ORIGINAL ARTICLE

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Dapplying different moments to anterior andposterior units. This is proposed in the seg-me 1-3

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48nted arch approach to space closure. Momentsplied to the anterior unit must be sizeable enough tovent buccal movement of the roots; on the other

nd, moments on the posterior unit must be of enoughgnitude to induce translation. The moment-to-forceF) ratios, at the bracket, required for these move-nts have been described in various studies.4-8The application of differential moments induces

ferential stress in the periodontal ligament,9 whichn aid in anchorage control.10 In the segmented archproach to space closure, type A anchorage is estab-hed when the anterior unit (alpha) moves by con-lled tipping and the posterior unit (beta) is keptble with translation, thus using differential stress. Ifcessary, subsequent root movement of the anteriorit and translation of the posterior teeth can berformed.

T-loops are recommended to obtain the necessary

gingival horizontal wire (G dimension), loop height (Hdimension), loop eccentricity, and gable bends to thewire were also studied. G and H dimensions increasethe MF ratio delivered by the loop at the bracket. For aconstant H dimension, the increase of G dimensionapproaches an MF ratio equal to the height of the loop.Another effect of the increase in both G and Hdimensions is the decrease of the loops load-deflectionrate, reducing force variation during deactivation. Theauthors also showed that an off-center T-loop place-ment, close to 1 unit, increases the MF ratio of this unit,decreasing the MF ratio of the opposite unit. Theapplication of angulations to the loops can also increasethe MF ratios in 1 unit; the effect on the opposite unitis a variable that depends on the geometry of the bends.The eccentricity also introduces vertical forces in thesystem, as predicted by static equilibrium.

In Group A anchorage, placement of the T-loopnear the alpha unit and the bends near the beta unit wasoriginally introduced by Burstone.3 In this study, acomposite T-loop made of 0.018-in beta-titanium alloy(TMA) wire was used for the loop part (alpha) weldedto a 0.017 0.025-in TMA wire for the posterior part(beta).

Melsen et al12 studied the effects of vertical forces

bined PhD/orthodontics student.rint requests to: Dr Rodrigo F. Viecilli, Department of Oral Facialelopment, Orthodontics Section, Indiana University School of Dentistry,1 W. Michigan St, Indianapolis, IN 46202; e-mail, rviecill@iuppi.edu.mitted, February 2004; revised and accepted, May 2004.9-5406/$32.00yright 2006 by the American Association of Orthodontists.

:10.1016/j.ajodo.2004.05.025elf-corrective T-loop dpace closuredrigo F. Viecilliianapolis, Ind

roduction: The current approach to measuring T-loochorage does not consider active unit angulations andps during movement introduced by rotation can considethods: In this study, geometric modifications were detth, where there was no movement of the posterior teesults: An optimal beta-titanium alloy 0.017 x 0.025-in Trformed with LOOP software (dHAL Orthodontic Softwterior unit-position effect on the final force system. Thed without geometric correction of the brackets have sigsegmented arch approach to space closure. Conclu

ces were combined to produce an ideal T-loop desigstem. The effects and force systems are estimatesistance, assuming relatively constant behavior of the cehtly from what happens in vivo. The finite elementroducing the geometric corrections should be usedntofacial Orthop 2006;129:48-53)

ifferential tooth movement can be achieved byign for differential

e systems in patients requiring differentialduring space closure. The angulations andmodify the force system acting on the teeth.d during controlled tipping of the 6 anteriors configuring a type A anchorage situation.spring was designed by using a simulation

Athens, Greece) to allow compensation forystems produced by this T-loop spring withnt differences that should be considered in: The effects of steps, angles, and verticalt would provide a more determinate forceon simplified locations of the centers of

of rotation. These simplifications might differd or an accurate spring tester capable ofure a precise force system. (Am J Orthod

ce system to accomplish the objective described

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American Journal of Orthodontics and Dentofacial OrthopedicsVolume 129, Number 1

Viecilli 49ative to the center of resistance of the anterior unit ine A anchorage using a composite T-loop. Estimationthe vertical force moments is important when estab-hing the final design of a loop.

