American Journal of ORTHODONTICS

Founded in 1915 Volume 82, Number 5 November, 1962

Copyright 0 1982 by The C. V. Mosby Company

ORIGINAL ARTICLES

The segmented arch approach to space closure

Dr. Burstone

Charles J. Burstone, D.D.S., MS. Farmington, Conn.

The clinical application of frictionless attraction springs using the segmented arch technique is described. Differential space closure is achieved by varying the force system between the anterior and posterior segments. A specially designed force transducer allowed accurate force and moment determination for each spring design. By duplicating predetermined spring geometries, the orthodontist can reproduce the required force system within narrow ranges. The most important considerations in the clinical use of attraction springs are the amount of distal activation, the angulation differential between the anterior and posterior teeth, and the centricity or eccentricity of the loop. Improvements in design have lead to a more efficient, hygienic, and comfortable mechanism for space closure.

Key words: Segmented arch technique, extraction, space closure, forces, retraction, protraction

S pecialized precalibrated springs and as- semblies for space closure have been an integral part of the segmented arch technique in the treatment of pa- tients requiring extraction therapy.‘, * New knowledge concerning the biomechanics of spring design, along with the development of new materials, has made pos- sible improvements which simplify the mechanics, improve the biologic response, and offer a more hy- gienic appliance.3-J

At least six goals should be considered for any uni- versal method of space closure: (1) Differential space

closure. The capability of anterior retraction, posterior protraction, or a combination of both should be possi- ble. (2) Minimum patient cooperation. Headgear and interarch or intermaxillary elastics should not be a major component in controlling differential horizontal tooth movement during space closure. Their depen-

From the Department of Orthodontics, School of Dental Medicine, University of Connecticut Health Center. This work was supported by NlHiNIDR Research Grant DE-03953.

In order to achieve these objectives, the clinician must have an appliance which delivers the required force system.6 He should also be aware of how root length and the nature of the periodontal support will influence the force system. Emphasis in this article will be on design principles and the clinical usage of attrac- tion mechanisms for space closure. Since some patients may require protraction of posterior teeth and others will require anterior retraction, I use the general term attraction to describe the over-all process of space clo- sure or the appliances used for that purpose.

0002-9416/82/l 10361+ 18$01.80/O 0 1982 The C. V. Mosby Co. 361

dence on patient cooperation is reflected in a lack of precision and may limit treatment possibilities. Head- gear and elastics may have other applications in treat- ment. (3) Axial inclination control. (4) Control ofrotu- tions and arch width. (5) Optimum biologic response. This includes rapid tooth movement with a minimum lowering of the pain threshold. In addition, tissue damage, particularly root resorption, should be at a minimum. (6) Operator convenience. The mechanism should be relatively simple to use, requiring only a few adjustments for the completion of space closure.

Fig. 1. Composite TMA 0.018-0.017 by 0.025 inch retraction spring. A 0.018 inch round T spring is welded directly to a 0.017 by 0.025 inch base arch.

; = 6.0 M T z 5.6

1126 gm-mm 1002 gm-mm

201gm

> Direction of Tooth

Movement

Fig. 2. The change in the force system after 1 mm. of canine retraction using the spring shown in Fig. 1. Force magnitude decays only 33 mm. To obtain 201 Gm., 6 mm. of activation is required.

CHARACTERISTICS OF THE FORCE SYSTEM

Precise control over centers of rotation of teeth and the biologic response during space closure, regardless of the appliance used, requires an optimal force system with certain characteristics. Our understanding of these characteristics is the key to predictable attraction. To illustrate the characteristics of the force system, the composite TMA 0.018-0.017 by 0.025 inch retraction spring will be used (Fig. 1). Typically, the spring is activated 6 mm. and delivers approximately 201 Gm. of distal force at the start of retraction (Fig. 2). After the canine moves distally 1 mm., the force will be reduced by 33 Gm. to 168 Gm. The rate of decay of the

force ( FX ) is called the load-deflection rate, and it

averages 33 Cm. per millimeter. The low load-deflec- tion rate i.s important in this spring. since it cnahles the orthodontist to deliver optimal magnitudes 01’ three. High-load deflection springs as vertical loops dissipate force rapidly: hence, one must activate to very high force levels in order to produce any significant tooth movement.

For example, for a typical vertical loop in a 0.0 I8 by 0.025 inch steel wire, the load-deflection rate might approximate 1,000 Gm. per millimeter (the actual force is dependent on the exact shape). For controlled tipping movements around the apex of the canine, 100 Gm. is more than adequate force. A millimeter activation of the edgewise vertical loop would produce an exces- sively high force of 1,000 Gm.; moreover, as the canine moves, the force magnitude changes rapidly (100 Gm. for every 0.1 mm. of movement). Since the load-deflection rate is so high, it would be impossible for a clinician to activate the loop to produce an op- timum magnitude of force. To deliver 200 Gm. of force, the required activation would be 0.2 mm. Not only is it practically impossible to activate such a small distance, the force of 200 Gm. would be dissipated rapidly over the remaining 0.2 mm. of activation. Thus, orthodontists who use high-force load-deflection mechanisms must use high force values that have un- desirable sequelae, which include anchorage loss. pain, and undermining resorption. In contrast, a retraction spring with a low load-deflection rate of 33 Gm. per millimeter allows for the delivery of optimal force levels, since an error in activation of 1 mm. results in an error of only 33 Gm. Furthermore, as teeth move distally, the reduction in force is small. giving greater constancy of force at optimal levels.

At a 6 mm. activation, along with the 201 Gm. of force, a moment which tends to move the canine root distally is created (Fig. 2). The moment value approx- imates 1,129 Gm .-mm. The moment-to-force ratio on the canine is 5.6, which suggests that the center of rotation of the canine as it tips distally approaches the apex. After 1 mm. of retraction, the moment-to-force ratio is almost the same (6.0). We are thus observing two important characteristics of our force system: ( 1) The required moment-to-force ratio to give us the needed center of rotation and (2) the change of the

moment-to-force ratio as the tooth moves

It is desirable to maintain a constant center of rotation during retraction of the anterior teeth. This necessitates

a relatively constant M/F ratio where (5X$3) is

small. On the other hand, we should purposely increase the M/F ratio on the posterior teeth to enhance anchor-

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Segmented arch approach to space closwe 363

age during space closure. As the clinical use of the segmented arch attraction mechanisms are described, the above characteristics of the force system should be kept in mind. They are (1) force magnitudes and direc- tion, (2) force constancy (low load-deflection rates), (3) proper moment-to-force ratios, producing the desired centers of rotation, and (4) force constancy, that is, control over the change in moment-to-force ratio with respect to deflection.

The attraction mechanisms that will be described are basically frictionless springs. All of the required force system is built into the springs, and one does not depend upon an arch wire along which the brackets slide for control. We have rejected the concept of slid- ing mechanisms because of the high frictional values that are inherent since brackets are so far from the centers of resistance of teeth. In recent years, so-called power arms or extensions have been used to deliver the force closer to the centers of resistance of the teeth. Although this eliminates a great amount of the friction for sliding mechanisms, the force is never placed exactly at the center of resistance and frictional prob- lems still exist which make prediction of the force sys- tem poor.

The attraction mechanisms described in this article usually have 6 to 7 mm. distal activations. Although it is convenient to have large activations since few reacti- vations are required, the major reason for the large activation relates to the delivery of an optimal force system. Large activations are required to deliver opti- mal levels of force and to deliver them more constantly. It is to our advantage to have the lowest load-deflection rate possible, and with a low load-deflection rate a large activation is required in order to build up the needed force level. The fact that few reactivations are needed is a pleasant by-product of this force system and the way it is developed.

