American Journal of ORTHODONTICS Volume 73, Number 5 Mey, 1979

ORIGINAL ARTICLES

Preadjusted edgewise appliances: Theory and practice Michael Meyer, D.D.S.,’ and Gerald Nelson, D.D.S. Berkeley, Calif.

S cience divides itself most broadly into two categories: (1) pure or theoretical science and (2) applied or technological science. Technology evolves in its own empirical fashion. Most technical innovations do not arise out of precise scientific principle but, rather, are the result of experience and practical intuition. In orthodontics, evolution of bracket design has occurred precisely in this fashion.

In July, 1928, Edward H. Angle published the first in a series of three articles describing the edgewise appliance. In the second article of the series’ he recommends angulation of posterior brackets to produce desired tooth movement without resorting to detailed arch wire adjustments: “This permits the use of the arch in its simplest form, or that freest from bends, which of course has its advantage” (Fig. 1). Angle’s idea was later expanded by other clinicians to include tipping of maxillary anterior brackets and, finally, angulation of rectangular slots of maxillary anterior brackets. Just as with Angle’s tipped posterior brackets, anterior bracket tipping and slot angulation produce desired tooth movement without arch wire adjustments.

In 197 1 an edgewise appliance that represents the logical extension of Angle’s original concept was made commercially available. All of the brackets had incorporated into them control of tooth movement in three planes of space, thereby producing, in conjunction with arch wires, tip, torque, and in/out movement simultaneously on all teeth. Many manufacturers now offer similar appliances. The objective of all of these appliances is the same: to produce desired tooth movement with a minimum amount of wire adjustments.

Since these appliances are preadjusted, except for arch form, and contain within them the potential for a complex array of simultaneous tooth movements, careful consideration of basic mechanical principles seems in order if we are to use them to advantage.

Design considerations in edgewlse treatment

The rotating and translating effects of a single force applied to an object, such as a tooth, are described in the terms of moments. Moments are measured by the product of the

*Assistant Rofessor of Orthodontics, Department of Growth and Development, University of California at San Francisco.

OOOZ-9416/78/0573-0485$01.40/O 0 The C. V. Mosby Co. 405

486 Meyer and Nelson .4m. J Onhod. Mav 1978

Fig. 1. Edward H. Angle suggested angulating posterior brackets to produce desired tooth movement in a 1929 article in the Dental Cosmos.’

F c d

r!l

Fig. 2. The rotating effects of a single force applied to an object are described in terms of moments. Moments are defined as force(F) times distance (6): M = Fd. Note that two movements oocur: rotation and translation.

applied force times the shortest distance from the center of rotation of the tooth to the line of the force, as shown in Fig. 2. If two parallel forces of equal magnitude are applied to a tooth in opposite directions, they cancel each other as linear forces and produce a pure rotation of that tooth. These paired forces are called a couple. A couple creates moments of rotation. The moment of a couple can be measured by multiplying one of the forces of the couple by the distance separating the lines of the forces. When a couple is operating, the moment of rotation is the same at all points in the body being acted upon regardless of the point of application of the forces’ (Fig. 3, A).

All of the forces delivered by the interaction of a wire in a preadjusted edgewise bracket can be described in terms of moments or couples or their combinations.

Preadjusted edgewise appliances 407 vdu?w 73 Number 5

t

0 0

m

Fig. 3. A, Moments of rotation. Two equal forces are acting in the same plane on this body. The moment of rotation (M = Fd) is the same at points A, 8, C, D, or any other selected~point. 6, Tip. Built-in tip produces a moment of rotation as a result of the force couple (F, and Fz). C$ Torque. Built-in torque produces a moment of rotation as a result of a force couple (F, and F2).

In ordei to produce simple mesial or distal tipping movement, a bracket configuration that creates a couple at the bracket-wire interface is used as shown i’n Fig. 3, B. Since we are dealing with a couple force system, the couple may be produced by a bracket tipped on its base or a slot that is angulated within the bracket. The rotational moment on the tooth is incidental to the means of force application.

The same design principle applies to preadjusting for torquing tooth movements. Torque, as we use the term in orthodontics, simply means a rotational force in a labiolin- gual or buccolingual direction. Torquing forces are developed by the interaction of rectangular wires in rectangular wire slots. This interaction produces a couple at the bracket, as shown in Fig. 3, C. For design purposes, the slot may be “torqued” relative to the base of the bracket, or the bracket base may be “torqued” relative to the tooth surface. The resultant force is exactly the same if the bracket placement is correct. Note Fig. 4, A and B to make a comparison. In A the stem of the bracket is angulated to the bracket slot, while in B the bracket stem is parallel to the bracket slot.