In most studies, the authors have considered force/ment gauges as an experimental method for evalu-

ng force systems in T-loops.3,11,13,14 Others havensidered theoretical approaches. Theoretical simula-ns with computers began almost 30 years ago.15,16e finite element method is a theoretical alternative

loop design evaluation.17 The LOOP softwareAL Orthodontic Software, Athens, Greece) uses a

oretical approach.18,19 Another 3-dimensional soft-re has also accurately evaluated vertical and T-

aped loops.20,21Many different T-loop designs attempt to movements.3,14,22 The force system tables show the force

stem on the anterior unit, assuming space closurecurs on the same plane during movement. Theseles reproduce the actual force system when T-loopsviding symmetric movement are used (type B an-

orage). In this situation, the geometry changes ap-ximately the same amount on each segment, affect-

the neutral position and moments of the loopportionally to bracket positions. This maintains thece system similar to what it would be if the occlusalnes were coincident during movement.The previously published type A T-loop approachesnot consider the geometric changes of angles and

ps between brackets during space closure.3,14 Inse studies, both terminals of the spring tester were

pt on the same plane during measurements.The measurements in this study allow evaluation of

ether geometry changes between brackets couldnificantly affect the force system during the desiredvement. It was hypothesized that angles and steps in

ly 1 unit, such as in type A anchorage cases,nificantly affect the force system. An accurate force

stem for clinical application should consider thisect. LOOP software can simulate the effects of theseometries in the T-loop force system, a simulation thatnnot always be performed with conventional springters.Our ultimate goal was to obtain a T-loop optimizedrotation of the anterior unit. The loop is self-

rrective because, if its force system is measured withth terminals on the same plane, it compensates forstem changes introduced by the bracket geometrydification. To show this compensation, new mea-

rements of the loop were taken simulating what could

a real dynamic clinical environment, rotating the

terior unit during space closure.poofTERIAL AND METHODS

Virtual 0.017 0.025-in TMA T-loops constructedth LOOP software were used. The interbracket dis-ce considered to establish the ideal loop behaviors 23 mm.A detailed description and the reliability of theOP software were shown in a previous study.18 Thetual wire consists of small segments of straight wire2 dimensions (0.25 mm) connected to each other endend. Each segment is considered a long slender beamt bends with the application of forces and moments.

hen a loop is designed and activated, the deflectionults are mathematically calculated for each smallam and extrapolated for the whole wire when it isgaged to the brackets. The material of the segments isumed to behave in the elastic and proportionalge. Only bending moments and forces are consid-d to determine the final force system.Type B symmetric T-loop values obtained by a

ring tester from another study14 and by LOOP soft-re were compared, to confirm relative softwareiability and correspondence with experimental val-s (Table I). For this study, MF ratios are moreportant than absolute values of moment and force.e spring tester used to obtain the experimental resultss also described previously.23For loop construction, the desired force system wasa horizontal force of approximately 150 to 300

ms-force (gf; the force exerted by 1 g of mass inndard Earth gravity, 9.806 m/s2), (2) a posterior MFio of approximately 8.5-11 mm, and (3) an anteriorF ratio of approximately 6-8 mm.

To determine the final loop design, a description ofangulations and steps in the anterior unit during

ace closure was necessary, so that changes in thece system caused by the geometry could be evalu-d by the software in each space-closure position. The

nter of rotation of the anterior unit is estimated to bear the apex of the roots, for a MF ratio of approxi-tely 7. Although small variations in the center ofation are possible with very small variation onterior MF, a medium value was established for thisdy. The MF variation for the posterior unit is baseda center of resistance positioned occlusally when

mpared with the anterior unit.A simulation of anterior segment rotation (Fig 1)

s performed with an orthodontic calculator (Dentalvement Analysis, Libra Ortodonzia, Arezzo, Italy).24ps and angles between anterior (canine bracket) andsterior units were measured at the beginning and endmovement. Then a linear geometry variation for each

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American Journal of Orthodontics and Dentofacial OrthopedicsJanuary 2006

50 Viecillillimeter of movement was assumed for the sake ofplicity.This change in geometry shows that the loop design

ould aim for a force system with small compensa-ns in beta (posterior) and alpha (anterior) MF ratiosring retraction, if we consider that measurements areen with bracket slots on the same plane. This meanst a correction for the changing bracket geometryuires that the alpha MF ratio should decrease with

activation. The MF ratio in beta should increase withactivation.

Several trials for previously published basic loopsigns3,14,22 were evaluated for best performance in

intended force system, considering geometric mod-ations. The trials showed that a loop with goodrking range must be located next to the anteriorachment and have no residual moment and only antivation moment. To provide enough posterior mo-nt, a curved V-bend along the posterior part of thep and a slight opening of the posterior ear werede, initially keeping the same MF in alpha positionssociation). This provides a decrease in alpha MFring deactivation, if both brackets are on the samene during movement. By using this design, the

terior units MF ratioprovided by the loop activa-n moment combined with the posterior curved V-nddecreases with loop deactivation. Moreover,ta MF ratio increases during loop deactivation.

