimental study3

on centers of rotation with transverse forces, the occlusoapical position of the center of resistance varies depending on the transverse direction of loading around the long axis.

One study4 used bonded power arms for interdental space closure—follow-ing bracket placement, bonded power arms were placed on the cervical por-tion of the crown of the central incisors, with hooks placed at the same height as the center of resistance of the teeth. These were connected by elastics. The authors observed that translational movement took place.

A study on stress analysis of the periodontal ligament (PDL) under various orthodontic loadings5 was carried out using 3D finite element analysis of a hu-man maxillary canine. The maximum principal stresses in the PDL produced by various orthodontic forces were determined. Newton tipping forces produced stresses at the cervical margin of the PDL which were as high as 0.196 N/mm2

and apical stresses up to –0.034 N/mm2, while rotatory forces of two equal but opposing forces of 0.5 N at the cervical margin of the crown produced cervical margin stresses ranging between –0.035 and 0.051 N/mm2 and apical stresses of between 0.0018 and 0.0027 N/mm2. It was determined6 that the center of resistance of a human canine is located at around two-fifths of the root length from the alveolar margin.

Evaluation of the power arm in bringing about bodily movementScientific Innovation


A 3D computer model based on finite-element techniques was used for this purpose.6 A model of the mandibular canine was constructed on the average anatomical morphology, and 396 isoparametric elements were considered. The three principal stresses (maximum, minimum, and intermediate) and von Mises stresses were determined at the root, alveolar bone, and PDL. It was observed how the distribution of stress is not the same for the three structures studied. In all loading cases for buccolingually directed forces, the three prin-cipal stresses were very similar in the PDL. The dental apex and bony alveolar crest zones are the areas that suffer the greatest stress when these types of movements are produced.

Research was carried out7 to determine the stress that appears in the tooth, PDL, and alveolar bone when a couple and horizontal forces were applied to obtain the bodily movement of a mandibular canine and its changes depend-ing on the degree of loss of the supporting bone by means of finite element analysis with no bone loss and after reducing the supporting bone to 2, 4, 6, and 8 mm. This study shows that the stresses increased as the level of bone support decreased.

According to Proffit,8 bodily movement of a tooth requires a moment-to-force ratio of 8:1 to 10:1. To achieve bodily movement, the center of rotation has to be at infinity. During bodily movement of the tooth, the PDL has to be loaded uniformly from alveolar crest to apex. According to Marcotte,9 trans-lation of a tooth occurs when every point on the tooth moves in a parallel straight line in the direction of force. This occurs when the center of rotation of the tooth is at infinity. If the line of action of an applied force passes through the center of resistance of a tooth, the tooth will respond with pure bodily movement (translation) in the direction of the line of the applied force.2

When the force application takes place at a distance from the center of re-sistance, the force alone applied at the bracket will not result in translation. To achieve translation at the level of the bracket, a couple and force are required that are equivalent to the force system through the center of resistance of the tooth. A moment-to-force ratio of 10:1 typically produces translation. This type of tooth movement produces uniform stress in the periodontium.13

The purpose of this study was to evaluate the effectiveness of the power arm in bringing about bodily movement and determine the ideal length and location of the power arm.

METHODS

Since finite element analysis will give the results based on the nature of the modeling systems, the procedure for modeling is the most important step. Linear-elastic behavior of the tooth, PDL, and bone structures have been con-sidered.

There are three basic steps involved: preprocessing, processing, and post-processing. Preprocessing consists of construction of the geometric model and its conversion finite element, material property data representation, defin-ing the boundary conditions, and loading configuration. Processing includes solving the system of linear algebraic equations. Postprocessing consists of interpretation of the results.

Construction of the geometric modelThe purpose of the geometric modeling phase is to represent geometry in terms of points, lines, areas, and volume.

In this study, the geometric model of the maxillary right canine is developed from grid radiographs (Fig 1) and computed tomography (CT) scans (Fig 2)

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Ansari et al Scientific Innovation

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(Philips Brilliance, Royal Philips Electronics). The cut sections of the tooth are traced and matched ac-cording to Wheele dimensions and morphology10 (Fig 3).