Each of these brackets must be positioned somewhat differently un the band to receive an unadjusted arch wire. For example, in the lower molars, the bracket illustrated in Fig. 4, A must be welded slightly more gingivally on the band to receive an unadjusted wire than the bracket illustrated in Fig. 4, B. Bracket-to-band positions are determined at the factory according to the bracket design requirements. If one chooses to weld his own attachments, brackets should be positioned according to the bracket slot, not the center line of the bracket base. Brackets with torque built into the bracket face will have a different relationship to their base than brackets with torque in the bracket base. The slot is therefore the most consistent point from which to judge bracket position.

In/out forces applied to a tooth to position it labiolingually or buccolingually will have

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Fw-

Fig. 4. A, Bracket stem at angle to slot. B, Bracket stem parallel to slot. Brackets are positioned on band so that resultant torque is the same; that is, the slot/tooth positions are identical if bracket placement is guided on the slot. C, In and out. Buccai and lingual movements are accompanied by rotational moments of small magnitudes due to force couple Fw (arch wire) and Fr (resistance of bony socket).

Fig. 5. Arch wire bends in a standard appfiance offer a visual image of tooth position. In the preadjusted drawings, the magnitude of adjustments is concealed to some extent, since the adjustments are in brackets rather than in the arch wire.

both rotational and translational effects. Fig. 4, C shows that such forces on the crown produce a moment on that crown. Preadjusted appliances alter the distance between the wire and the tooth surface in varying amounts around the arch to accomplish in-and-out positioning. Rotational moments on each tooth result.

Dynamics and ctinical imp#u?lions

Fig. 5 illustrates a standard edgewise appliance and a preadjusted appliance. Torque, tip, and in-and-out adjustments are all built into the bracket of the preadjusted appliance as shown in A and B. The magnitude of each preadjustment in such appliances should be based on the judgment of the individual practitioner. Many variations of preadjustment prescriptions are commercially available. These commercial variations range from stock appliances that offer a total set of preadjustments to those that allow the practitioner to determine the preadjustment on each tooth.

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Table I. Deviation angle for edgewise wire with 0.003 inch corner radius

Wire size (inches) *

0.016 x 0.016 0.016 x 0.022 0.016 x 0.022 0.016 x 0.026 0.016 x 0.026 0.017 x 0.017 0.017 x 0.017 0.017 x 0.022 0.017 x 0.022 0.017 x 0.025 0.017 x 0.025 0.018 x 0.018 0.018 x 0.018 0.018 x 0.022 0,018 x 0.022 0.018 x 0.025 0.018 x 0.025 0.019 x 0.025 0.021 x 0.021 0.021 x 0.025

0.0215 x 0.025 0.0215 x 0.028 0.022 x 0.022

0.018inchslot

16.68 9.28

7.27

8.16

5.37

4.48

2.19

1.63

1.37

0.022 inchslot

27.45

20.04

Rotates

22.31

17.68

Rotates

17.47

14.04 10.52 5.00 3.88 2.30 1.97 0.90

*Sizes in millimeters can be determined by multiplying values expressed in thousandths of an inch by 25.4.

The preadjustments are designed to produce ideal final tooth position. The complexity of forces acting through such an appliance is impressive and deceptive. Built-in adjust- ments, for the most part, cannot be easily seen clinically. Comparable adjustments placed in an arch wire are strikingly apparent, as shown in Fig. 5. Furthermore, each bracket has its maximum adjustment from the beginning. Incremental adjustments are achieved by gradually increasing the wire size, rather than by sequential wire adjustments. Final ideal tooth positions result from maximum expression of the preadjusted attachments. Maxi- mum slot expression is achieved by placement of “full-sized wires” (that is wire size and bracket-slot size nearly the same). Iffull-sized wires are not used, complete expression of built-in adjustments will not occur. Final, ideal tooth positions may then have to be achieved by careful wire adjustments.

