opus loop

Continuous arch wire closing and verification. Part H

loop design, optimization,

Raymond E. Siatkowski, DMD Akaroa, New Zealand

A systematic approach to closing loop design for use in continuous arch wires was presented in Part I. The design process used Castigliano's theorem to derive equations for moment-to-force ratio (M/F) in terms of loop geometry. The equations were used to optimize designs by optimizing M/F to produce tooth movement via translation. Further refinements were performed by use of finite element simulations of designs. In Part II the predicted results are verified experimentally. The result of this process is a new design, the Opus loop, which is capable of delivering a nonvarying target M/F within the range of 8.0-9.1 mm inherently, without adding residual moments by twist or bends (commonly gable bends) anywhere in the arch wire or loop before insertion. The resulting precise force systems delivered with nonvarying M/F can move groups of teeth more accurately to achieve predetermined anteroposterior treatment goals for esthetics and/or stability. The experimental results show that the loops must be bent accurately to achieve their design potential. The negative impact on M/F of various dimensional changes to the loop design are presented. Experimental data is presented illustrating the improved performance of the new design over standard available designs. Suggested applications of the design for varying anchorage requirements are presented, along with a case report in which rigorous protraction requirements were met. (Am J Orthod Dentofac Orthop 1997;112:487-95.)

T h e systematic theoretical derivation of a new loop design, the Opus 70 loop (Fig. 1), was presented in Part I of this article. The design goal was to produce a closing loop capable of delivering an inherent M/F of between 8.0-9.1 ram, the range necessary to achieve, translatory movement of groups of teeth when a continuous arch wire is used.

Part II continues the process with experimental verification of the design criteria via load, displacement, and moment measurements of actual samples of the loop. Clinical applications for the loop design in continuous arch wires and a case report are presented.

Systems for measuring uniplanar forces, moments, and displacements for orthodontic closing loops have been developed by Solonche et al. 1 and Gjessing. 2 Extension to measure these in all three p lanes of space were developed by Faulkner et al? and Drescher et al. 4 The latter are complex systems that are beyond the needs of this study. Gjessing's system 2 is well suited to the study's requirements and was replicated in concept.

Supported by a grant from the American Association of Orthodontists Foundation. Reprint requests to: Dr. Raymond E. Siatkowski, P. O. Box 118, Akaroa, New Zealand. Copyright © 1997 by the American Association of Orthodontists. 0889-5406/97/$5.00 + 0 8/1/77119

MATERIAL AND METHODS

Test runs of the various loops were performed on the experimental apparatus. Siamese twin brackets, 0.018 × 0.025 inch, were epoxied to an aluminum bracket mount threaded into the load cell (BL32!, Sensotec, Columbus, Ohio) and to the moment transducer. The load cell measures pure force and is insensitive to moments. The moment transducer, using four strain gages in a 45-degree rosette (EA-13-250TK- 350LE, Measurements Group, Inc., Raleigh, N.C.), is insensitive to applied force and measures pure moment. Activation is performed by the digital micrometer (350- 712-10, Mitutoyu, Paramus, NJ), transmitted to the load cell end via a swivel joint with no vertical play to a square rod, which slides through a nonstick resin-lined square barrel. The moment transducer can twist hori- zontally, but its center is constrained from moving vertically. The digital micrometer therefore measures displacement and provides loop activation.

The system was calibrated by application of known forces by dead weights up to 500 gm to the load cell and known couples up to 2400 gm-mm to the moment transducer. Both were linear and insensitive to temperature changes within a tested range of 15 ° to 30 ° C.

Closing loops made in stainless steel and TMA wire (Ormco Corp., Glendora, Calif.) were tested. Wire sizes were 0.017 × 0.025 inch in TMA and primarily 0.016 × 0.022 inch in stainless steel, although some tests were performed with 0.018 × 0.025 inch s.s. wire. Inter-

487

488 Siatkowski American Journal of Orthodontics and Dentofacial Orthopedics November 1997

I_ --lOmm -1

lm__mt ( 1 ~

_1

T lOmm

--~ ~ -Up to 1.5mm

Fig. 1. Dimensions of standard Opus 70 loop.