After choosing the basic model, the final loopensions were determined by iteration, optimizingmaximum loop height and gingival extension,

nsidering patient comfort and maximizing the work-range.The T-loop chosen for an ideal activation moment

d a horizontal force has 8 mm of height and 16 mmG dimension and is activated 6 mm. The wire is

ble I. Comparison of experimental values of real T-loop0.025-in TMA wire; loop has 1-mm step between v

nsidered in equilibrium

ivation MF (mm)experimental

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26.4 26.013.9 13.810.3 10.28.2 8.37.0 7.16.0 6.2

F, MF ratio at bracket in alpha position; MF, MF ratio at the brA 0.017 0.025 in.The specific asymmetric loop position was chosen

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intprovide a maximum MF ratio to the anterior unit foractivation of 6 mm. The vertical force moments inpect to the center of resistance of the anterior unitre considered during the iteration process. The an-ior attachment used was a Burstone canine bracketrmco, Glendora, Calif). In most cases, this avoidsrtical force moments at the beginning of the forcestem application, in respect to the center of resistancethe anterior unit. The LOOP software terminals areuivalent to the mesial terminal of the molar tube andtal terminal of the canine bracket. This distance wasto 23 mm.Figure 2 shows the loop dimensions before preactiva-

n bends, and Figure 3 shows the loop with preactivationnds inserted in the posterior unit. Figure 4 depicts theloop activated 6 mm inserted in its terminals, with thepective force system delivered to the teeth.Once the design was defined, force system mea-

rements were taken. First, the software brackets wereintained on the same plane during movement to

1. Controlled tipping of anterior segment for 7 mmace closure. CRes, center of resistance; CRot, centerrotation.

LOOP software values for virtual T-loop, with 0.017legs, so couple of both horizontal forces must be

l MF (mm)software

MF (mm)software

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6.024.3 23.1 61.713.4 12.8 127.09.8 9.5 193.68.0 7.8 258.96.7 6.8 327.95.9 6.1 390.3

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maasure the chosen T-loop force system in 1-mmervals, producing the Table III data. Then the same

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American Journal of Orthodontics and Dentofacial OrthopedicsVolume 129, Number 1

Viecilli 51p was evaluated, modifying the bracket geometrieseach millimeter of movement, according to values inble II. This process produced Table IV data.

SULTS

Table I shows symmetric T-loop data comparison.though the theoretical horizontal forces are highern the experimental, relative values, important fors study, are approximately the same.Table II shows the angulations and steps during

ace closure. The angles and steps are based onntrolled tipping of the anterior segment with a centerrotation located at a medium horizontal position

ove the roots of the 6 anterior teeth. Figure 1 showssimulation of anterior unit rotation. The angles and

ps during movement modify the geometry between2 terminals, affecting the resulting moments on

ch segment. This geometry development progres-ely increases the anterior MF ratio and decreases thesterior MF ratio at the brackets.Table III shows the force system of the T-loop

thout the angles and steps between brackets; this isoriginal approach in the literature to describe T-loop

ce systems. As this table shows, the new loop designn support the development of the geometry betweenments.Table IV shows the force system of the same T-loop

th the geometric correction of brackets. Unlike Table, Table IV values include bracket modificationsuced by controlled tipping, which occurs clinically.ble IV represents the clinical T-loop force systemting on the patients teeth.

SCUSSION

Fig 2. Loop dimensions without preactivation bT-loop length without preactivation bends; IBD,When comparing the values in Table I, we can seet the MF values are similar. Small differences

affbiocurred as expected, because of the mathematicallculations of the software and the standard deviationerent to the error of the spring tester and springnufacturing. LOOP software reports higher forces,previously pointed out by Halazonetis.18 It displayslues higher by 12%, as seen in Table I. This might beorrection factor for the force system tables, in which88% horizontal force value has been included.In the T-loop force system, the geometric modifi-

tions will tend to significantly increase the momentthe anterior unit and decrease the moment on the

sterior unit. Moreover, these geometric changes will

G, T-loop apical wire; H, T-loop height; L,acket distance.

3. Loop passive position inserted in beta unit withactivation bends. Radius of curvature decreasesar beta unit. Small opening of distal ear of loop alsoreases moment in beta and decreases force level for-mm activation. IBD, interbracket distance.oc

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American Journal of Orthodontics and Dentofacial OrthopedicsJanuary 2006

52 Viecilliflection rate of the system will decrease. Clinically,values of Table II can help identify the position ofcenter of rotation. For instance, when the movement

proaches uncontrolled tipping, angulations and stepsve a higher rate of increase per millimeter of spacesure. If the movement approaches translation, fewer

gulations and steps are observed. These examplesggest that loop adjustment might be necessary toep the center of rotation at the desired position.

