Understanding Space Closure in Orthodontics (2016 PDF)

special article Understanding the basis of space closure in Orthodontics for a more efficient orthodontic treatment Gerson Luiz Ulema Ribeiro1, Helder B. Ja...

special article Understanding the basis of space closure in Orthodontics for a more efficient orthodontic treatment Gerson Luiz Ulema Ribeiro1, Helder B. Jacob2 DOI: http://dx.doi.org/10.1590/2177-6709.21.2.115-125.sar Introduction: Space closure is one of the most challenging processes in Orthodontics and requires a solid comprehen- sion of biomechanics in order to avoid undesirable side effects. Understanding the biomechanical basis of space closure better enables clinicians to determine anchorage and treatment options. In spite of the variety of appliance designs, space closure can be performed by means of friction or frictionless mechanics, and each technique has its advantages and disad- vantages. Friction mechanics or sliding mechanics is attractive because of its simplicity; the space site is closed by means of elastics or coil springs to provide force, and the brackets slide on the orthodontic archwire. On the other hand, frictionless mechanics uses loop bends to generate force to close the space site, allowing differential moments in the active and reac- tive units, leading to a less or more anchorage control, depending on the situation. Objective: This article will discuss various theoretical aspects and methods of space closure based on biomechanical concepts. Keywords: Space closure. Biomechanical. Anchorage. 1 Professor, Universidade Federal de Santa Catarina (UFSC), Undergraduate How to cite this article: Ribeiro GLU, Jacob HB. Understanding the basis of and Graduate Programs, Department of Orthodontics, Florianópolis, Santa space closure in Orthodontics for a more efficient orthodontic treatment. Dental Catarina, Brazil. Diplomate of the Brazilian Board of Orthodontics and Facial Press J Orthod. 2016 Mar-Apr;21(2):115-25. Orthopedics (BBO). DOI: http://dx.doi.org/10.1590/2177-6709.21.2.115-125.sar 2 Professor, Texas A&M University, Baylor College, Department of Orthodontics, Dallas, Texas, USA. Submitted: January 27, 2016 Revised and accepted: February 02, 2016 » Patients displayed in this article previously approved the use of their facial and intraoral photographs. » The authors report no commercial, proprietary or financial interest in the prod- ucts or companies described in this article. Contact address: Gerson Luiz Ulema Ribeiro Centro de Ciências da Saúde, Curso de Odontologia - Florianópolis/SC - Brazil E-mail: [email protected] © 2016 Dental Press Journal of Orthodontics 115 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 special article Understanding the basis of space closure in Orthodontics for a more eicient orthodontic treatment INTRODUCTION space closure as well as some methods to close space Space closure is one of the most challenging pro- sites, based on biomechanical concepts. cesses in Orthodontics. Tooth extraction, molar dis- talization, expansion of dental arches, interproximal ANCHORAGE reduction, among other things, have been part of the Anchorage is something that provides a secure hold. orthodontic armamentarium to correct malocclusion In Orthodontics, it can be deined as the ability to pre- and allow dental space gain with which the orthodon- vent tooth or teeth movement while moving another tist should deal. The ability to close spaces, especially tooth or group of teeth. In modern Orthodontics, the those resulting from tooth extraction, is an essential skill success of orthodontic treatment generally relies on required during orthodontic treatment. Space closure the anchorage protocol planned for each speciic case. mechanics without knowledge can result in failure to Anchorage should be established at the beginning of achieve an ideal occlusion. Current knowledge in bio- treatment and its preparation is a very important part of mechanics, allied with the development of new material orthodontic treatment.5 and techniques, made signiicant upgrading possible in Depending on the treatment planning, one tooth or space closure, which has simpliied mechanics.1,2,3 group of teeth can be classiied as an active unit, while the The biomechanical basis of space closure enables cli- other is classiied as the reactive or passive unit. In general, nicians to determine anchorage and treatment options, these two units play diferent roles during space closure. reach the prognosis of various alternatives, as well as de- The active unit is normally afected by the majority of cide speciic adjustments that can improve the outcomes movements, while the other unit resists to movement (an- of care. In order to achieve