Table I. Activation (ram) at 100 gm and M/F when centered and off-centered at 13 mm IBD for various loops

Activation M/F (mm) M/F (ram) Loop (mm) centered @centered

8 mm Vertical 0.9 3.9 6.7 10 mm T 1.7 4.6 7.7 Opus 90 1.6 5.8 8.6 Opus 90 X-legs 2.5 5.1 6.2 Opus 70 1.6 5.5 8.7

0.017X.025 TMA 3.1 5.5 8.4 0.018X.025 ss 1.0 5.6 8.7 7 mm high 1.2 3.0 5.9 12 mm long 2.0 5.5 8.7

64 degrees 2.0 4.8 7.2 8 mm long 1.5 3.0 8.0 End 9 mm high 1.6 5.5 7.6

Formed in 0.016 x 0.022 inch s.s., 0.018 × 0.025 inch s.s., and 0.017 × 0.025 inch TMA; 13 mm IBD, helix end 100 gin; 0.016 × 0.022 ss unless otherwise noted; 10 mm height and length unless otherwise noted.

bracket distance (IBD) was varied in 2 mm steps between 13 and 7 mm, simulating space closure. Each loop was tested at the center of the IBD and then off-centered with one vertical leg 1.5 mm from the moment transducer bracket.

A test run consisted of incremental activations, dis- placing the load cell end, measuring displacements (loop activations) for applied loads of 50, 100, 150, and 200 gm; simultaneous measurements of activation force were made via the load cell at its end and moment at the other end. The loop was then reversed and all test runs were repeated to measure the moment at the loop's other end so that M/F could be determined at both brackets for each test. Each test run was repeated at least once. If values differed, that run was repeated yet again and calculated mean values were used.

Moment measurements were made by use of a 10 mm T-loop in 0.016 × 0.022 inch s.s. wire in the off-centered position with a 13 mm IBD loaded to 100 gm to check measurement variation. Repeated 12 times, the resulting

M/F variation had a standard deviation of 0.10 mm with a maximum range of +0.14/-0.16 mm.

RESULTS Experimental Findings

A summary of initial findings for various loops tested in the experimental apparatus at 13 mm interbracket distance and 100 gm activation force is shown in Table I. The M/F was first measured with the loops centered in the interbracket distance. No loop generated M/F within the desired range of 8.0 through 9.1 mm in this position without gable bends. When placed at 1.5 mm from the anterior bracket, the helix end of non-gabled Opus loops could achieve the desired M/F range.

The dimensions of the standard Opus 70 loop are shown in Fig. 1. Wire size and Young's modulus have little effect on M/F although both have major impact on load-deflection rate, F/D (see activation for 100 gin, Table I). The greatest negative impact on M/F in the off-centered position is crossing the loop legs (Opus 90 vs. Opus 90 X-legs: 8.6 falls to 6.2) and decreasing loop height (Opus 70 vs. Opus 70, 7 mm high: 8.7 to 5.9 mm). Decreasing the loop angulation decreases M/F (Opus 70, 12 mm long vs. 12 mm long at 64 degrees: 8.7 to 7.2 ram). Dropping the anterior end of the loop decreases M/F (Opus 70 vs. Opus 70, end 9 mm high: 8.7 to 7.6 ram). Increasing loop length beyond 10 mm does not increase M/F, contrary to theoretical prediction (Opus 70 vs. Opus 70, 12 mm long) but decreasing loop length decreases M/F (Opus 70 vs. Opus 70, 8 mm long: 8.7 to 8.0 mm). Placing "lingual" comfort bends in the anterior of the loop, putting the end out of plane, does not degrade M/F or F/D.

Neither the 8 mm vertical loop with one 3.5 mm diameter helix nor the 10 mm high, 10 mm long T-loop can achieve the desired M/F range in any

American Journal of Orthodontics and Dentofacial Orthopedics Siatkowski 489 Volume 112, No. 5

20.8 @

10

5

E E

-5

m

m

w

\

e -

50 100 150 200 I I ~ ~ FORCE (g)

range

= ._

o

-- OPUS 70

=_ ~ - -~ 10mm

o ~ 8mm

Fig. 2. M/F at each bracket as a function of activation force for Opus 70 loop without residual moments and T-loop and standard vertical loop with residual moments via symmetrical gable bends. All loops off-centered in 13 mm interbracket distance in 0.016 × 0.022 inch s.s. wire. Almost identical values are obtained for Opus 70 loop when tested in 0.018 × 0.025 inch s.s. wire and 0.017 × 0.025 inch TMA.