When a starting MF of 8.7 on the posterior unit, asown in Table IV, still does not provide translation, itassumed that the distribution of periodontal stress on

posterior teeth will still be more uniform than in theterior unit, because the canines slightly displace thenter of resistance apically.

As seen in Table III, this loop provides a small rateincrease in beta MF ratio at the beginning of

activation and an even smaller rate of decrease inha moment during deactivation, making it ideal to

pport the modifications in the force system intro-

4. Force system of T-loop activated 6 mm deliveredteeth. Higher moments are acting in beta. Activationment of spring in alpha provides controlled tipping.uple of vertical forces compensates for momentferential: equilibrium. Burstone canine bracket isint of anterior insertion. Auxiliary molar tube is pointposterior insertion.

ble II. Angle and step variations during space closurepping at apices of maxillary incisors is assumed)ce closure (mm) Step (mm) Angle ()

0 00.2 3.20.4 6.40.6 9.60.8 12.81.0 16.01.2 19.21.4 22.2ced by geometry changes, as shown in Table IV. Theutral position in Table III is 3 mm. Considering

progles and steps (Table IV), neutral position is reducedthat the loop exerts an acceptable horizontal force

til the end of space closure. After 7 mm of spacesure, the loop still provides 191 gf of horizontalce, with MF of 8.6 mm delivered to the anterior unit.e posterior unit has an MF of 11.6 mm. It isportant to consider the moment of the couple of therizontal forces separated by the step between theckets when analyzing equilibrium of the appliance.is explains the significant reduction in the verticalce values in Table IV.The intrusive forces acting posterior to the center of

istance in the end of space closure might assist inering MF ratios in alpha, keeping the force system

ective. If, during the last millimeters of deactivation,ace closure becomes more difficult, a possible solu-n is to add a chain elastic or spring between the units,

ble III. Force system of T-loop without geometryrrection of bracketsce closure)

MF(mm)

MF(mm)

Fv (gf)

Fh(gf)

88% Fh(gf)

6.3 8.7 33.9 326.0 286.96.1 9.6 45.9 291.4 256.46.0 10.7 57.6 258.9 227.86.0 12.1 69.6 225.6 198.55.9 13.9 81.8 192.2 169.15.8 16.6 94.3 157.5 138.65.7 20.7 107.1 121.4 106.85.7 28.7 120.1 83.5 73.5

F, MF ratio at bracket in alpha position; MF, MF ratio atcket in beta position; Fv , vertical force in alpha position; Fh,izontal force; 88% Fh, correction of horizontal force based ontware error.

ble IV. Force system of same T-loop with geometryrrection of bracketsce closure)

MF(mm)

MF(mm)

Fv (gf)

Fh(gf)

88% Fh(gf)

6.3 8.7 33.9 326.0 286.96.6 8.9 29.5 307.0 270.16.9 9.1 23.4 290.5 255.67.2 9.4 21.8 272.0 239.47.5 9.7 19.3 253.5 223.17.8 10.2 18.1 233.7 205.78.1 10.8 17.9 212.5 187.08.6 11.6 15.7 190.6 167.7

F, MF ratio at bracket in alpha position; MF, MF ratio atcket in beta position; Fv , vertical force in alpha position; Fh,izontal force; 88% Fh, correction of horizontal force based ontware error.viding about 50 gf to lower the MF ratios.This loop design is similar to the one introduced by

Burstone in his original article3; however, there aresmall changes in dimensions and in the placement ofbedethedimun

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4. Christiansen RL, Burstone CJ. Centers of rotation within theperiodontal space. Am J Orthod 1969;55:351-69.

5. Burstone CJ, Pryputniewicz RJ. Holographic determination of

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American Journal of Orthodontics and Dentofacial OrthopedicsVolume 129, Number 1

Viecilli 53nds, as well as in force system behavior duringactivation. Opening the anterior ear of the loop, as in

original design, would allow us to decrease H and Gensions yet would increase MF ratio in the anterior

it during deactivation. An increase in MF ratio of theterior unit can reduce working range, because thisect will already be a result of the geometry devel-ment during space closure. Although the new loopvides a small reduction of the anterior units MF

io (Table III), the geometry affects the final forcestem, ultimately increasing it (Table IV).