ANTERIOR RETRACTION (GROUP A ARCHES)

It is convenient to classify an extraction arch by the differential space closure required between the anterior and the posterior teeth. A Group A arch is one in which posterior segments must remain in their original posi- tion and the full space is used for anterior retraction. A Group B arch requires that approximately one half of the space be used for retraction. A Group C arch re- quires that approximately all space be closed by pro- traction of the posterior teeth.

Group A arches tend to be of two types: In one the anterior teeth are badly crowded, and separate canine retraction is indicated. In the other the anterior teeth have adequate arch length, and the movement that is needed is en masse space closure of all six anterior

Fig. 3. Posterior anchorage unit. A, Posterior teeth are con- nected by a buccal (stabilizing) segment from second premolar to second molar. B, Upper 0.036 inch stainless steel trans- palatal arch. C, Lower 0.036 inch stainless steel low lingual arch.

teeth. En masse space closure in the segmented arch techniques uses two principles-the two-tooth concept and segmental movement.

Early in treatment, the posterior teeth are joined together to form a posterior anchorage unit. The an- chorage unit consists of the right and left posterior teeth which are connected by a buccal stabilizing segment and a transpalatal lingual arch in the maxillary arch and a low lingual arch in the mandibular arch (Fig. 3). During space closure, conceptually one should think of only two teeth-an anterior tooth comprising the in- cisors and the canines which have been connected and a posterior tooth which includes molars and premolars. The attachment on the posterior tooth (segment) is a 0.018 by 0.025 inch auxiliary tube on the first molar, and the one on the anterior tooth (segment) is an auxil-

A

ANTERIOR SEGMENT

Fig. 4. Specialized attachments on the first molar and canine, Gingivally placed horizontal and vertical auxiliary tubes are used to connect the anterior segment and posterior segment during attraction and en masse root movement.

iary vertical tube on the canine bracket (Fig. 4). Al- though adjustments are still possible within the indi- vidual segments during space closure, the orthodontist should concern himself primarily with only the force system that will be applied to the anterior and posterior auxiliary tubes.

The two-tooth concept has a number of advantages during space closure which are not found in continuous arch therapy:

I. Working between the two auxiliary tubes sim- plifies the determination of the force system. In a con- tinuous arch, one must be concerned with the actions and reactions between all attachments which makes it practically very difficult to determine the forces and calibrate an attraction mechanism. Using the two-tooth concept, only the forces between two attachments need be analyzed.

2. A large distance between the molar and the ca- nine auxiliary tubes allows for a superior and more conveniently used force system. The load-deflection rates are lowered, and the shapes of the springs are not so critical in producing both the desired force and the moment-to-force ratio. Furthermore, with the large ac- tivations that are required, they are easily placed in the mouth.

3. The rigidity of the anterior and posterior seg- ments is not dependent upon the attraction mechanism. Typically, it is necessary to have less rigid springs for attraction springs and greater rigidity for control of the anterior and posterior units. Rigidly connecting the teeth of the anterior and posterior units allows the clinician to maintain the desirable tooth positions which are obtained during initial alignment and many times are present at the beginning of treatment.

4. Wires of increasing rigidity may be used in the anterior segment independent of the attraction springs to align the anterior teeth simultaneously with space closure. In most patients, however, one should use a relatively rigid wire as soon as possible to obtain full control over the incisor axial inclinations.

5. Extraneous forces are minimized in the posterior teeth since buccal segments remain in place and are not continually changed as with therapy requiring different

D

Fig. 5. Types of segmental en masse space closure. A, Blocks represent anterior and posterior segments. 8, One-stage trans- lation. C and D, Two-stage space closure. The ant&or seg- ment is initially tipped around a center of rotation near the apices of the incisors. Root movement follows with a center of rotation near the incisor bracket.

arches or continual adjustment and retying of a given arch.

The principle of en masse space closure, using segmental movement, is demonstrated in Fig. 5. The block diagrams represent the anterior and posterior segments. In Fig. 5, B, the space is closed by translat- ing both the anterior and posterior segments as a unit. This is the approach taken in Group B arches. In Group A arches, where one would like to prevent posterior segments from displacing anteriorly, two stages of space closure are accomplished (Fig. 5, Cand D). In the first phase the anterior segment is tipped with a center of rotation near the apex of the incisors, followed by a second phase of root movement where the center or rotation is moved occlusally to the bracket or the incisal edge (en masse root movement). This form of en masse space closure differs from other techniques. For in- stance, with Begg treatment, all six teeth are retracted; however, each tooth has its own center of rotation re- quiring individual root springs on each of the teeth for

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Segmented arch approach to space closure 365

Fig. 6. The 0.018-0.017 by 0.025 inch composite anterior re- traction spring (upper arch). Premolars will be extracted at this stage in treatment. Retraction spring inserts into the vertical tube on the canine and the horizontal tube on the first molar.

correction of both mesiodistal and labiolingual axial inclination. In segmental space closure, all of the teeth in the anterior segment, since they are treated as a unit, remain in good first- and second-order alignment to each other. If root movement is required, only one root spring is needed on a side.

True segmental movement, that is, treating the an- terior segment as a unit, is easily carried out on patients who have correct axial inclinations between the canines and the incisors relative to each other. If a discrepancy exists, separate canine or incisor root movement may be indicated following space closure, or some correc- tion is possible during space closure.

With incisor roots that are too far lingual, en masse anterior movement can be carried out; however, rigid- ity is needed only in the first- and second-order direc- tions. Freedom of movement in a third-order direction can be allowed. For example, if the incisors are mark- edly flared, the anterior segment can be undersized to allow roots to displace anteriorly during space closure. In the lower arch, where the canines eventually must be translated distally but the incisors are to be tipped around the apex, the entire anterior segment is tipped around the apex of the lower incisor. During en masse root movement, the anterior segment is rounded or un- dersized so that, as the canine root is moved distally, the incisor roots will not be moved to the lingual.

Anchorage control during en masse space closure

In patients with Group A arches, where little an- terior displacement of the posterior teeth is allowed, two stages of space closure are planned-en masse controlled tipping followed by en masse root move- ment. The calibrated mechanism is a composite TMA spring comprising two different cross sections of wire,

Fig. 7. During activation, an activation moment is produced by the vertical loop and the T loop, tending to move roots into the extraction site. The T loop design is superior, since more wire is placed apically. The improperly designed double vertical loop produces no moment, since wire lies occlusal to the brackets.

a 0.018 inch round T loop welded to a 0.017 by 0.025 inch base arch (Fig. 6).

