Optimizing the design of preactivated titanium T-loop springs with

TECHNO BYTES

Optimizing the design of preactivated titanium T-loop springs with Loop software Renato Parsekian Martins,a Peter H. Buschang,b Lidia Parsekian Martins,c and Luiz Gonzaga Gandini Jrc Araraquara, Brazil, and Dallas, Tex A TMA (Ormco Corp, Glendora, Calif) T-loop spring (TTLS), preactivated with a gable bend distal to the loop, holds promise for producing controlled tipping of the canines and translation of the posterior segment. However, there is currently no consensus as to where the preactivated gable bend or the loop should be placed, what the height of the loop should be, or how the interbracket distance changes the moments produced. Using the Loop software program (dHal, Athens, Greece), we systematically modified a .017 ⫻ .025-in TTLS (10 ⫻ 6 mm) that was preactivated with a 45° gable bend distal to the loop, and simulated the effects. As the gable bend was moved posteriorly, the moment increased at the posterior bracket more than it decreased at the anterior bracket. As the loop was brought closer to the anterior bracket, the posterior moment decreased at the same rate that it increased anteriorly. As the loop was increased in size, the moments increased both posteriorly and anteriorly. As the interbracket distance increased, the posterior moment decreased, and the anterior moment remained constant. We concluded that the size of the loop should be slightly increased, to 10 ⫻ 7 mm, and it should be placed 2 mm from the anterior bracket, with a preactivation bend of 45°, 4 to 5 mm from the posterior bracket (after 4 mm of activation). (Am J Orthod Dentofacial Orthop 2008;134:161-6)

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artial or en-masse retraction of anterior teeth with segmental mechanics offers more control and predictability than continuous arch mechanics. The advantages of using 2 brackets for retraction (auxiliary tube of the molar and the canine or vertical tube crimped on the anterior segment) rather than several brackets include greater interbracket distance (IBD), simpler planning, greater control of the force, and the possibility of using differential moment mechanics.1 Although there are only 2 brackets, careful planning is needed to determine the force system required. Because the system is statically indeterminate, it cannot be easily described. A .017 ⫻ .025-in TMA (Ormco Corp, Glendora, Calif) T-loop spring, (TTLS) has been proposed for group A anchorage control in a 2-bracket system.2,3 The 10 ⫻ 6-mm TTLS is displaced anteriorly to produce controlled tipping (less moment) and preactivated posteriorly with a gable bend to produce translaa

Assistant professor, FAEPO/UNESP and FAMOSP/GESTOS, Araraquara, São Paulo, Brazil. Professor, Baylor College of Dentistry, Dallas, Tex. c Professor, Faculdade de Odontologia de Araraquara, UNESP, Araraquara, São Paulo, Brazil. Supported by CAPES/Brazil. Reprint requests to: Renato Parsekian Martins, Faculdade de Odontologia de Araraquara, UNESP, Araraquara, São Paulo, Brazil; e-mail dr_renatopmartins@ hotmail.com. Submitted, November 2006; revised and accepted, April 2007. 0889-5406/$34.00 Copyright © 2008 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2007.04.034 b

tion (more moment). The moment to force (MF) ratios recommended for controlled tipping and translation are 7/1 and 10/1, respectively.4-7 Importantly, the recommended values (which reflect the distance between the line of application of force and the tooth’s center of resistance in the experimental model analyzed) are too high for protrusive canines with crowns inclined mesially. Intrusive forces with protrusive canines further reduce the MF ratio required for any kind of movement.8 The 10/1 MF ratio recommended for producing translation of the posterior teeth might also be too high, since the posterior teeth are shorter and wider than the canines. This locates the centers of resistance closer to the bracket (which is also more apical with auxiliary molar tubes) than the center of resistance of the canines. Vertical loops9 and symmetrical designs of the TTLS10-12 have been well analyzed in the literature; however, asymmetrical designs have not been as widely studied. Although asymmetrical TTLS has been widely used in a 2-bracket system for retraction and the effects of a gable (V) bend between 2 brackets in a straight wire have been reported, there is no consensus about where this gable bend should be placed with a TTLS.13,14 Assuming a 23-mm interbracket distance, a gable bend below the posterior extremity of the loop (with 4 mm of activation) is located approximately halfway between the 2 brackets. In this position, the TTLS produces higher moments 161

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Fig 1. Changes of the MF ratios at the anterior and posterior brackets, separated by an IBD of 23 mm, produced by the displacement of the gable bend distally by increments of 1 mm from a position below the distal horizontal extremity of the loop (located 10 mm from the posterior bracket).