Although this loop is larger than other T-loopscussed in the literature, patient comfort is not jeop-ized, because in the anterior region the patient

ually has enough space to place a larger loop withoutnificant interference of the soft tissues.Plans for future studies on this topic include an

aluation of this appliances clinical behavior and thevelopment of a new loop design for posterior pro-ction. Further investigation on root movement strat-ies would also be beneficial.

NCLUSIONS

In this study, the effect of steps, angles, and verticalces was conbined to produce an ideal T-loop design,ing to provide a more determinate force system.

e effects and force systems are estimations based onplified locations of the centers of resistance, assum-relatively constant behavior of the centers of

ation. These simplifications might differ slightlym what happens in vivo. The finite element methodan accurate spring tester capable of reproducing theometric corrections might be beneficial to ensure acise force system.

The author thanks Professor Charles J. Burstone,iversity of Connecticut, for his inestimable help andas and Dr Demetrios Halazonetis, University ofhens, for accepting the suggestions to improve theftware that made this article possible.

FERENCES

Burstone CJ. Rationale of the segmented arch. Am J Orthod1962;48:805-22.Burstone CJ. The mechanics of the segmented arch technique.Angle Orthod 1966;36:99-120.Burstone CJ. The segmented arch approach to space closure.Am J Orthod 1982;82:361-78.centers of rotation produced by orthodontic forces. Am J Orthod1980;77:396-409.Vanden Bulcke MM, Burstone CJ, Sachdeva RCL, Dermaut LR.Location of centers of resistance for anterior teeth duringretraction using the laser reflection technique. Am J OrthodDentofacial Orthop 1987;91:375-84.Tanne K, Koenig HA, Burstone CJ. Moment to force ratios andthe center of rotation. Am J Orthod Dentofacial Orthop 1988;94:426-31.Ngerl H, Burstone CJ, Becker B, Kubein-Messenburg D.Centers of rotation with transverse forces: an experimental study.Am J Orthod Dentofacial Orthop 1991;99:337-45.Tanne K, Sakuda M, Burstone CJ. Three-dimensional finiteelement analysis for stress in the periodontal tissue by orthodon-tic forces. Am J Orthod Dentofacial Orthop 1987;92:499-505.Hart A, Taft L, Greenberg SN. The effectiveness of differentialmoments in establishing and maintaining anchorage. Am JOrthod Dentofacial Orthop 1992;102:434-42.Burstone CJ, Koenig HA. Optimizing anterior and canine retrac-tion. Am J Orthod 1976;70:1-19.Melsen B, Fotis V, Burstone CJ. Vertical force considerations indifferential space closure. J Clin Orthod 1990;24:678-83.Hoenigl KD, Freudenthaler J, Marcotte MR, Bantleon HP. Thecentered T-loopa new way of preactivation. Am J OrthodDentofacial Orthop 1995;108:149-53.Burstone C, van Steenbergen E, Hanley KJ. Modern edgewisemechanics and the segmented arch technique. Glendora (CA):Ormco; 1995.Koenig HA, Burstone CJ. Analysis of generalized curved beamsof orthodontic applications. J Biomech 1974;7:429-35.DeFranco JC, Koenig HA, Burstone CJ. Three-dimensional largedisplacement analysis of orthodontic appliances. J Biomech1976;9:793-801.Haskell BS, Spencer WA, Day M. Auxiliary springs in contin-uous arch treatment: part 1. An analytical study employing thefinite-element method. Am J Orthod Dentofacial Orthop 1990;98:387-97.Halazonetis DJ. Design and test orthodontic loops using yourcomputer. Am J Orthod Dentofacial Orthop 1997;111:346-8.Halazonetis DJ. Understanding orthodontic loop preactivation.Am J Orthod Dentofacial Orthop 1998;113:237-41.Raboud DW, Faulkner MG, Lipsett AW, Haberstock DL. Three-dimensional effects in retraction appliance design. Am J OrthodDentofacial Orthop 1997;112:378-92.Raboud D, Faulkner MG, Lipsett AW. A segmental approach forlarge three-dimensional rod deformations. Int J Solids Structures1996;33:1137-56.Marcotte MR. Biomechanics in orthodontics. Philadelphia: BCDecker; 1990.Solonche DJ, Burstone CJ, Vanderby R. A device for determin-ing the mechanical behavior of orthodontic appliances. IEEETrans Biomed Eng 1977;24:538-9.Fiorelli G, Melsen B. Biomechanics in orthodontics CD-ROM,version 2.0. Arezzo, Italy: Libra Ortodonzia; 2001.

Self-corrective T-loop design for differential space closureMATERIAL AND METHODSRESULTSDISCUSSIONCONCLUSIONSAcknowledgmentsREFERENCES