The PDL thickness of 0.25 mm is automatically generated around the model of the root.5 The bone is modeled around the PDL.

The tracing of the cross sections of the tooth is done with AutoCAD software and is imported into ANSYS to build the model of the canine tooth. With the imported model of the cross sections, a wire frame is obtained. With it, shapers are constructed and the virtual tooth model similar to the original is developed (Fig 4).

Fig 1 Grid radiographs of the maxillary canine.

Fig 2 CT scan images of the maxillary canine.

Fig 3 Outline of the maxillary canine used for modeling.

Fig 4 Traced cross section of the canines.



Conversion of the geometric model to finite element analysisThe tooth here is called a continuum or a domain, and the subdomains are called the elements. This process is called discretization. The elements could be one-, two-, or three-dimensional and in various shapes.

It is essential that the elements are not overlapping but are connected only at the key points, which are called nodes. The joining of elements at the nodes and eliminating duplicate nodes is referred to as meshing.

Elements were generated in the ANSYS software. The shape and type of the element are important in the accuracy of the analysis. The element type is a hexahedral quadratic element commercially named SOLID 95. These elements have 20 nodes, quadratic behavior on deflection, and 3 degrees of freedom at each node (Fig 5). The maxillary right canine model is meshed with 22,784 elements and 95,611 nodes (Fig 6).

To establish the natural anatomy (material in homogeneity), the teeth were con-nected to the surrounding alveolar bone through the PDL. Therefore, convergen-ces of all these nodes were established to create the connectivity of the model.

The power arm is modeled as a beam element, taking the cross section of the arm into consideration. It is connected to the enamel part of the tooth at differ-ent locations, such as the incisal, middle, and cervical thirds. The vertical length of the power arm is considered from the point of attachment to the point of ap-plication of force. The vertical length of the power arm was varied (Figs 7 to 9).

Material property data representationTo simulate the natural tooth, material properties were assigned.11 The model was made of isotro-pic material, which has identical physical proper-ties along all three axes.

The material properties used in this study were taken from previous finite element stud-ies.5,12,13 Modulus of elasticity and Poisson ra-tio of the tooth, PDL, bone, and power arm are shown in Table 1.

The Young modulus and the Poisson ratio of these structures were previously described.12

Fig 5 Hexahedral quadratic element (SOLID 95).

Fig 6 Finite element analysis of the tooth and periodontium.

P WX

U BV

N

O

A

K

SL

T

M

5

4

6

32

1

Y

I

Q J

Z

R

Y

Z

X

Table 1 Material properties

Young modulus (N/mm2) Poisson ratio

Tooth 20,300 0.30000

Periodontal ligament 0.68000 0.49000

Bone 140,000 0.38000

Power arm 201,000 0.33000



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Fig 7 Power arm attached at the incisal third, extending (a) to the center of resistance, (b) 2 mm above the center of resistance, and (c) extending 2 mm below the center of resistance.

Fig 8 Power arm attached at the middle third, extending (a) to the center of resistance, (b) 2 mm above the center of resistance, and (c) extending 2 mm below the center of resistance.

Fig 9 Power arm attached at the cervical third, extending (a) to the center of resistance, (b) 2 mm above the center of resistance, and (c) extending 2 mm below the center of resistance.

a

a

a

b

b

b

c

c

c



Defining the boundary conditionsIf an element is constructed on the computer and a force is applied to it, it will act like a free-floating, rigid body and will undergo a translatory or rota-tory motion or a combination of the two without experiencing deformation. To study its deformation, some of the degrees of freedom (movement of the node in each direction: x, y, and z) for some of the nodes must be restricted. Such constraints are termed boundary conditions. Boundary conditions were defined at all peripheral nodes of the bone with 0 degrees of movement in all directions (Fig 10).

Application of forcesTo find the center of resistance of the tooth, a force of 1 N is applied at the middle third of the crown.

To study the effect of the power arm on the movement of the tooth, a load of 1 N is applied to the tip of the power arm from the mesial to distal direction. This load is repeated for different lengths of the power arm and at different locations.