anteriorly than posteriorly. This is an inappropriate force system for retraction with group A anchorage. To determine the optimal force system for the TTLS, clinicians need to understand the effects of changing the springs’ physical characteristics (ie, location of the gable bend, height of the TTLS, and so on). Because patients’ tooth sizes vary, it is also important to understand how the IBD affects the force system. Loop software (dHal, Athens, Greece) predicts the forces and moments that a spring produces at the level of the brackets.15,16 It can be used to evaluate existing springs and plan future designs and modifications. This study will demonstrate the application of Loop software to the TTLS,2 modified and preactivated according to Marcotte3,17 (group A anchorage) to maximize its design. Our specific aims were to evaluate the effects of anteroposterior gable bend displacement, loop height, anteroposterior position of the loop, and different IBD. Our findings show that, as the bend is moved posteriorly (ie, as the V distance decreases), the MF ratio at the posterior bracket increases substantially more than the MF ratio decreases anteriorly (Fig 1). More specifically, the posterior ratio increases approximately 3 times as much as the anterior ratio decreases, regardless of how much the bend moves. The ratios increase more at the posterior bracket because there is less wire behind the bend; this makes it stiffer and less flexible. Although moving the

bend backward increases the MF ratio posteriorly, there is a trade-off because of loss of moment anteriorly; this could lead to uncontrolled tipping. Maximizing the MF ratios posteriorly could lead to tipping and extrusion of posterior teeth, causing canting of the occlusal plane. The differences between the anterior and posterior moments imply the existence of vertical forces, necessary to achieve equilibrium. In the simulated scenario, the vertical forces, which are in opposite directions on each bracket, shift directions when the gable bend is placed about 8 mm (roughly a third of the IBD) from the posterior bracket. The anterior moment increases when the loop is moved anteriorly. As the loop is moved closer to the anterior bracket (Fig 2), the MF ratio increases anteriorly and decreases posteriorly. This concept has already been reported similarly in a different preactivation.12 For every millimeter that the loop is moved forward, the anterior and posterior MF ratios increase and decrease similarly. Since the loop’s primary deficiency is its relatively low anterior MF ratio, it often helps to place the spring as close as possible to the anterior bracket. The anterior MF ratio stabilizes at about 2.5 mm from the anterior bracket, whereas the posterior ratio continues to decrease. A 2-mm distance from the anterior bracket offers a reasonable position to place the loop clinically. Clinicians can also alter both MF ratios by changing the

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Fig 2. Changes of the MF ratios at the anterior and posterior brackets, separated by an IBD of 23 mm, produced by anterior loop displacement in increments of 1 mm.

MF Ratio

Anterior (Alfa)

Posterior (Beta)

14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 (4 X 10 mm)

(6 X 10 mm)

(7 X 10 mm)

(8 X 10 mm)

Height of the loop Fig 3. Changes of the MF ratios at the anterior and posterior brackets, separated by an IBD of 23 mm, produced by changes only in the loop height by increments of 1 mm, only on the vertical extensions.

vertical aspect of the loop; this effectively increases its size. By maintaining the gable bend in the same place and lengthening only the vertical extensions of the

loops, both MF ratios increase (Fig 3). This can be partially explained by the increase in the amount of wire, which provides more flexibility and less force, that has been added to the system. This was already

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MF Ratio

Anterior (Alfa)

14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Posterior (Beta)

4.5 mm

30 27 25 23 Interbracket Distance (mm)

20

Fig 4. Changes of the MF ratios at the anterior and posterior brackets produced by an increase of the IBD, without modifications of the loop distances and the gable distance from the loop itself.

demonstrated in different designs of TTLSs.10,11 The difference in the MF ratios between the anterior and posterior brackets diminishes as the height of the loop increases, since the posterior MF ratio increases at a slightly greater rate than the anterior. It is reasonable to assume that, as the differences decrease, the vertical forces acting on the system also decrease. However, the anatomy of the vestibule limits the advantages of longer loops, since excessive loop height will impinge on soft tissue. If the bend maintains its position relative to the loop and the IBD is increased by increasing the amount of wire behind the gable bend, the anterior MF ratio remains relatively constant as the IBD increases from 23 to 30 mm (Fig 4). However, the MF ratio at the posterior bracket decreases at a decelerating rate over the same range and approaches zero at 30 mm. This is equivalent to the application of a simple force, without control, such as finger springs produce. By maintaining the same distance from the bend to the distal bracket, as the IBD increases, the force system remains relatively constant. Because the position of the bend produces the greatest effect on the force system, and IBD difference are commonly found among patients, it is clinically important to understand how these 2 components work together to alter the force system (Fig 5). Overall, the relationships between relative IBD and MF ratio resem-