As has been pointed out previously, the T loop tends to optimize design by placing additional wire further apically. Fig. 7 shows three loops-a vertical, a double-vertical loop with one arm falling occlusally below the level of the brackets, and a T loop. In order to control the root apices so that they do not displace forward, a moment (root distal and crown mesial) must be applied by the retraction mechanism. A typical ver- tical loop produces a moment tending to move the canine root distally, but the moment-to-force ratio is too low. By placing additional wire apically, as in the T loop, the magnitude of this moment increases with respect to the force. The double vertical loop design is improper, since additional wire falling occlusally completely eliminates the needed moment, and no moment whatsoever is produced during activation. It is not the amount of additional wire that is placed in the loop that is important but, rather, where the wire is placed. The additional wire serves two purposes: It lowers the load-deflection rate and at the same time, if properly placed, increases the moment-to-force ratio.3

In earlier designs that were used with the segmented arch technique, helices were placed to lower the load- deflection rate. With the introduction of beta-titanium wire (TMA), it has been possible to simplify the design so that a T loop by itself will have a relatively low load-deflection rate and a large maximum springback. The heavier base arch which fits into the auxiliary tube of the first molar is important, since it allows positive orientation of the spring and, more significantly, it is capable of withstanding, without permanent deforma- tion, the higher moments that are needed for anchorage control. Furthermore, the use of a heavier base arch tends to increase the moment-to-force ratio on the an- terior teeth, since any bending in the occlusally posi- tioned part of the spring tends to minimize this ratio. It should be noted that the retraction spring is not centered but is positioned mesially. The rationale for eccentric positioning will be discussed in greater detail later. In this instance, it is used to enhance the moment-to-force

B position < position

2571 gm-mm 0

1126 gm-mm

201 gm -B h-201 gm

M - = 12.6

M F

- = 5.6 F

Fig. 8. Force systems produced at 6 mm. activation of 0.016 0.017 by 0.025 inch anterior retraction spring. Note differential moment-to-force ratio between the anterior segment (CX posi- tion) and the posterior segment (6 position). Large moment at the p position is instrumental in anchorage control.

ratio (better anchorage control) on the posterior seg- ment during space closure and give better axial-incli- nation control over the anterior teeth.

Fig. 8 describes the basic force system. The forces and moments are those that are produced at a full acti- vation of 6 mm. Depending upon the activation, this force system can be varied somewhat so that the num- bers that are given should be looked upon as represen- tative. The forces are delivered to two teeth, an anterior tooth (segment) and a posterior tooth (segment). For convenience, it is useful to talk about the two positions where the spring is attached. The alpha (a) position is the vertical tube on the canine and the beta (/3) position is the horizontal tube on the first molar. A summary of the force system follows:

1. The force is 201 Gm. in a distal direction (alpha position) and 201 Gm. mesially (beta position).

2. An alpha moment of 1,126 Gm .-mm. and a beta moment of 2,571 Gm.-mm. are produced.

3. A 63 Gm. vertical force is present in an intrusive direction at the alpha position and in an extrusive di- rection at the beta position.

The alpha moment-to-force ratio is 5.6, which im- plies that the center of rotation during space closure would approach a point near the apex of a typical in- cisor. The beta moment-to-force ratio on the posterior segment is 12.8. This ratio suggests that if the posterior teeth move forward at all, the roots will displace at a faster rate than the crowns. The load-deflection rate of the spring averages 33 Gm. per millimeter.

Clinical use

The force system from the retraction assembly has been measured using an apparatus which simulta-

Fig. 9. Angulation bends are placed in the retractron spring to increase the moment-to-force ratio. Geometry of spring with C.C angulation bends and a fl bend in front of molar tube.

neously measures forces and moments at both the alpha and beta positions.‘. ’ This allows the assembly to be calibrated in such a manner that the clinician need only duplicate the proper shape to the wire in order to get the desired force system. The distal force is produced by the number of millimeters of activation. From Table I. it can be seen that 6 mm. of activation is required to produce approximately 200 Gm. of force. Although the spring during activation produces moments in the de- sired direction, they are insufticient to deliver the needed moments and differential M/F ratios between

the anterior and posterior segments. For that reason, angulation bends are placed in the springs. as shown in Fig. 9. The bends in a 0.018 inch round spring are referred to as alpha bends, and the tip-back bend im- mediately in front of the auxiliary tube on the molar is called the beta bend. These bends will vary somewhat, dependent upon the intertube distance. However, the described shape is representative of what is needed at the beginning of space closure in most situations.

It is very important to place the angulation bends properly, since the neutral position of the spring can be affected. This is true not only of the assemblies and segmented arch-attraction springs but of any loop. If a gable or angulation bend is placed in a loop, the loop will tend to cross when it is engaged in the adjacent brackets and, therefore, the magnitude of force will be greater than anticipated.:’ The retraction spring is shaped so that if moments alone are used to place the spring into the auxiliary tubes, the vertical arms of the spring will be 1 mm. apart. Thus, the neutral position. the position where force is 0 Gm., is I mm. To aid the clinician in achieving the proper angulation, templates are used. Rather than to measure the angles, it is more expeditious to duplicate the shape of the spring from a template. The exact shape of each spring described in

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Segmented arch approach to space closure 367

Fig. 10. En masse retraction. A, A 0.021 by 0.025 inch anterior segment is in place for true segmental space closure with a 0.017 by 0.025 inch TMA attraction spring. 6, Low-stiffness multistrand wire in the anterior segment allowed canine to re- tract to gain space for anterior alignment. Following alignment, a rigid anterior segment was placed.

this article is based on the templates found in the seg- mented arch syllabus (University of Connecticut, 1982). Tables giving the force system are based on these templates.

En masse retraction springs which are used for re- traction of six anterior teeth are shown in Fig. 10. The anterior retraction spring is initially activated 6 mm. Tooth movement is allowed to proceed until approxi- mately 3 mm. of space is closed, and then the spring is reactivated (Fig. 11). In certain cases, it may be neces- sary to contour springs somewhat labiolingually for comfort and if a shallow mucobuccal is present, a shorter spring is used. It should be remembered that the higher the spring is occlusogingivally, the greater the activation moment-to-force ratio will be, with better control over axial inclinations.

Detailed force system

The force system and the change in forces over a range of 6 mm. of activation is shown in Table I. The A column gives the number of millimeters of activation, and other columns to the right give the force system. At

Fig. 11. To activate springs, either the base arch is bent gingi- vally at distal aspect of molar tube (lower) or a rope ligature tie (upper) is used.

COMPOSITE RETRACTION SPRING t.0 18”-.017” x .025”)

25-1 , , , , , , , , , , ( , 0 .s 1.0 15 2.0 25 3.0 35 4.0 4.5 50 5.5 60

Deflection (mm)

Fig. 12. The load-deflection rate is low and relatively constant. Rate is lowest at full activation.

6 mm. of activation, the force is 201 Gm. For each millimeter of space closure, the force will drop about 33 Gm. The load-deflection rate is plotted in Fig. 12. Note that the load-deflection rate is relatively constant and has a tendency to be smaller at higher activations, which is the range where the spring is used. Many springs, like vertical loops, tend to increase their load- deflection rate with increasing activation. Since we do not want the force to decay rapidly within activation range, it is advantageous to have the lowest load-de- flection rates at the maximum activation.

By definition, the neutral position is that position of activation where the spring delivers no horizontal force. In the first line of the table, the force system for the neutral position (0 mm. activation and 0 Gm. force) is given. The moment at the neutral position is referred to as the residual moment. In the alpha position (M,), it is 231 Gm.-mm., and in the beta position (M,) it is 2,358 Gm.-mm. As the assembly is activated, both the horizontal force and the alpha and beta moments in- crease for each millimeter of activation. The rate of increase of the beta moment is not as great as that of the

COMPOSITE RETRACTION SPRING (.O 18”- .O 17”~ ,025”)

COMPOSITE RETRACTtON SPRING (.018”- .017”x .025”)

0’ I ) I , , , , , I 0 .5 1.0 15 2.0 2.5 30 3.5 4.0

, , , 4.5 5.0 5.5 6.0

Deflection (mm)

I I I 1 I I I I I 5 IO I5 20 25 3.0 35 4.0 4.5 5.0 5.5 A.0

Deflection hm)

Fig. 13. The slope of (Y moment is steeper than that of p mo- Fig. 14. Differential moment-to-force ratios between the 01 and @ ment, reflecting eccentric placement of the T loop and the two positions. As spring deactivates, a tip-back effect is placed on wire cross sections. the posterior teeth.