It would be a mistake to believe that the preadjusted appliance reacts clinically in the same way as a conventional edgewise appliance. It reacts in a significantly different manner, and, if it is to be used to advantage, clinical differences must be thoroughly understood. Torque, tip, and in/out adjustments operate within the appliance concur- rently. Nevertheless, it is of some benefit to consider each of these preadjustments indi- vidually as well as the interplay between them.

Torque forces in wires and brackets

Placement of the first rectangular arch wire brings anterior and posterior torquing forces immediately into play. The nature of the forces delivered depends on wire size as it relates to slot size. Table I lists the nominal deviation angle, or “slop,” for different wire sizes in an 0.018 and 0.022 inch (0.457 and 0.559 mm.) bracket slot. The nominal devia-

Fig. 6. A, When torque in a bracket is designed by a manufacturer to be 7 degrees, the 7 degrees refers to the angle between the bracket slot and the bracket base. B, Root artgulation (often measured in head films), when related to the bracket slot, might ba in the range of 20 degrees. C, Because of the resistance presented by the lingual wall of the anterior bony socket, anterior torquing couples can result in mesial movements of the posterior teeth.

tion angle is the amount of rotation the wire can undergo before it engages the bracket slot. The effect of an average wire corner radius is included in the table.

Clinically, the deviation angle will depend upon the exact dimensions of a specific point in the bracket slot, the corner radii of the specific wire being used, and each specific bracket. If the preadjusted torque is to be fully realized, full-sized wires must be used. If smaller wires are used, the built-in torque will not be fully expressed. For example, let US

suppose that the built-in torque of a maxillary incisor bracket is 7 degrees. This measure- ment refers to the angle formed between the face of the crown and the floor of the bracket slot, as shown in Fig. 6, A. In an incisor with a normal anatomic relationship between its crown and root, a 7 degree built-in slot torque will produce a root angulation of approxi- mately 20 degrees, as shown in Fig. 6, B. This expression, however, depends upon the fit of the wire to the slot.

A wire that completely fills the slot will produce 20 degrees of root angulation. Referring to Table I, one can calculate the degrees of torque expressed as a function of the

Preadjusted edgewise appliances 491

Fig. 7. A, Orthographic projection of buccal root axes as seen from the anterior aspect showing arrangement of teeth relative to alveolar bone. B, Relative orientation of axes of roots of teeth as seen in the anterior view of skull. (From Dempster, W. T., Adams, W. J., and Duddles, FL A.: Arrangement of the Roots of the Teeth, J. Am. Dent. Assoc. 67:779-797, 1963. Copyright by the American Dental Association. Reprinted by permission.)

wire size. An 0.0215 by 0.028 inch (0.546 by 0.711 mm.) wire in an 0.022 inch (0.559 mm.) bracket will produce 18.2 degrees of root torque (20 degrees - 1.97 degrees). An 0.018 by 0.025 inch (0.457 by 0.635 mm.) wire in an 0.022 (0.559 mm.) slot will produce 8 degrees of root torque. A 0.017 by 0.025 inch (0.432 by 0.635 mm.) arch wire in an 0.018 inch (0.457 mm.) slot appliance will deviate 4.48 degrees, producing 13.52 degrees of root torque. It is of interest to note that an 0.018 by 0.018 inch (0.457 by 0.457 mm.) wire in an 0.018 inch (0.457 mm.) slot will deviate only 2.19 degrees, while at the same time providing more interbracket resiliency than a 0.017 by 0.025 inch (0.432 by 0.635 mm.) wire.

As torque is applied to the anterior teeth, resulting forces are transferred to the posterior teeth. Impact on maxillary posterior anchorage is significant, as illustrated in Fig. 6, C. Torquing couples created by the maxillary anterior brackets will tend to cause mesial movement of the maxillary posterior teeth and flaring of the incisors. If such movement is not desirable, according to the dictates of the given case, anchorage en- hancement must be designed into the treatment plan at an earlier stage than needed with a conventional appliance. Anchorage loss will occur if this is not done.