ble those previously described for changing the position of the bend. Relative to the V distance, the effects of different IBDs are small at the anterior bracket, probably because there is no change in the relationship between the loop itself and the anterior bracket. The effects are larger on the posterior bracket because of the increase in flexibility allowed by the greater length of the wire. Inversion of the moments (or the vertical forces) occurs relatively closer to the posterior bracket as the IBD increases. With a large IBD, the gable bend should be placed more distally, if a greater moment is required posteriorly. The Loop software indicates that this specific TTLS used can be optimized by changing the parameters evaluated in this study. First, it is better to place the gable bend relative to the posterior bracket (Fig 5) rather than the spring (Fig 4) because there is less variation of the posterior MF ratio. Placing the spring about 2 to 2.5 mm from the anterior bracket also has clinical advantages, because this position provides the best compromise between the anterior and posterior MF ratios. Although a longer TTLS provides higher anterior and posterior MF ratios, the depth of the vestibule will limit the actual height of the TTLS. Based on our clinical experience, a height of 7 mm appears reasonable for maximizing the MF ratio and minimizing impingement of the vestibule, although longer loops have been proposed.5,15,18 Figure 6 is an

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27 mm (Alfa)

25 mm (Alfa)

23 mm (Alfa)

20 mm (Alfa)

27 mm (Beta)

25 mm (Beta)

23 mm (Beta)

20 mm (Beta)

MF ratio

30 mm (Alfa) 30 mm (Beta)

14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Posterior

Anterior

1 2 3 “V” distance (mm)

4

5

6

7

Fig 5. Changes of the MF ratios at the anterior and posterior brackets at various IBDs produced by the mesial displacement of the gable bend in millimeters from the distal bracket. The loop distance is kept constant at 4.5 mm.

MF ratio

Anterior (Alfa)

Posterior (Beta)

14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1

2

3

4

5

6

7

8

“V” distance (mm) Fig 6. Changes of the MF ratios at the anterior and posterior brackets, separated by an IBD of 23 mm, produced by the mesial displacement of the gable bend in millimeters from the distal bracket. The loop distance is kept constant at 2 mm, and the height of the loop is 7 x 10 mm.

example of such a spring, illustrating the changes in MF ratios on both anterior and posterior brackets as the gable bend is moved along the IBD. We suggest that the gable bend should be positioned about 4 to 5

mm from the posterior bracket with a TTLS of the group A anchorage. Although this is an acceptable configuration of the TTLS, other factors alter the system of forces, including preactivations in other

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areas of the spring, the horizontal limits of the loop, and the deactivation of the spring with movement. Clinicians should consider all of these dynamic factors when using this TTLS. We thank Larry White and Rodrigo Viecilli for their contributions to this article. REFERENCES 1. Burstone CJ. Rationale of the segmented arch. Am J Orthod 1962;48:805-22. 2. Burstone CJ. The segmented arch approach to space closure. Am J Orthod 1982;82:361-78. 3. Marcotte MR. Biomechanics in orthodontics. Philadelphia: BC Decker; 1990. 4. Burstone CJ, Pryputniewicz RJ. Holographic determination of centers of rotation produced by orthodontic forces. Am J Orthod 1980;77:396-409. 5. Gjessing P. Biomechanical design and clinical evaluation of a new canine-retraction spring. Am J Orthod 1985;87:353-62. 6. Tanne K, Koenig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94: 426-31. 7. Kuhlberg A. Space closure and anchorage control. Semin Orthod 2001;7:42-9.

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8. Melsen B, Fotis V, Burstone CJ. Vertical force considerations in differential space closure. J Clin Orthod 1990;24:678-83. 9. Faulkner MG, Lipsett AW, el-Rayes K, Haberstock DL. On the use of vertical loops in retraction systems. Am J Orthod Dentofacial Orthop 1991;99:328-36. 10. Faulkner MG, Fuchshuber P, Haberstock D, Mioduchowski A. A parametric study of the force/moment systems produced by T-loop retraction springs. J Biomech 1989;22:637-47. 11. Burstone CJ, Koenig HA. Optimizing anterior and canine retraction. Am J Orthod 1976;70:1-19. 12. Kuhlberg AJ, Burstone CJ. T-loop position and anchorage control. Am J Orthod Dentofacial Orthop 1997;112:12-8. 13. Ronay F, Kleinert W, Melsen B, Burstone CJ. Force system developed by V bends in an elastic orthodontic wire. Am J Orthod Dentofacial Orthop 1989;96:295-301. 14. Burstone CJ, Koenig HA. Force systems from an ideal arch. Am J Orthod 1974;65:270-89. 15. Viecilli RF. Self-corrective T-loop design for differential space closure. Am J Orthod Dentofacial Orthop 2006;129:48-53. 16. Halazonetis DJ. Design and test orthodontic loops using your computer. Am J Orthod Dentofacial Orthop 1997;111:346-8. 17. Marcotte MR. Personal communication to R.P. Martins, January 30, 2003. 18. Siatkowski RE. Continuous archwire closing loop design, optimization, and verification. Part I. Am J Orthod Dentofacial Orthop 1997;112:393-402.