position without inducing residual moments (for example, via gable bends). When symmetric bends are placed in the loop legs sufficient to generate M/F within the desired range when positioned 1 to 1.5 mm from the anterior bracket with 100 gm activation, as shown in Fig. 2, both of these loops cannot maintain M/F within the desired range throughout all activation force levels, although the T-loop per- forms significantly better than the vertical loop. In contrast, the Opus 70 loop maintains M/F within the desired range at all activation force levels without residual moments (again, there is little difference between Opus 70 loops with 0.016 × 0.022 inch s.s., 0.018 × 0.025 inch s.s., and 0.017 × 0.025 inch TMA; the differences are too small to be apparent on the vertical scale of Fig. 2).

The M/F at the posterior end is also shown in Fig. 2. The gabled T and vertical loops generate

posterior moments that are in the same direction as the moments at the anterior ends, whereas the Opus 70 loop's posterior moment is in the opposite direction (note that the loops are all positioned in the off-centered, not centered, position in the IBD). All loops here when in a continuous arch have sufficient vertical stiffness to inhibit intrasegmental expression of the vertical forces generated by unequal anterior and posterior moments (the Opus 70 loop has 0.5 mm vertical deflection for 100 gm vertical force in 0.016 × 0.022 inch s.s. and 0.7 mm in 0.017 × 0.025 inch TMA). Therefore, the sum of the moments have the potential to express as occlusal plane change of the entire arch (with the caveat that if gabled loops are left tied in for a very long time, the anterior and posterior segments will eventually begin to form two occlusal planes at an angle ap- proaching the total of the gable bends' angles). The

490 S ia t kowsk i American Journal of Orthodontics and Dentofacial Orthopedics November 1997

n

10

-5

• " - - - ~ ' - - ~ I Desired range ¢-

o

e -

5

I I I B D ( m m ) 5 15

e OPUS 70 o~-O10mm T-loop no gable bends

Fig. 3. M/F at each bracket as a function of interbracket distance (IBD) for off-centered 0.016 inch x 0.022 inch s.s. Opus 70 and T-loops without residual moments for 100 gm activation force.

2000

1500

A

E

i 1000

5 0 0

0 0

- lw° tnhg aTbll; ~

I I I i I 50 100 150 200

FORCE (g)

70

Fig. 4, Total moments expressed by off-centered 0.016 × 0.022 inch s.s. Opus 70 and gabled T-loops as a function of activation force for 13 mm interbracket distance.

1 0 -

5

E

LI.

0

-5

° o °

13

°°"°t °° " ° D , ° .

" ' . , ' ' ' = , . [ 3 , , o . . . , . o 0 1 1

°0 , °° . ° . . 193

I Desired range

E

e-

5

I I I , [ FORCE(g) 50 100 150 200

Fig. 5. M/F at each bracket as a function of activation force while varying IBD (13, 11,9, 7 mm) for off-centered 0.016 x 0.022 inch s.s. Opus 70 (without residual moments, by definition).

sum of the moments are additive for the T and vertical loops, increasing the total moment attempt- ing to change occlusal plane, whereas the Opus 70 loop total moment is the difference between the moments at the two ends they being in opposite directions, decreasing the tendency to change occlusal plane. On the basis of the clinical observation that, when intruding mandibular incisors using a

American Journal o f Orthodontics and Dentofacial Orthopedics S i a t k o w s k i 4 9 1

Volume 112, No. 5

E ,E 1000 03

I - z uJ

O

. - - I <~ I.- O 5 0 0 I--

1500 -

1 5 0 g

~ = ~ / / ~ 1 0 0 g

~ 50g

] ~ , , , I , , , , I , , , , I

0 5 10 15 IBD (mm)

Maximum

Fig. 6. Total moment expressed by off-centered 0.016 x 0.022 inch s.s. Opus 70 loop as a function of interbracket distance while varying activation force.

base arch s with 40 gm vertical force with the remain- ing mandibular teeth connected by a continuous arch stepped gingivally to the incisors, no detectable change to the posterior occlusal plane occurs, an arbitrary safe maximum total moment of 1200 gm-mm (40 gm × 30 mm, incisor to molar distance) seems prudent, and--although perhaps overly con- servative--is used hereinafter.