Table I. Composite anterior (canine) retraction spring (TMA 0.018-O. 17 by 0.025 inch)

1 F,, FL, (mm .) (cm.) (cm.)

0.0 0.0 113.5 0.5 15.4 107.7 I .o 33.0 102.1 1.5 50.8 97.1 2.0 68.5 92.4 2.5 84.7 87.5 3.0 102.3 83.2 3.5 118.7 79.4 4.0 135.6 75.9 4.5 151.9 72.4 5.0 167.7 69.1 5.5 183.9 65.9 6.0 200.6 63.3

i = Distal activation. F,, = Horizontal force. F\ = Vertical force. M,,Anterlor moment. Mp = Posterior moment. F/h = Load-deflection rate. M,,/F = Anterior moment-to-force ratio. MB/F = Posterior moment-to-force ratio.

MCI MP FlA M,,IF MfiiF (Cm.-mm.) (Cm.-mm.) (Cm.-mm.) (mm.) (mm.)

231 I -2,358.4 0.0 0.0 0.0 322. I -2,384.5 30. I 22.3 171.9 414.6 -2,408.8 35.3 12.6 74.7 496.6 -2.431.4 35.7 9.8 48.3 575. I -2,450. I 35.3 8.4 3.5.9 655.0 -2,470.2 32.6 7.7 29.2 728.7 2.488.2 34.7 7.1 24.3 797.6 -2.506.0 33.4 6.7 21.1 869.3 -2,521.6 33.8 6.4 18.6 940.4 -2535.3 32.3 6.2 16.7

1,001.6 -2,550.4 31.6 6.0 15.2 1,070. I -2,559.6 32.5 5.9 13.9 1,126.4 -2,571.4 33.2 5.6 12.8

alpha moment. The two slopes of the alpha and beta moments in respect to deflection can be seen in Fig. 13. The difference in the rate of increase between alpha and beta moments is very important in producing a unique force system. It allows a differential in the moment-to-

force ratio change (v) as the spring deactivates.

This can be appreciated if M/F is plotted against de-

flection (Fig. 14). Note that the alpha moment-to-force ratio remains about the same from about 6 mm. to 3 mm. or less of activation. Thus, with an initial 6 mm. activation as the teeth retract 3 mm., there is little change in the center of rotation on the anterior teeth. On the other hand, the beta moment-to-force ratio rap- idly increases as space closes. The objective of the anterior retraction mechanism is to give good control

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Segmented arch approach to space closure 369

over the center of rotation of the anterior segment as it retracts and to minimize mesial displacement of the posterior segment. A brief discussion of how this is accomplished follows.

The alpha moment-to-force ratio during the range of activation from 6 mm. to 3 mm. remains relatively constant (Table I). At 6 mm., the moment-to-force ratio is 5.6; at 3 mm., it increases to 7.1. This small increase tends to move the center of rotation slightly in an apical direction but, for all practical purposes, the center of rotation is relatively constant. This should be compared to a retraction mechanism such as a vertical loop where the moment-to-force ratio within I mm. of deactivation can change radically. This concept will be considered in further detail in the section on en masse translation. Large angulations are placed in the 0.018 inch component of the spring, with alpha angulations averaging 105 degrees. This angulation is responsible for the residual moment in the alpha position of 231 Gm.-mm. Since the activation is large, the clinician has great leeway in using the springs to approach the de- sired force system. A few degrees error in the angula- tion will not significantly change the M/F ratio or the center of rotation of the anterior segment. Similarly, as the anterior teeth retract and their axial inclinations change, a few degrees would not significantly alter the center of rotation. By contrast, for vertical loops with their small-angulation bends (gable bends), the shape is very critical and, as the teeth move, the centers of rotation of the anterior teeth change markedly.

Anchorage control with the TMA retraction spring is accomplished in a number of ways. The forces that are used are relatively low in magnitude. The initial forces are under 200 Gm., with an average force of about 150 Gm. during the retraction period. The low load-deflection rate allows the clinician to determine accurately the magnitude of this force and an error of 1 mm. would produce an error of only 33 Gm. The springs are prefabricated, which allows their geometry to be constant, and hence the force system can be accu- rately calibrated in the laboratory. The key to anchor- age control of the posterior segment is not only the low force magnitude but, even more, the differential of moment-to-force ratio between the alpha and the beta positions. The moment-to-force ratio at the posterior segment is much higher, being 12.8 at 6 mm. of acti- vation. After 3 mm. of retraction, the moment-to-force ratio increases to 24.6. Thus, as space closes initially, the posterior segment would translate forward or the roots would move slightly forward, if there is move- ment at all. After some space is closed, the moment-to- force ratio increases to the point where the spring pro- duces a definite tip-back action on the buccal segment.

Table II. Variation in force system (standard deviations) TMA 0.018 by 0.025 inch retraction spring Nonstandard springs

A ML2 MP (mm.) (Gm.-mm.) (L-i-., (Gm.-mm.)

1.0 63.4 4.8 161.5 1.5 61.3 4.1 160.2 2.0 63.6 3.3 158.0 2.5 64.6 3.6 157.1 3.0 65.1 4.0 156.1 3.5 71.1 3.2 155.7 4.0 70.8 3.4 156.0 4.5 71.6 4.5 157.5 5.0 74.7 4. I 157.6 5.5 76.5 6.1 159.0 6.0 83.1 5.7 160.2

h = Distal activation. M, = Anterior moment. Mp = Posterior moment. FH = Horizontal force.

In a sense, then, one could recoup any space loss pro- duced during the beginning of space closure. Anchor- age control is a function not only of the initial moment- to-force ratio on the posterior segment that prevents these teeth from tipping into the extraction site but also of a gradually increasing ratio which, during space clo- sure, produces a definite tip-back action. The control of anchorage is also related to the posterior anchorage unit of multiple teeth rigidly joined together with buccal stabilizing segments and a lingual arch.

The force system given in Table I is based on a typical spring shape and tube geometry. However, it may be necessary to modify the force system, depend- ing upon individual patient needs. Although it is not common, some patients might require a center of rota- tion closer to the center of resistance of the upper in- cisor and, if so, the moments in the alpha position can be reduced. If one is able to place the center of rotation at the apex of the upper incisors, in many patients with flared incisors root movement at a later stage is not necessary.

The bend that would be varied the most is the beta angulation. In the prototype given, at 6 mm. of activa- tion, (M/F), is 12.8. For translation of a posterior seg- ment forward, the ratio might more closely approach 10 to 1. The 12.8 ratio gives a safety factor in minimizing anchorage loss. However, too much moment could eventually create a steepening of the upper plane of occlusion or too much tip-back on the molars. If this presents a problem, some reduction in the beta moment is indicated. Typically, the beta angulation can vary between 25 and 35 degrees. If a headgear is attached to

Fig. 15. En masse root spring using a 0.017 by 0.025 inch TMA wire. The roots of all six anterior teeth are moved as a unit. In this instance, root movement is being carried out before spare closure.

the posterior segment, depending upon direction and point of application, moments which alter the balance of moment-to-force are created. This must be taken into consideration in the beta angulation. For instance, in an open-bite situation, one might not place any beta angu- lation in the base arch and, instead, rely on an occipital headgear posterior to the center of resistance to develop the necessary moment to prevent the posterior segments from tipping forward.