Torquelike tooth movements may occur in the lower posterior segments even during

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Fig. 8. Excessive lingual crown torque. In the lower molars, leveling may produce undesired lingual crown angulation. For example, the center of resistance of a lower second molar is slightly buccal to the molar attachment. During leveling, an intrusive force produces a lingual tipping movement if the force vector is lingual to the center of resistance.

leveling with round wires. The normal root angulation of the lower molars is already markedly lingual, as shown by Dempster and associates3 (Fig. 7). The intrusive force of a leveling arch wire applied to these teeth will produce a lingual rotational moment, as shown in Fig. 8. A mandibular laminagram in Fig. 9 illustrates the situation. In a con- ventional appliance this lingual tipping is counteracted by the first rectangular arch wire (if no lingual torquing is bent into the arch wire). In the preadjusted appliance, lingual tipping is not corrected until the wire size adequately fills the bracket slot. If full-sized wires are never used to finish, lingual crown tip of lower posterior segments, especially second molars, may persist throughout treatment.

Built-in tip in brackets

Careful study of untreated “normal” occlusions has shown that, in general, root apices are distal to their respective crowns. 4, 5 Each tooth will, of course, vary in the amount of distal root position. The general objective of built-in tip is to accomplish this mesiodistal crown-root angulation. 6 Built-in bracket tip creates reciprocal forces that begin acting with placement of the first arch wires. A force couple working in the mesiodistal direction will have a strong tendency to move crowns toward the mesial, as shown in Fig. 10, A. As such, the relative anteroposterior position of the teeth must be given careful consideration. Early anchorage enhancement may be necessary if mesial movement of buccal segments is to be avoided.

Generally, the further that roots are positioned distal to their crowns, the more arch length will be required, as seen in Fig. 10, B. If this arch length is not provided, ideal overbite and overjet cannot be achieved. For example, maxillary incisors that are positioned with their roots distal to their crowns will occupy more space mesiodistally than if the roots are upright over the crowns. If an ideal anterior relationship is to be

Volume 73 Number 5 Preadjusted edgewise appliances 493

Fig. 9. Laminagram of lower second molar. Because of the natural lingual inclination of the lower second molar, the center of resistance will lie buccally to an intrusive force applied at the attachment. Such a force will produce lingual tipping movements.

achieved, then the maxillary posterior teeth must be farther to the distal. If the posterior teeth are not positioned to accommodate the arch length required by distal positioning of incisor roots, ideal anterior relationship is not possible. Care must also be taken to provide the additional necessary arch length in borderline extraction cases.

Any auxiliary mechanics employed during treatment that act in the anteroposterior direction will have either a transient additive or opposing action to the built-in tip of the appliance. For example, a high-pull headgear force applied to the maxillary first molars (distal root tip 5 degrees) with a conventional face-bow may enhance the distal tipping action of the brackets, causing excessive distal root position of the first molar and exces- sive mesial tip of the crown, as seen in Fig. 10, C. Similarly, space-closing mechanics in the maxillary arch will create mesial crown-tipping moments on the crown of the first molar. This mesial crown tip will be additive to the built-in tip of the first molar bracket. Excessive mesial crown tip will result if compensations are not made (Fig. 11).

In-and-out preadjustments

The most subtle ingredient of the preadjusted appliance is the in-and-out preadjust- ment. The final, precise interdigitation of a finished case often depends upon small,

494 Meyer and Nelson

Fig. 10. A, Oaring effect. Built-in adjustments to position roots distal to their crowns may, unless properly controlled, produce mesial crown movement rather than distal root movement. 6, When a tooth is positioned with distal root tip, the effective mesiodistal crown width is increased. C, Additive forces on the first molar which may result in excessive distal root tip. a, High-pull face-bow with outer bow short and high. b, Closing force in an extraction case. c, Built-in distal root tip (5 degrees) in the preadjusted molar assembly.

individualized in-and-out adjustments that cannot be expected to be built into any stock appliance. For this reason, it is extremely important to pay careful attention to the relative positions of the teeth within the arch and the interdigitation of the opposing den&ion. Arch wire adjustments will more often be required to correct in-and-out adjustments than tip or torque adjustments. Furthermore, special extraction cases, such as those involving removal of maxillary first premolars or maxillary and mandibular second premolars, will not lend themselves precisely to the prescribed in-and-out preadjustments. First-order wire adjustments may be required in these cases. Although in-and-out positioning creates rotational moments of all of the teeth within the arch, the magnitude of these moments is relatively small and may be disregarded.

Volume 73 Number 5 Preadjusted edgewise appliances 495

Fig. 11. Excessive distal root tip on an upper first permanent molar.