A comparison of the T and Opus 70 loops when neither have induced residual moments but are off-centered is shown in Fig. 3 for varying interbracket distance with 100 gm activation force. Only the Opus 70 can achieve M/F within the desired range, and it does so at all interbracket distances.

The total moment for the off-centered and gabled T-loop compared with the Opus 70 loop for varying activation force levels is shown in Fig. 4 for an interbracket distance of 13 mm. The Opus 70 loop exceeds the "safe" maximum beyond 170 gm activation whereas the gabled T-loop exceeds it beyond 110 gin. Fig. 2 shows that the gabled T-loop exceeds the desired M/F range at less than 80 gm activation; the gabled T-loop has a very narrow range of acceptable performance (80-110 gm in s.s. at 13 mm IBD) when used in a continuous arch.

The M/F for the off-centered Opus 70 loop as a function of activation force, varying interbracket

T a b l e II. Activation (mm) necessary to achieve various activation forces for the Opus 70 loop formed in 0.016 × 0.022 s.s., 0.018 x 0.025 s.s., and 0.017 × 0.025 inch TMA wires

Force (gin)

Activation (ram)

0.016 × 0.022 s.s. 0.018 × 0.025 s.s. 0.017 x 0.025 TMA

50 0.8 0.5 1.8 100 1.6 1.0 3.1 150 2.4 1.5 4.4 200 3.1 2.0 5.6 250 3.8 2.5 7.0

distance in four 2 mm steps between 13 and 7 mm simulating space closure, is shown in Fig. 5. It is only beyond 150 gm at 7 mm IBD, the end of space closure, that the anterior M/F falls outside the desired range. The total moments from Fig. 5 are summed at each position and shown in Fig. 6. The total moment exceeds the safe maximum only when the activation force is 200 gm and the IBD is greater than 9 mm. Activation force levels above 170 gm may need to be avoided at the beginning and the very end of space closure with this loop.

Last, the activation distance needed to achieve various activation force levels for an Opus 70 loop of standard dimensions for the three wire types used to form the loops tested are shown in Table

492 S ia t kowsk i American Journal of Orthodontics and Dentofacial Orthopedics November 1997

a) Max imum Anchorage Inc isor retract ion after canines retracted

Force: 100-150 g/side Max imum act ivat ion (ram)

0.016 x 0.022 S.S. 0.018 x 0,025 S.S. 2.5 1.5

0.017 x 0.025 TMA 4.5

= = _ _

b ) Moderate A n c h o r a g e Anter ior retract ion and poster ior prot ract ion

Force: 150-200 g/side Max imum act ivat ion (mm)

0.016 x 0.022 s.s. 0,018 x 0.025 S.S. 3.0 2.0

0.017 x 0.025 TMA 5.5

__ =

C ) Minimal Anchorage Poster ior prot ract ion

Force: 75 g/side + CI Ill elastics (150 g/side) Max imum act ivat ion (mm)

0.016 x 0.022 S.S. 0.017 x 0.025 TMA 1.0 2.5

16 ° twist to generate l ingual root torque on incisors on ly

Fig. 7. A, Maximum anchorage retraction situations: suggested closing loop placement and maximum activations. B, Moderate anchorage situations: suggested closing loop placement and maximum activation distances. C, Minimal anchorage situation (posterior protraction only required), 0.018 inch slot: suggested closing loop placement and maximum activation distances when space exists between canines and premolars. If space were distal to lateral incisors, loop would be placed just distal to lateral incisors.

II. Because there are no residual moments induced in this loop via gable or other bends or twists, the loop's neutral position, 6 the position at which there is no activation force exerted, is exactly the spacing of the vertical legs as bent. If the horizontal spacing between the vertical legs is 1 mm when the arch wire is formed, there will be no activation force when that spacing is 1 mm after the arch wire is tied in. It is therefore possible to achieve precisely the defined activation force desired by simply increasing that horizontal spacing by the activation amount in millimeters shown in Table II. This is in contradistinction to loops requiring residual moments, as shown by Burstone and Koe- nig, 6 where it is extremely difficult for the clinician to

judge the amount of activation force being delivered after the arch wire is tied in.