The data that are presented are based upon a typical intertube distance before space closure. The force sys- tem from the standardized spring geometry will change somewhat, depending upon the intertube distance. In addition, the moment-to-force ratios needed are depen- dent upon the geometry of the teeth, particularly the root length and the nature of the periodontal attach- ment. It is important for the clinican to monitor his patients carefully and to modify the moment-to-force ratio in both the alpha and the beta positions when required. For example, the space closure in periodon- tally involved teeth where the alveolar crest has been lost requires lurger moment-to-force ratios, since the center of resistance will be found further apically.

Variation in the force system can also be produced by operator error in duplicating the shape of the spring. To test this variation, a laboratory technician fabricated three springs approximately, using a template with min- imum attention to accuracy. Each spring was tested three times for a total of nine sets of data. Table II gives the standard deviations for the entire group of springs. The standard deviation for the horizontal force at 6 mm. of activation was only 2.9 percent; variation for Ma and M, was larger (7.4 percent and 6.2 percent). Some of the variation, such as variation in the cross section of the wire, is not under the control of the orthodontist. Greater accuracy by the orthodontist in reproducing the shape of the spring can reduce the variation; however, as shown by the above data, the

400 gm

- I 1Omm

- c-- 400gm

(yp10 (~~ZlO

Fig. 16. A 10: 1 moment-to-force ratio produces translation if the brackets are 10 mm. from the center of resistance. Transla- tion can be produced with a single force placed 10 mm. apical to the brackets (lower diagram) or by applying a force and a couple at the bracket (upper diagram). The effect is identical.

retraction springs are relatively unforgiving of mistakes in shape and activation.

Following en masse tipping movement, the entire anterior segment is moved as a unit with a center of rotation near the bracket of the central incisor. Fig. 15 shows a 0.017 by 0.025 inch TMA root spring. The spring is basically a straight wire between the auxiliary tube of the molar and the vertical tube of the canine. A welded 0.018 inch TMA vertical pin inserts into the canine vertical tube. V-bends or curvatures are placed to produce the desired moments. During the time of root movement, it is not necessary to replace either the posterior anchorage unit or the anterior segment. The root springs act beyond simple root movement in that they function to align the anterior and posterior seg- ments in three dimensions. Similar to retraction, one should think of root movement as a two-tooth move- ment between the anterior tooth (segment) and the posterior tooth (segment).

EN MASSE TRANSLATION FOR GROUP B ARCHES

Patients who require equal displacement for both the anterior and posterior segments can take advantage of en masse translation. Since en masse translation re- quires greater force magnitudes, and since practically the center of rotation is not constantly maintained, a greater anchorage loss of the posterior segments is in- evitable.

Ideally, one would like to deliver a force system as shown in Fig. 16. If one assumed a 10: 1 moment-to- force ratio for translation (the ratio is dependent on the root-alveolar bone geometry and the axial inclina-

I I I I I I I I I I

01 02 03 04 05 06 07 08 QV IO

Activation (mm)

Fig. 17. Change in moment-to-force ratio of a 6 mm. high verti- cal loop. A rapid change occurs in the M/F ratio over 0.1 mm. of deactivation. The center of rotation of a typical incisor moves from the apex (M/F = 7.0) to translation (M/F = lO.O), and then to the bracket (M/F = 12.0).

tions of teeth; hence, this number is given only a repre- sentative value) 4,000 Gm.-mm. and 400 Gm. should be delivered to the anterior and posterior segments. A method for producing this force system would be to place a gingival extension 10 mm. below the level of the brackets and to attach a rubber elastic at this point. Unfortunately, it is not practical to have a gingival extension placed so far apically. It should be noted that, with the elastic, the moment-to-force ratio would be constant at 10: 1 throughout the period of space clo- sure, although the force magnitude is reduced.

If a vertical loop is used for space closure, it is difficult to obtain the 10: 1 moment-to-force ratio from the activation moment (the moment automatically pro- duced by activation). A vertical loop could be extended gingivally to 10 mm., and the moment-to-force ratio would be only 4: 1. Even with the addition of wire gingivally, as in a T loop, it is not possible with one cross section of wire to deliver a 10: 1 moment-to-force ratio by the activation moment alone.

Since a vertical loop does not deliver high enough moment-to-force ratios for a translation, it has been common practice to place a gable bend or angulation so that a residual moment is produced. Fig. 17 shows the change in moment-to-force ratio for 1 mm. activation of a 6 mm. high vertical loop (a 20 degree angulation with an 8.4 mm. interbracket distance). At 1 mm. of activation, the moment-to-force ratio is under 3. At this point in time, the tooth is tipping, with the crown mov- ing in one direction and the root in the opposite direc-

Segrnmted urch approach to spnw do,sura 371

Fig. 18. A 0.017 by 0.025 inch TMA attraction spring. T loop is centrally placed between canine and molar auxiliary tubes. Typ ical activation is 7 mm.

tion. After 0.5 mm. of tooth movement, the root is still being displaced labially, but not so much as the moment-to-force ratio approaches 5.0. Only after the teeth have moved 0.8 mm. does the moment-to-force ratio approach 6 and 7, where one would expect con- trolled tipping around the apices of the incisors. Thus, even with the gable bend for the first 0.8 mm., one has little more than uncontrolled tipping, with a center of rotation somewhere between the apex and the center of resistance. In the last 0.2 mm., the center of rotation rapidly changes, so that the teeth first tip around the apex, translate, and then finally correct their axial in- clinations, rotating around a point of the crown. If the vertical loop is left in long enough, the axial inclina- tions of the teeth will give the appearance of genuine translation. In reality, what has happened is that the teeth at first tipped with roots being displaced forward, followed at a later stage by root movement lingually.

The rapid change in moment-to-force ratio with the vertical loop is problematic. Biologically, it is not de- sirable to keep changing areas of stress in the periodon- tal ligament. It is also very difficult to produce the moment-to-force ratios that are needed. An error of 1 or 2 mm. in activation completely changes the center of rotation. As has been pointed out previously, in order to use a vertical loop or any loop, one must know the neutral position (the position where the force is zero). when a gable bend is placed in the loop, the amount of activation is automatically increased, since the vertical arms cross and the neutral position is changed. If the orthodontist does not recognize this, he might be acti- vating 2 mm. instead of what he believed to be 1 mm. This could lead to either permanent deformation of the loop and/or moment-to-force ratios that are too low, leading to uncontrolled tipping movements. Overall, the vertical loop with gable bends is very unforgiving

Fig. 19. Typical angulation required for the 0.017 by 0.025 inch attraction spring. A 0.018 or 0.020 inch TMA wire is welded anteriorly for insertion into the canine vertical tube.

Fig. 20. Shape of 0.017 by 0.025 inch TMA attractjon sprmg used for protraction of posterior teeth. Loop is placed off center to the distal aspect. Angulation bends are increased as the LY position is approached. Anterior part of spring is to the left.

Table III. Attraction spring TMA 0.017 by 0.025 inch centered

A (mm.) ,& (ilk,

0.0 0.0 4.9

0.5 28.4 5.4 1 .o 50.1 5.5 1.5 72.1 6.1 2.0 94.7 6.6 2.5 116.7 1.2 3.0 140.7 8.0 3.5 162.7 8.6 4.0 185.0 9.4 4.5 208.8 10.1 5.0 232.9 10.9 5.5 257.5 11.6 6.0 281.8 12.3 6.5 307.3 12.9 7.0 333.4 13.6

a = Distal activation. F,, = Horizontal force. F\. = Vertical force. M,, = Anterior moment. MB = Posterior moment. F/rl = Load-deflection rate. h&,/F = Anterior moment-to-force ratio. MS/F = Posterior moment-to-force ratio.