Determination of the center of resistance The level of force application, at which no rotation occurs, was considered to be the line on which the center of resistance lies (Fig 11).

The present study was undertaken to determine the effect of the power arm in different situations. The power arm was attached at three different areas of the crown of the tooth (incisial, middle, and cervical thirds) and with different vertical lengths passing 2 mm above and 2 mm below the center of resistance. Thus, nine situations were simulated.

In the incisal third, the power arm was attached:

At the level of the center of resistance (the length of the power arm was 16.6 mm)2 mm above the center of resistance (the length of the power arm was 18.6 mm)2 mm below the center of resistance (the length of the power arm was 14.6 mm)

Fig 10 Finite element analysis of the tooth and power arm showing loading and bound-ary conditions.

Fig 11 Determination of the center of resistance.

Center of resistance

13.27 mm

5 mm

100 N



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In the middle third, the power arm was attached:


In the cervical third, the power arm was attached:


To verify bodily movement, the center of resis-tance is considered, as shown in Fig 12.

RESULTS

The results of the study for different situations are discussed below. When a force of 1 N is applied on the tip of the power arm in a mesial to distal direction, it caused bodily movement of the tooth.

To analyze bodily movement, the center of re-sistance was considered.

Power arm attached at the incisal third Displacements are shown in Figs 13 and 14. Re-sults in the x direction are considered. At the cen-ter of resistance and 2 mm above and below it, teeth moved bodily by 0.008 mm.

Fig 12 Center of resistance on the axis of the tooth.

Fig 13 Stress patterns when the power arm is attached at the incisal third, labial view.

Fig 14 Stress patterns when the power arm is attached at the incisal third, palatal view.



Power arm attached at the middle thirdDisplacements are shown in Figs 15 and 16. Results in the x direction are considered. At the center of resistance and 2 mm above and below it, teeth moved bodily by 0.012 mm.

Power arm attached at the cervical third Displacements are shown in Figs 17 and 18. Results in the x direction are considered. At the center of resistance and 2 mm above and below it, teeth moved bodily by 0.013 mm.

It was observed that there was no difference in the results when length of the power arm increased by 2 mm above the center of resistance and decreased by 2 mm below the center of resistance compared to the power arm passing through the center of resistance for a particular site of attachment.

All measurements of bodily movement were made at the center of resis-tance when the power arm was attached in different areas.

Fig 15 Stress patterns when the power arm is attached at the middle third, labial view.

Fig 16 Stress patterns when the power arm is attached at the middle third, palatal view.

Fig 17 Stress patterns when the power arm is attached at the cervical third, labial view.

Fig 18 Stress patterns when the power arm is attached at the cervical third, palatal view.



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DISCUSSION

Although some authors17 have suggested that the length of the power arm is more important, this study concluded that the point of attachment is more important. Earlier studies did not use finite element analysis; in this study, finite element analysis was used to study the effect of both the length of the power arm and the point of attachment of the power arm to the tooth. It was noticed that regardless of the length, the point of attachment is more important.

This study investigated the effect of force on a maxillary canine using the power arm. The objective was to evaluate the effectiveness of the power arm in bringing about bodily movement for different sites of attachment with differ-ent lengths. To achieve this, finite element analysis was used. The linear-elastic behavior of the tooth, PDL, bone, and power srm were considered.

When force was applied to the power arm during analysis, different col-ors, from blue to red, represented the displacement patterns generated on the tooth. This palette of colors representing the displacement patterns of the tooth is expressed in N/mm2; red represents the positive values suggestive of backward movement (opposite to the direction of force), while blue repre-sents negative values suggestive of forward movement (toward the direction of force). Intermediate colors show overall displacement of teeth.