DISCUSSION

On the basis of these findings, suggested applications of Opus closing loops for various situations are shown in Fig. 7. It is appropriate to begin with a straight wire and bend the arch wire in a torquing turret to achieve incisor axial inclination control by inducing wire twist ("lingual root torque") just enough to eliminate labiolin- gual wire-bracket play in the incisor brackets. The amount of such twist is dependent on the wire/ bracket sizes and slot torque used 7 and should be removed distal to the Opus loop (leaving the wire


Fig. 8. A, Opus 70 closing loop arch wire before insertion. Note apical anterior comfort bend. B, Opus 70 closing loop arch wire tied in but not activated. The 10 mm high loop does not intrude excessively into mucobuccal fold with standard bracket heights. Clinically, the loop allows better oral hygiene of adjacent teeth than a vertical loop at the same location. It is also more comfortable for the patient because the apical leg has more net area than a vertical loop, to deflect adjacent buccal soft tissues instead of tending to dig into those tissues. C, After activation for anterior retraction and posterior protraction.

twist in place while forming closing loops provides a lingual comfort cant to the loops). If the loops are located distal to the canines, wire twist should be removed mesial to the canines to prevent inappropriate canine lingual root torque (Fig. 8). A torquing turret has been designed for use with TMA wire. s Maximum incisor twist is appropriate for posterior protraction (Fig. 7, C).

In Figs. 7 and 8, suggested maximum activation force is achieved by the suggested maximum activation distance for the three wire types tested. The desired M/F will be delivered throughout the activation range and anchorage requirements will be met as long as the suggested maximum activation distances are not exceeded. This simplifies the activation regimen considerably over previously available closing loops, and the clinician can safely increase the appointment intervals during space closure without concern for loss of anchorage control as long as the patient can be trusted to report

any damage to appliances if it occurs between appointments.

Although less so than with other closing loop designs, Opus loops do have the potential to steepen the cant of occlusal plane in the maxillary arch and flatten it in the mandibular arch. Although steepen- ing occlusal plane can be useful for overtreatment of Class III relationships (and flattening occlusal plane for Class II relationships), that potential should be monitored for possible intervention. Such intervention could be reducing maximum activation force levels or using an occipital headgear with short and high outer bows to generate a moment tending to flatten maxillary occlusal plane.

The configuration for patients with maximum posterior anchorage requirements is shown in Fig. 7, A. For the most severe anchorage required to achieve treatment goals, second molars, if available, could be included with the posteriors and/or a Combi headgear used. For less severe or moderate

494 S ia t kowsk i Amel~can Journal of Orthodontics and Dentofacial Orthopedics November i997

D t

Fig. g. A, Buccal view of unactivated protraction loop (0.018 × 0.025 inch s.s. Opus 90) tied in 0.022 inch slots. The mandibular arch wire is 0.018 x 0.025 inch s.s. Loop height and length are 10 mm and helix diameter is 1 mm. Incisor segment has 16 degrees of lingual root torque. B, Frontal view of Opus 90 protraction loop, activated for 75 gm with 150 gm Class III elastics (worn 24 hrs/day and changed daily) in place. Activation was 1 mm every 5 weeks. C, Frontal view at debonding. I), Superimposition: before protraction (solid lines) and end of treatment (dotted line: change noted).


anchorage, the canines could be incorporated with the anteriors as in Fig. 7, B.

The configurat ion for poster ior pro t rac t ion is shown in Fig. 7, C (for 0.018 inch slot). This si tuation might occur late in t r ea tmen t of a Class I I pa t ient who exhibits more horizontal mandibular growth than originally anticipated, in the mandibular arch when less mandibula r horizontal growth than ant icipated occurs, or in u n c o m m o n situations such as the case repor t to follow. The closing loop arch wire genera tes the momen t s required and some of the pro t rac t ion force. Most of the pro t rac t ion force is genera ted by the large anter ior m o m e n t and by the intermaxil lary elastics to a rigid rectangular arch wire in the opposing arch. Intermaxi l lary Niti closed coil springs capable of delivering 150 gm force can be substi tuted for the elastics. The potent ia l exists for changing occlusal p lane in the opposing arch. Should such cant changes begin to be observed, the intermax- illary force can be reduced.