Ml2 MP FIA MC/F MgIF (Gm.-mm.) (Gm.-mm.) (Gm.-mm.) (mm.) (mm.)

1,361.9 - 1,410.4 0.0 7. -7 1,464.o -1.501.8 55.1 52.0 53.4 1,556.l -1,583.7 43.6 31.2 31.7 1,641.l - 1,663.4 44.1 22.8 23.1 1,724. I - 1,740.3 44.8 18.2 18.4 1,801.2 - 1,815.7 43.7 15.4 15.6 I ,875.S -1,887.l 47.8 13.3 13.4 I .943.5 -1,955.l 45.0 12.0 12.0 2,009.5 -2,019.9 44.6 10.9 10.9 2,074.9 -2,085.9 46.9 9.9 10.0 2,131.2 -2.145.6 49.4 9.2 9.2 2,187.5 -2,206.3 48.9 8.5 8.6 2.243.8 -2,261.6 48.6 8.0 8.0 2,293.8 -2.316.9 50.7 7.5 7.5 2,348.8 -2,361.6 52.0 7.0 7.1

of shape inaccuracies and inaccuracies in the amount of for translation, and a large residual moment must be distal activation. The TMA attraction spring has been placed in the spring. Overall, the effect is similar to that designed to eliminate many of the problems inherent in of a vertical loop where the moment-to-force ratios in- the use of a vertical loop (Fig. 18). The key to its crease during deactivation, but this change is more design is the attempt to make the moment-to-force ratio gradual and hence biologically sounder and more con- more constant. This is accomplished by lowering the trollable. load-deflection rate of the spring and by the use of the T The spring is placed centrally between the two aux- loop design, which increases the activation moment by iliary tubes for two reasons. The most important is that placing wire more apically. Unfortunately, this is not it allows the same rate of change of the moment-to- sufficient to give a high enough moment-to-force ratio force ratio in both the alpha and the beta positions.

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Segmented arch approach to space closure 373

Furthermore, it is simpler to place a symmetrical angu- Table IV. Variations in force system lation in the spring. A typical angulation is shown in (standard deviations) TMA 0.017 by Fig. 19, and the force system of this spring is given in 0.025 inch attraction spring (standard Table III. spring)

At the neutral position, there are relatively equal moments in the alpha and beta positions, with the alpha moment 1,362 Gm.-mm. and the beta moment 1,410 Gm.-mm. It should be noted that this spring requires a rather large residual moment. Let us now follow what happens to the spring beginning with the force system at 7 mm. of activation. At 7 mm., the alpha and beta moments are approximately equal-2,349 Gm.-mm. and 2,368 Gm.-mm. The moment-to-force ratio is 7.0 in both the alpha and the beta positions, and hence the teeth would be expected to undergo controlled tipping near their apices. The centers of rotation that are de- scribed in this section are only representative; neverthe- less, the trend in change of these centers applies to any clinical situation. The actual moment-to-force ratios required for different centers of rotation will vary, de- pending on the teeth and their support. As the teeth move 1 mm., the moment-to-force ratio is 8.0. The center of rotation has moved slightly past the root apex in an apical direction. After the teeth have moved 2 mm. (M/F = 9.2), translation begins; after 3.5 mm. of movement (M/F = 12), root movement is initiated; and at 4 mm., it is continuing. The moment-to-force ratio is increased over 3 mm. of tooth movement but, unlike the simple vertical loop, this change is gradual.

A (mm.) ,G?Il%U?l., MO

(Gm.-mm.)

1.0 43.6 2.2 61.3 1.5 40.1 2.2 59.8 2.0 41.8 2.2 56.4 2.5 39.8 3.3 50.7 3.0 34.1 2.6 46.7 3.5 35.0 2.6 43.5 4.0 33.7 3.5 38.1 4.5 29.4 4.2 33.9 5.0 25.3 4.0 29.8 5.5 26.9 4.1 24.5 6.0 24.5 5.1 18.3 6.5 23.2 5.3 14.7 7.0 20.4 6.2 11.5

A = Distal activation. M, = Anterior moment. FH = Horizontal force. Mg = Posterior moment.

in Table IV are based on averages from five springs which were shaped as accurately as possible. The stan- dard deviations are considerably under 1 percent for all forces and moments. During space closure, the loop of the spring should be maintained centrally between the two auxiliary tubes. A welded vertical pin (0.018 or 0.020 inch TMA) is welded anteriorly for insertion into the vertical tube of the canine. The posterior part of the assembly is bent distal to the first molar or a tie-back loop is welded to the spring (Fig. 11).

The(v) for 1 mm. of deactivation at 7 mm. of

activation is only 1. With a vertical loop,

large with tipping, translation, and root movement oc- curring over 0.2 mm. The greater constancy of the moment-to-force ratio of the TMA attraction spring simplifies the determination of the force system and gives a better biologic response. Nevertheless, one still must carefully observe the progress of space closure and, on the basis of this monitoring, determine the appropriate time for reactivation. During the first stages of space closure, some tipping of the posterior and anterior segments should be noticed. The spring should nor be reactivated and should be left in place until the axial inclinations are correct. Normally, this means that no new activation is required until approximately 3 mm. of space closure has been produced. If one were to leave the spring in place after 3 mm. or so of space closure, no further space will close; if it is left in place too long, exaggerated root correction would be ob- served, followed by increased space in the extraction site.

With carefully bent springs, using a template, vari- ation is at a minimum. The standard deviations shown

POSTERIOR PROTRACTION FOR GROUP C ARCHES

The challenge of space closure lies at two extreme situations-Group A arches where posterior anchorage must be preserved and the Group C arches where posterior teeth must be brought forward through most of the extraction site. It is an error to close the extrac- tion site blindly and then rely on intermaxillary elastics or headgear to correct an intermaxillary discrepancy or an asymmetry in occlusion. For example, in some Class II patients, it is far better to carry out differential mechanics to allow mandibular posterior teeth to be displaced forward.

There are two possible strategies for encouraging posterior teeth to move forward. The first of these in- volves the placement of differential residual moments in the alpha and beta positions. Fig. 20 shows the pas- sive shape of a 0.017 by 0.025 inch attraction spring. The loop has been posteriorly positioned (one third of

Fig. 21. Posterior protraction with a 0.017 by 0.025 inch TMA attractjon spring. Placing the loop off center encourages posterior teeth to displace forward.

Table V. Posterior protraction TMA 0.017 by 0.025 inch posterior positioned

1 FH Fb M,, MB F/A (mm.) (Cm.) (Cm.) (Cm.-mm.) (Cm.-mm.) (Cm.-mm.)

0.0 0.0 137.6 2S73.9 -214.6 0.0

0.5 35.5 122.4 2.570.0 -367.3 70.0 I .o 74.3 108.5 2,561.g -516.2 78.1 I .5 113.5 95.4 23558.0 -664.7 77.4 2.0 153.1 82.9 2,543.0 -809.7 78.7 2.5 190.5 71.5 23533.2 -947.8 75.3 3.0 230.1 60.9 2,518.9 - I ,080.2 79.8 3.5 269.2 50.4 2,502.4 - 1.215.2 78. I 4.0 309.0 40.3 2,486.R - 1,346.4 79.6 4.5 348.4 31.2 2.480.4 - I ,477.6 78.4 5.0 387.4 22.6 2,472.5 - 1,595.5 79.0 5.5 427.2 14.1 2,461.3 -1,715.7 79.1 6.0 466.4 6.7 2,448.g - 1,832.O 79.1

h = Distal activation. F,, = Horizontal force. Fv = Vertical force. M,, = Anterior moment. Mg = Posterior moment. F/A = Load-deflection rate. M,/F = Anterior moment-to-force ratio. MB/F = Posterior moment-to-force ratio