According to Proffit,8 bodily movement of a tooth requires a moment-to-force ratio between 8:1 and 10:1. To achieve bodily movement, the center of rotation has to be at infinity. During bodily movement of the tooth, the PDL has to be loaded uniformly from alveolar crest to apex. According to Marcotte,9 translation of a tooth occurs when every point on the tooth moves in a parallel straight line in the direction of force. This occurs when the center of rotation of the tooth is at infinity. If the line of action of an applied force passes through the center of resistance of a tooth, the tooth will respond with pure bodily move-ment (translation) in the direction of the line of the applied force.2

When the force application takes place at a distance from the center of resis-tance, the force alone applied to the bracket will not result in translation.14 To achieve translation at the level of the bracket, a couple and force are required equivalent to the force system through the center of resistance of the tooth. A moment-to-force ratio of 10:1 typically produces translation. This type of tooth movement produces uniform stresses in the periodontium. Caputo et al1 reported that an appropriate combination between gable bend angles and force magnitude is needed to produce the moment-to-force ratio for bodily movement.

Pure translation is difficult to achieve, even with perfect fixed appliance mechanics.15 The tipping tendency of a canine under retraction cannot be fully controlled even with close-fitting, heavy wires, and low-friction brackets. Vollmer et al16 found that it is very difficult to achieve pure translation with the realistic canine model.

The above-mentioned authors used bracket systems in their studies to achieve bodily movement. However, Chun et al,4 in conjunction with bracket systems, used bonded power arms attached to a button, which were placed on the cervical portion of the crown, with hooks placed at the same height as the center of resistance of the teeth. These were connected by elastics, allowing the applied force to pass through the centers of resistance. They observed that translation movement took place.

Proffit8 extended the power arm toward the center of resistance, with hooks integrated into the brackets, which can be used to shorten the moment arm and thereby decrease the amount of tipping when elastics or springs are used to slide teeth mesiodistally along an archwire.



Smith and Burstone2 reported that if a hook is positioned in such a way that its height is at the center of resistance, an elastic force to the hook will translate the tooth, even though the hook itself is attached to the bracket.

An extensive search through the literature revealed that the use of the pow-er arm without bracket systems to achieve bodily movement has not been attempted. All earlier studies used the power arm with the bracket system and concluded that if the length of the power arm is extended to the level of the center of resistance, it brings about bodily movement regardless of the site of attachment.

Also, evaluation of the efficacy of the power arm in achieving bodily move-ment by varying its length and the site of attachment at the same time was not possible earlier, probably due to a lack of advanced techniques. However, the emergence of finite element analysis has now made it feasible to simulate situ-ations where the length (both in the vertical and horizontal directions) of the power arm can be changed along with its site of attachment, so the effect of the power arm can be studied in various situations.

Two situations were simulated: (1) attachment at three different areas of the crown of the tooth (incisial, middle, and cervical thirds) but extending to the cen-ter of resistance, and (2) a power arm of different vertical lengths (2 mm above and 2 mm below the center of resistance) attached at three different areas.

In the first situation in this study, bodily movement of 0.008 mm was achieved when the power arm was attached at the incisal third of the crown. It was observed that the amount of bodily movement achieved at this site of attachment did not vary when the vertical length of the power arm was varied. The three levels were at the center of resistance, 2 mm above the center of resistance, and 2 mm below the center of resistance.

The power arm was attached at the middle third of the crown of the tooth, and a force of 1 N was applied on the power arm at different levels in relation to the center of resistance. In the present study, 0.012 mm of bodily movement was achieved at the middle third and remained unchanged at any of the levels of the power arm in relation to the center of resistance when a force was ap-plied to it.

Similarly, 0.013 mm of bodily movement was observed when the power arm was attached at the cervical third of the crown. Here again, the length of the power arm was adjusted in such a way that the force applied on it acted at three different levels. At all three levels, the amount of bodily movement achieved was identical, again reinforcing the fact that the length of the power arm does not bring about differences in tooth movement.

This proves that the amount of bodily movement achieved when the power arm was attached at the middle third of the crown was the same regardless of the height/length of the power arm in relation to the center of resistance.

This was made possible by finite element analysis, and it presented a striking revelation in contrast to the other studies2,8 that reported that bodily move-ment of teeth was achieved only when the power arm was positioned in such a way that its height was at the center of resistance.