Appliance placement

Accurate placement of an appliance is crucial for consistently excellent treatment results, regardless of whether or not the appliance is preadjusted. However, correct placement is probably even more important in the preadjusted appliance, since the natural tendency is to place an unadjusted wire. Because much of the preadjusted appliance’s potential tooth movement rests unseen in the bracket, it is important to understand the general limit of placement error for each of the preadjustments. Generally, attachments are designed to “fit” at the midpoint of the clinical crown. The use of bands to hold the attachments places obvious confines to the placement of brackets. Extreme vertical varia- tion is unlikely.

Direct bonding makes possible a new dimension of possible vertical placement of attachments but, even with the possible variability with bonded attachments, extreme variation seems unlikely. As shown in Fig. 11 a 3 mm. occlusal displacement of the bracket from dead center on the crown of a mandibular first premolar results in a 15 degree alteration in the applied torque and a .04 mm. alteration in the applied in/out. Generally, the mandibular first premolar has the greatest occlusogingival buccal curvature of any tooth, so Fig. 12, A picks the most extreme variation to be expected with an excessive 3 mm. vertical displacement. Less vertical displacement on a similarly curved tooth or the same displacement on a tooth with less buccal curvature will produce corres- pondingly less torque and in-and-out alteration. For example, in younger patients it is often difficult to position the appliance in the occlusogingival center of the crown because of the level of the gingiva. With the resulting occlusal displacement of the appliance, special attention should be paid to the lingual crown torque on the mandibular first and second premolars .

If one considers a 3 mm. vertical displacement unlikely, and there is “slop” in most rectangular wire/bracket engagements, it seems reasonable to suppose that significant al- terations of the tooth positions will not occur from an appliance that is not placed dead center on the crown. Naturally, bracket placement should not vary from one tooth to an-

496 Meyer and Nelson

Fig. 12. A, Bracket placement variations in the vertical direction have a moderate effect on torque and on in-and-out adjustments. If a full-size arch wire is not used, the “slop” between the arch wire and bracket slot would probably exceed error from placement variations. B, A 3 degree error in band placement will result in a 0.68 mm. deflection of the root tip. Errors of 6 to 10 degrees in placement of the band to bracket are not uncommon. C, Regress films should be taken after leveling to check root positions. Midcourse corrections in band placement can then be made.

other, but special clinical circumstances that require bracket positions that are not ideal will not create significant torque or in-and-out errors.

Tooth-position errors created by attachment misplacement for built-in tip have the potential to be much more significant. The limited space between adjacent roots allows a very small margin of error for root placement. One primary objective of all orthodontic treatment is to ensure a regular bone thickness between parallel roots. Attachment mis- placement that creates an alteration in the designed tip will jeopardize this objective.

Fig. 12, B, illustrates an approximate deflection of 0.7 mm. at the tip of a root displaced by a 3 degree error during appliance placement. It is relatively easy to make a 3 degree tipping error during appliance placement, especially on premolars, maxillary lateral incisors, and mandibular incisors. Furthermore, root position and form are very difficult to judge clinically, especially if crown contour is unusual.

Periapical roentgenograms during early treatment progress can provide valuable in- formation to verify appliance position. Once the case is leveled and spaces are closed, long-cone x-rays (with the root parallel to the film) will illustrate root position. Where misplacement has occurred, the brackets or bands should be reset. Valuable treatment time may be required to recover from placement errors if they are not discovered early. If the appliance is to be used as designed, then accurate and consistent appliance placement is important - more important than placing the appliance in any preordained idealized position on the tooth.

ng the appliance

Although the preadjusted appliances represent a significant improvement in our treat- ment procedures, it is imperative to understand that the quality of the treatment still rests

Volume 73 Number 5

Preadjusted edgewise appliances 497

with the skill of the orthodontist and not with the refinements of the appliance. Preadjusted appliances facilitate treatment remarkably well, but they are not perfect, and the excellent clinician will not use them without thinking. Our experience has led us to pay careful attention to the following:

1. One should be very careful with anchorage. Early enhancement and/or early application may be necessary.

2. One should watch for excessive lingual crown tipping, especially in the lower posterior segments. One may choose to alter arch width of the arch wires to introduce counteractive tipping moments. Be certain to finish cases with full-sized wires if the maximum preadjustment is required.