---__ MJF MpIF (mm.) (mm.)

x x 12.5 10.4 34.5 7 0 22.5 5.9 16.6 5.3 13.3 5.0 10.9 4.7 9.3 4.5 8.0 4.4 7.1 4.2 6.4 4.1 5.8 4.0 5.2 3.9

the interbracket distance from the molar tube) and the ping around the apices of the posterior teeth. As the angulation bends are increasingly larger as one ap- spring deactivates over 2.5 mm., the moment-to-force proaches the alpha position. The force system that is ratio will rise slightly to 5.9. Thus, controlled tipping produced is given in Table V. At the neutral position, with a relatively constant beta moment-to-force ratio is very little moment is produced in the beta position (214 present throughout 2.5 mm. of space closure. The Gm .-mm.) and a very large moment in the alpha posi- alpha moment-to-force ratio at the 4 mm. activation is tion (2,574 Gm.-mm.). At 4 mm. of activation, 309 8 .O. The anterior segment might retract initially a small Gm. is produced. Let us now compare the moment-to- amount; however, after 1 mm. of space closure, the force ratios between the alpha and beta positions fol- ratio is 10.9, and if the anterior teeth move at all, they lowing a 4 mm. activation. At the 4 mm. activation, the would tend to translate lingually. After 2 mm. of deac- beta moment-to-force ratio is 4.4. Since the auxiliary tivation, the alpha ratio is 16.6. In this range, as the tube lies 1 mm. apical to the bracket slot, one might spring continues to work out, any anterior movement anticipate tooth movement approaching controlled tip- would be reflected by crown flaring and lingual root

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Segmented arch approach to space elosure 375

Posterior Segment Anterior Segment

100 gm (FE) 185 gm WS) 185 gm (FS) ?- +- < 285 gm (FT)

>

Fig. 22. Force system for posterior protraction using a Class II elastic or a Class Ill elastic. The anterior segment will resist lingual movement while the posterior segment tips forward. Moments are built into a centrally placed 0.017 by 0.025 inch TMA attraction spring.

Fig. 23. Posterior protraction using force system described in Fig. 22. Class II elastic increases force to the posterior seg- ment. Angulation in spring prevents the incisors from tipping lingually.

Table VI. Posterior protraction attraction spring TMA 0.017 by 0.025 inch centered with 100 Gm. elastic

(nit.) (2, (2) M,iF MB/F (mm.) (mm.)

0.0 0 100 100 1,362 1,410 x 14.1 0.5 28 100 128 1,464 1,502 52.0 11.7 1.0 50 100 150 1,556 1,584 31.2 10.6 1.5 12 100 172 1.641 1,663 22.8 9.7 2.0 95 100 195 1,724 1,740 18.2 8.9 2.5 117 100 217 1,801 1,816 15.4 8.4 3.0 141 loo 241 1,876 1,887 13.3 7.8 3.5 163 100 263 1,943 1.955 12.0 7.4 4.0 185 loo 285 2,009 2,020 10.9 7.1

3 = Distal activation. Fs = Horizontal force of spring. FE = Horizontal force of elastic. M, = Anterior moment. Mp = Posterior moment. FT = Total horizontal force on posterior segment. M,/F = Anterior moment-to-force ratio. MB/F = Posterior moment-to-force ratio.

movement. Differential mechanics are in effect; this allows the posterior teeth to move forward by con- trolled tipping and the anterior teeth (if they move at all) to move slightly labially. A side effect is possible anterior extrusion because of the vertical extrusive force on the incisors.

This spring is designed to encourage posterior pro- traction by utilizing the following principles: (1) the loop is placed off center; this produces a more constant center of rotation in the beta position. By contrast, in the alpha position, the moment-to-force ratio rapidly increases so that if these teeth move at all, they will tend to move forward rather than posteriorly. (2) The force is kept under 300 Gm. to minimize anterior re- traction or root movement. Buccal protraction using

0.017 by 0.025 inch TMA off-center attraction springs is shown in Fig. 21.

The second strategy that can be used for displacing posterior segments forward uses a symmetrically placed attraction spring with the use of either Class II or Class III elastics. By using intermaxillary elastics during space closure, one can minimize some of the side ef- fects that would be evident if the same elastics were used after all space is closed, and the entire arch must be displaced. In lieu of elastics, protraction headgear may also be considered.

The TMA attraction spring is centrally placed be- tween the auxiliary tube of the first molar and the verti- cal tube of the canine. Typical angulation is placed as in previously described Group B arches where en masse

Table VII. Posterior protraction attraction spring TMA 0.0 17 by 0.025 inch centered with I SO Gin. elastic .--_-.--... 1 F.5

(mm.) (Cm.) (& (c”n:., Me MU MJF M,jIF

(Cm.-mm.) (Cm.-mm.) (mm.) I mm )

0.0 0 150 150 1,362 0.5 28 150 178 1,464 I .o 50 150 220 1,556 1 .s 12 150 222 1,641

2.0 95 150 245 1,124 2.5 117 150 261 1,801 3.0 141 150 291 1,876 3.5 163 150 313 1,943 4.0 185 150 335 2,009

1,410 7

1,502 52.u 1,584 31.2 1,663 22.8 1,740 18.2 1,816 15.4 I.887 13.3 1,955 12.0 2,020 10.9

9.4 x.4 1.9 1.5 7.1 6.X 6.5 6.2 6.0

A = Distal activation. F, = Horizontal force of spring. F, = Horizontal force of elastic. M, = Anterior moment. MB = Posterior moment. F., = Total horizontal force on posterior segment. M,,/F = Anterior moment-to-force ratio. MB/F = Posterior moment-to-force ratio.

translation is desired. The spring is activated 4 mm. instead of the typical 7 mm. Fig. 22 shows the force system that is developed, incorporating both an attrac- tion spring activated to 4 mm. and an intermaxillary elastic of 100 Gm. The vertical forces of the elastics are not considered. The anterior segment at the alpha posi- tion will feel the force from the spring (F,) and the moment (MU). The posterior segment will feel two forces-the force from the spring (F,) and the force from the intermaxillary elastics (FE), giving a total force (FT). A differential moment-to-force ratio is pro- duced between the anterior and posterior segments since the force is different between anterior and posterior segments. Tables VI and VII give the force system, in its entirety, for elastics of two different strengths (100 Gm. and 1.50 Gm.). For a 150 Gm. elastic, during 3 mm. of deactivation starting from a 4 mm. activation, the beta moment-to-force ratio will increase from 6.0 to 7.9. Over this distance, the poster- ior teeth will tip forward with a center of rotation apical to the apices of the roots. The alpha moment-to-force ratio at 4 mm. is 10.9, implying translation or lingual root movement, and increases to 31 after 3 mm. of space closure. Overall, during space closure, the in- cisors will tend to come forward and/or their roots will move lingually (Fig. 23). By reducing the elastic force to 100 Gm., slightly higher /3 moment-to-force ratios can be produced, so that after space closure less poster- ior root correction is required. The tables give two possibilities in producing a differential force system. Others are possible, either by altering the alpha and beta moments through angulation in the attraction

springs or by increasing or decreasing the force of the intermaxillary elastics.