CASE REPORT

A 20-year old Japanese woman transfer patient previously had impacted maxillary canines extracted near the final stage of treatment with zero overjet but with 3 mm spacing distal to the maxillary lateral incisors bilaterally and the buccal teeth in Class III relationships. The maxillary spaces needed to be closed by protraction of the maxillary posterior teeth with no anterior retraction allowed. Protraction options were protraction headgear, tooth-by-tooth V-bend mechanics, 9 o r en masse protraction using the Opus 90 system of Fig. 9 (0.022 inch slots in place). The Opus 90 option was chosen, protracting four premolars and four molars without retracting four incisors (Figs. 9, A and B). The loop was activated 1 mm every 5 weeks, and the protraction was completed in three visits (Fig. 9, C). Superimposition of a cephalometric radiograph taken at the time of transfer (the beginning of protraction mechanics) with that at the end of treatment (Fig. 9, D) revealed no change in incisor position or inclination or any other structures other than protracted maxillary posterior teeth. 1°

The loop faces posteriorly with crossed legs. The crossed legs reduce the load-deflection rate so that a clinically practical activation of 1 mm produces 75 gm/side using 0.018 × 0.025 inch s.s. wire even though moment magnitudes are somewhat reduced. With legs crossed, the apical portion of the loop faces posteriorly so that the Opus 90 asymmetric moments result in the higher moment being delivered to the incisors.

Current cases in progress with 0.022 inch slots are being treated with 0.019 × 0.025 inch TMA in the Opus 70 configuration. This wire requires 20-degrees incisor twist to eliminate wire-bracket play. An additional 20 degrees of incisor twist may be placed when buccal teeth are being protracted.

CONCLUSIONS

This report presented a systematic approach to closing loop design for use in continuous arch wires by using Castigliano's theorem, then refined, using FEM simulations, and then verified experimentally. The result of this process is a new design, the Opus loop, which is capable of delivering a target M/F within the range of 8.0-9.1 mm inherently, without adding residual moments, so that more precise force systems with nonvarying M/F can be delivered by these closing loops formed in a continuous arch wire. Groups of teeth therefore can be moved more accurately to better achieve predetermined anteroposterior-posterior treatment goals for esthetics and/or stability. The experimental results show that the loops must be bent accurately to achieve their design potential.

Being free of residual moments, the design can produce a true rest period when deactivated and therefore could be used with future technology to produce intermit- tent force systems during space closure.

I gratefully acknowledge the contributions of Ann Hoyle, Philip Tilson, and Dorothy Grigor in the prepara- tion of this report, John Schultz in setting up and per- forming initial FEM simulations while at the Carnegie Mellon University Department of Mechanical Engineer- ing, Derek Barwood and James Hood for assistance in calibrating the experimental apparatus, and Jay Swope for his expertise in setting up the data acquisition for the experimental apparatus.

REFERENCES

1. Solonche DJ, Burstone CJ, Vanderby R. A device for determining the mechanical behavior of orthodontic appliances. IEEE Trans Biomech Eng 1977; BME-24(4): 538-9.

2. Gjessing P. Biomechanical design and clinical evaluation of a new canine retraction spring. Am J Orthod 1985;87:353~62.

3. Faulkner MG, Hay A, Fuchshuber P, Haberstock D. Development of a system for the measurement' of forces and moments created by orthodontic appliances. Proc VI lnt Cong on Expt Mech 1988;384-9.

4. Drescher D, Bouranel C, Thier M. Application of the orthodontic measurement and simulation system (OMSS) in orthodontics. Eur J Orthod 1991;13:169-78.

5. Burstone CJ. Deep overbite correction by intrusion. Am J Orthod 1977;72:1-22. 6. Burstone CJ, Koenig HA. Optimizing anterior and canine retraction. Am J Orthod

1976;70:1-20. 7. Sebanc J, Brantley WA, Pincsak J J, Conover JP. Variability of effective root torque

as a function of edge bevel on orthodontic arch wires. Am J Orthod 1984;86:43-51. g. Siatkowski RE. A new torquing turret for TMA wire. J Clin Orthod 1993;27:609-11. 9. Siatkowski RE. Force system analysis of V-bend sliding mechanics. J Clin Orthod

1994;28:539-46. Addendum: 1995;29:37-8. 10. Engel G, Spoher BM. Cephalometric and visual norms for a Japanese population.

Am J Orthod 1981;80:48-60.

opus loop

Documents