3. Consideration should be given to changing the preadjustment prescription from the stock prescription. If one’s mechanics call for the use of finishing wires that are not “full size,” altering the magnitudes of the preadjustments to com- pensate seems logical. An increase in maxillary incisor torque and a decrease in mandibular molar torque are examples of workable preadjustment changes. A review of Table I will indicate compensation necessary to accommodate various degrees of bracket-to-wire “slop.” In this regard, if the orthodontist is deter- mined to use low forces values but desires full expression of built-in adjustments, he should consider the use of square finishing wires. For example, use of 0.017 by 0.017 inch (0.432 by 0.432 mm.) or 0.018 by 0.018 inch (0.457 by 0.457 mm.) wires in an 0.018 (0.457 mm.) bracket offers good control with a remark- able improvement in resiliency and range of action over an 0.017 by 0.025 inch (0.432 by 0.635 mm.) or an 0.018 by 0.025 inch (0.457 by 0.635 mm.) wire. Not all manufacturers can provide individualized preadjustment prescriptions.

4. The line offorce application of extraoral appliances should be monitored. Outer bow adjustments may be necessary to control maxillary first molar tip. Consideration may also be given to reducing the distal root tip preadjustment of the maxillary first molar attachment.

5. Root positions should be monitored with periapical x-ray films during midtreatment. Once the case is level, twelve periapical films will show root position and reveal any misplaced bands. This will provide early detection of mispositioned roots.

6. Extraction cases present special consideration. So-called ‘ ‘extraction series” brackets are commercially available. Generally, these brackets have altered tip and rotational components to counteract unwanted tooth movement resulting from retraction forces. Logically, as the case is completed, these pread- justments will tend to position the teeth adjacent to the extraction site in an “overtreated” position. However, there is some question as to the necessity of overtreatment in extraction cases. Hatasakas has shown that roots overtreated in anticipation of posttreatment rebound will remain overtreated, leaving an unde- sirably thin interproximal bony thickness.

Cases involving extraction of mandibular second premolars will often re- quire wire compensations. The anatomy of the contact between a mandibular first premolar and a first molar usually will require a molar offset bend to proper- ly position the two teeth.

Maxillary first premolar extractions only will also require wire compensa-

498 Meyer and Nelson

tions. Usually, the maxillary first molar fits best in a Class II position if the mesiobuccal cusp is rotated mesially and the normal distal root tip is reduced. This molar position permits good occlusion with the mandibular first molar and first premolar and good marginal ridge approximation within the upper arch. The preadjustments of the maxillary first molar bracket will counteract efforts to place the first molar in this good Class II position. Wire adjustments or altered bracket position will be needed. Consideration should be given to the use of a standard, unadjusted attachment on the first molar for the upper first premolar extraction case.

7. Tooth size discrepancy cases present special problems. Preadjustments designed from ideal occlusion do not lend themselves without alteration to the positioning of unusually proportioned teeth.

8. It is necessary to prevent loss of control of the appliance. Early correction of unwanted movements must be made to prevent extension of treatment time. Correction is best made by resetting misplaced attachments. It is difficult to overcome inappropriate built-in bracket adjustments with arch wire adjustments.

Summary

The introduction of totally preadjusted appliances has had a significant impact on edgewise orthodontic treatment. It is important to understand the theoretical aspects of any technological improvement if it is to be used to advantage. On the other hand, theory cannot stand alone in a clinical discipline such as orthodontics. With this in mind, this article contains both theoretical considerations and practical clinical applications of pread- justed appliances. Problems with the “stock” preadjusted appliance are discussed, and suggestions for solving these problems are given. A strong recommendation is made that the individual practitioner carefully consider the preadjustment prescription that best suits the style of his treatment.

REFERENCES I. Angie, Edward H.: The latest and best in orthodontic mechanism, Dent. Cosmos 71: 260-270, 1929. 2. Thurow, Raymond C.: Technique and treatment with the edgewise appliance, St. Louis, 1962, The C. V.

Mosby Company. 3. Dempster, W. T., Adams, W. J., and Duddles, R. A.: Arrangement of the roots of the teeth, J. Am. Dent.

Assoc. 67: 779-797, 1963. 4. Andrews, Lawrence: The six keys to normal occlusion, AM. J. ORTHOD. 61: 297-309, 1972. 5. Holdaway, Reed A.: Bracket angulation as applied to the edgewise appliance, Angle Orthod. 22: 227-236,

1952. 6. Hatasaka, Harry: A radiographic study of roots in extraction sites, Angle Orthod. 46: 64-68, 1976.

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