One study4 reported that bodily movement took place when a bonded power arm was placed on the third of the crown with its height at the center of resistance of the tooth, similar to the above-mentioned situation.

From the present study, it can be argued that bodily movement can be achieved regardless of the length of the power arm (on the crown), not neces-sarily at the level of the center of resistance of the tooth (Fig 19). However, max-imum bodily movement was observed when the power arm was attached at the cervical third of the crown (0.013 mm) in comparison to middle (0.012 mm) and incisal (0.008 mm) thirds. The results obtained from this study suggest that the length of the power arm used was inconsequential in bringing about



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bodily movement. A force applied at the bracket level during orthodontic treatment would be sufficient to bring about bodily movement of the tooth without necessarily incorporating a power arm. However, the amount of bodily movement varies depending on the point of attachment.

CONCLUSION

The attachment of the power arm at the cervical third brought about maximum bodily movement, followed by the middle and incisal thirds. Variation in length of the power arm at different sites of attachment did not bring any change in the outcome. Thus, the point of attachment is critical in bringing about bodily movement.

REFERENCES

Fig 19 Diagram showing the power arm on the tooth.

1. Caputo A, Chaconas SJ, Hayashi RK. Photo elastic visualization of orthodontic forces during canine retraction. Am J Orthod 1974;65:250–259.

2. Smith RJ, Burstone CJ. Mechanics of tooth movement Am J Orthod 1984;85:294–307.

3. Burstone CJ, Nagerl H, Becker B, Kubein-Messenburg D. Centers of rotation with transverse forces: An experimental study. Am J Orthod Dentofacial Orthop 1991; 99:337–345.

4. Chun YS, Woo YJ, Row YC. Use of bonded power arms for interdental space closure. J Clin Orthod 2001;9:539–543.

5. McGuinness NJ, Wilson AN, Jones ML, Middleton J. A stress analysis of the peri-odontal ligament under various orthodon-tic loadings. Eur J Orthod 1991;13:231–242.

6. Puente MI, Galban L, Cobo JM. Initial stress differences between tipping and torque movements. A three dimensional finite element analysis. Eur J Orthod 1996; 18:329–339.

7. Cobo J, Arguelles J, Puente M, Vijande M. Dentoalveolar stress from bodily tooth movement at different levels of bone loss. Am J Orthod Dentofacial Orthop 1996;110:256–262.

8. Proffit WR. Contemporary Orthodontics, ed 3. St Louis: Mosby, 2000:341–342.

9. Marcotte MR. Biomechanics in Ortho-dontics. Burlington, Ontario: BC Decker, 1990:10–12.

10. Wheeler SM. Dental Anatomy, Physiology, and Occlusion, ed 8. St Louis: Saunder, 195–201.

11. Coolidge ED. The thickness of human periodontal membrane. J Am Dent Assoc 1937;24:1260–1270.

12. Tanne K. Stress induced in the periodontal tissue at the initial phase of the applica-tion of various types of orthodontic force: Three-dimensional analysis by means of the finite element method. J Osaka Univ Dent Soc 1983;28:209–261.

13. Geramy A. Alveolar bone resorption and the center of resistance modification (3-D analysis by means of the finite ele-ment method). Am J Orthod Dentofacial Orthop 2000;117:399–405.

14. Nanda R. Biomechanics in Clinical Or-thodontics. Philadelphia: WB Saunders, 1997:2–9.

15. McGuinness N, Wilson AN, Jones M, Middleton J, Robertson NR. Stresses induced by edgewise appliances in the periodontal ligament: A finite element study. Angle Orthod 1992;62:15–21.

16. Vollmer D, Bourauel C, Maier K, Jager A. Determination of the centre of resistance in an upper human canine and idealized tooth model. Eur J Orthod 1999;21:633–648.

17. Proffit W. Contemporary Orthodontics, ed 4. St Louis, Mosby: 2007.

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Scientific Innovation · Scientific Innovation 318 ORTHODONTICS The Art and Practice of Dentofacial Enhancement 1Senior Professor, Department of Orthodontics, Yenepoya Dental College,