In comparing the two strategies for posterior pro- traction, with and without intermaxillary elastics, the choice depends upon the treatment objectives. By plac- ing a loop off center, one can produce a differential moment-to-force ratio; however, this is produced at the expense of vertical extrusive forces in the anterior seg- ment. If one contemplates intruding or has intruded the anterior teeth, this method is not indicated. The use of intermaxillary elastics may alter the plane of occlusion, and particularly Class II elastics may undesirably steepen a plane of occlusion, erupting incisors in a Class II patient. This undesirable side effect can be minimized or eliminated by the use of a headgear to the upper arch which would produce a moment with re- spect to the center of resistance that flattens the plane of occlusion.

Since relatively low forces are capable of retracting six teeth, there is little logic to separate retraction of canines followed by retraction of the four incisors. For that reason, only patients who have anterior arch-length problems with anterior crowding require separate canine retraction. The force system that is used for retraction of the canine is similar to that for en masse space closure. The composite retraction spring is used in Group A arches, and the attraction spring is em- ployed in Group B and C arches (Fig. 24). The differ- ence lies in rotational control of the canine, which is achieved with a non&ding mechanism. Antirotation

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Segmented arch approach to space closure 377

Fig. 24. Canine retraction with a 0.017 by 0.025 inch TMA attraction spring (lower right). Antirotation bends have been placed in the spring. Rotation is controlled without the friction of a canine bracket sliding on an arch wire.

bends are placed in the retraction assemblies to prevent the canine from rotating as it retracts. It is also possible to use an arch wire to prevent rotation.

The TMA composite 0.017 by 0.025 inch retraction assembly is shown with antirotation bends (Fig. 25). Not only are bends and twists placed in the area of the spring, but a toe-in bend is placed immediately in front of the first molar. The angulation and distal activations are usually identical to those used for en masse space closure.

SUMMARY AND CONCLUSIONS

Treatment objectives differ in the extraction case from anterior retraction to posterior protraction. Differ- ential mechanisms can be successful because of differ- ences in the force system that they produce. It is impor- tant to control not only the magnitude of the force but also the moment-to-force ratios which produce the de- sired centers of rotation. In addition, a differential moment-to-force ratio between the anterior teeth (alpha position) and the posterior teeth (beta position) is in- strumental in anchorage control. It is desirable to main- tain a constant force level, and this was achieved by designing springs with low load-deflection characteris- tics. The rate of change or constancy of the moment- to-force ratio during deactivation typically is small. This constancy is varied between the anterior and pos- terior teeth to enhance anchorage and to control anterior axial inclinations.

Space closure by control of the force system is meaningful only if the clinician can practically produce the force system. The mechanisms that have been de- scribed are predictable for a number of reasons. The springs have been calibrated in the laboratory so that,

Fig. 25. Canine retraction. Antirotation bends are placed in a 0.017 by 0.025 TMA composite retraction spring. All other acti- vations are similar to en masse retraction.

for any given activation, both the forces and moments are known at both ends of the spring. The attraction mechanisms are prefabricated, and hence the geometry and wire cross sections are accurately duplicated. Moreover, the design of the springs uses the principle of low load-deflection rates and moment-deflection rates. These low rates ensure that the springs must have large distal activations and large angulation bends. With large activations, a clinical error of 1 mm. or so or of a few degrees is not that significant. Finally, the force system is predictable since we are basically deal- ing with frictionless springs and are not dependent upon sliding teeth along an arch wire for control.

Certain design features have been incorporated into retraction springs to optimize the force system:

1. The material used is beta-titanium, which sim- plifies the design and allows for direct welding of ma- terials. TMA has excellent spring-back properties with good formability. The wire cross sections are kept as small as possible, limited by the moments needed rather than the force. In one spring, a composite spring uses a heavier-base arch in order to ensure that an ade- quate beta moment is produced.

2. Additional wire that is placed into an attraction spring or loop is critical. Additional wire should be placed as far apically as possible to increase the activa- tion moment-to-force ratio. Indiscriminant placement of wire will reduce the moment-to-force ratio. The T loop design is employed to enhance this ratio.

378 H~rr.srorw

3. The loop centricity affects the rate of change of the moment-to-force ratio in the alpha and beta posi- tions. If equal rates of change are required, loops should be centrally placed. Where greater moment-to- force ratio constancy is required, loops should be dis- placed off center in the direction of those teeth (seg- ment) where constancy is needed.

4. The large interattachment distance between the auxiliary tube on the first molar and the vertical tube of the canine allows sufficient room for the large activa- tions required. In addition, it adds to the accuracy of determining the force system, since small errors in the shape or geometry of the spring will not radically change the forces produced.

Variation in moment-to-force ratios as well as force magnitude might be required for different clinical situ- ations. In the attraction mechanisms that have been described, the clinician varies the force by altering the amount of activation according to force tables. He may also alter the moment-to-force ratio by changing either the angulation or the amount of activation. Typically, this is accomplished by increasing or decreasing the distal activation rather than the angulation. Although the force system is complicated, clinical practice is not, since with calibrated springs the orthodontist need only reproduce a shape and decide on the number of milli- meters of activation. Another significant consideration is the centricity of the loop. Loops should not be placed anywhere mesiodistally. With the attraction springs de- scribed in this article, the general rule is as follows: If the posterior teeth and the anterior teeth are to move relatively equal amounts, the loop is centered. If posterior teeth are to be maintained, the loop is placed anteriorly, and if anterior teeth are to be maintained, the loop is placed posteriorly.

The attraction mechanisms that have been described are applicable to both the en masse space closure and canine retraction. En masse space closure is the prefer- able movement, since the force system is simpler, and

for that reason canine retraction should be employed only in those patients in whom anterior crowding is present.

Attraction mechanisms which deliver highly pre- dictable forces have been described. They are charac- terized by large activations; however, they deliver rela- tively low force magnitudes. Since activations are large, it is not necessary and it may be undesirable to reactivate them frequently. Reactivation depends on careful monitoring of how space closure is proceeding. An understanding of the force system and where and how to modify it, with an appliance that is capable of delivering a predictable force system, adds a new di- mension to the closure of space in the extraction case.

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Burstone, C. J.: The rationale of the segmented arch, AM J.

ORFHOD. 48: X05-21, 1962. Burstone, C. J .: Mechanics of the seymented arch technique, Angle Orthod. 36: 99-120. 1966.

Burstone. C. I., and Koenig, H. A.: Optimizing anterior and

canine retraction, AM. 5. ORTHOD. 70: I-20, 1976. Goldberg, J.. and Burstone, C. J.: An evaluation of beta

titanium alloys for use in orthodontic appliances, J. Dent. Res. 58: 593-600, 1979.

Burstone, C. J., and Goldberg, J.: Beta titanium: A new orth-

odontic alloy, AM. J. ORTHOD. 7: 121-132, 1980. Burstone, C. J.: Application of bioengineering to clinical orth- odontics. In Graber, T. M. (editor): Current orthodontic con-

cepts and techniques, ed. 2, Philadelphia, 1975, W. B. Saunders Company. pp. 230-258.

Solonche, D. J., Burstone. C. J., and Vanderby, R.: A device for determining the mechanical behavior in orthodontic appli-

ances, IEEE Trans. Biomed. Eng. 24: 538-539, 1977. Koenig, H. A., Vanderby, R., Solonche, D. J., and Burstone,

C. J.: Force systems from orthodontic appliances: An analytical and experimental comparison. J. Biomech. Eng. 102: 294.300,

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Yang. T. Y.. and Baldwin, J. J.: Analysis of space closing

springe in orthodontics, J. Biomech. 7: 21-28, 1974. Baeten. L. R.: Canine retraction: A photoelastic study, AM. J.

ORTHOD. 67: 11-23, 1975.

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