good treatment outcomes, it is chorage). It is convenient to classify an extraction arch by the crucial to understand the principles behind space closure. diferential space closure required between anterior and pos- Regulation of space closure is ultimately determined by terior teeth. One of the most widely used anchorage classi- the biomechanical forces applied to the teeth, variation ication (Fig 1) is applied to the segmented arch technique:5 in force and moment magnitude, moment-to-force ratio Group A arch is one in which posterior segments must (M/F), force-to-delection rate, and anchor unit.1 remain in their original position and the full space is used Due to the large number of mechanical options, for anterior retraction; Group B arch requires that approxi- special attention must be given to the selection of mately one half of the space be used for retraction; Group C the most appropriate model for each case. Certain arch requires that approximately most of the space be closed aspects must be considered, and precise control of by protraction of posterior teeth. Nowadays, a fourth type of tooth movement during space closure in three di- anchorage can be added to Burstone's classiication: absolute mensions is of preponderant importance to achieve anchorage. Clinically, it is very diicult to avoid movement treatment goals. In general, six goals should be in the passive unit; however, due to skeletal-based anchorage considered for space closure: 1) Differential space systems, signiicant steps have been taken towards achieving closure-anchorage control; 2) Minimum patient co- an absolute anchorage.1,2,3,5 operation; 3) Axial inclination control; 4) Control Traditionally, orthodontists have developed a variety of rotations and arch width; 5) Optimum biological of strategies and techniques to maintain anchorage.5-14 Un- response; and 6) Operator convenience. derstanding biomechanical concepts is essential to control Two basic biomechanical strategies can be used anchorage by promoting diferent types of tooth move- to close spaces: frictionless (closing loop mechanics) ment for the active teeth versus the reactive unit. From a and frictional (sliding mechanics). In the early 2010s, clinical perspective, delivering appropriate force systems 64% of Brazilian orthodontists used the technique (variation of force, moment magnitude, and moment-to- based on frictional mechanics, while only 20% of force ratio) is an important determinant of the resulting them used more than one technique.4 In spite of the tooth movement and maintenance of anchorage. variety of appliance designs available to the orthodon- tist, the techniques of either closing loops or sliding BIOMECHANICAL PERSPECTIVE mechanics have their advantages and disadvantages. The way a tooth moves is dependent on the nature This article will discuss various theoretical aspects of of the force system. The force system includes the force © 2016 Dental Press Journal of Orthodontics 116 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 Ribeiro GLU, Jacob HB special article and moments applied to the bracket and the actual force distribution on the periodontium. Force distribution is a Extraction space function of the tooth's center of rotation.15-22 By applying a Group A force (F) that does not pass through the center of resistance of the unit to be moved, the orthodontist produces a mo- ment (MF) which can cause tipping (Fig 2). The nature Group B of tooth movement can be controlled by applying a coun- teracting moment (M). The applied M acts in the oppo- Group C site direction of the MF, and moves the root(s) towards the space. As the magnitude of the applied couple increases, Absolute the rotation of the tooth would move the crown away from the space. The moment-to-force ratio can determine the quality of tooth movement (Fig 3).1-9,13,18,20,22 0% 25% 50% 75% 100% The retraction force applied by a spring to the active Posterior segment Anterior segment unit is reciprocally applied to the reactive unit. To pre- serve anchorage, the orthodontist desires greater force for anterior teeth and smaller force for posterior teeth to- Figure 1 - Anchorage classification: Group A space closure includes, on aver- age, 25% of posterior anchorage loss and 75% of anterior retraction; Group B wards the space; external or extra-arch mechanisms must space closure includes more equal amounts of anterior and posterior tooth be included (i.e., headgear or miniscrew). Other possibil- movement; Group C space closure includes, on average, 75% posterior pro- traction and 25% of anterior retraction. Absolute anchorage includes practi- ity is diferential M/F between active and reactive units. cally 100% of anterior retraction. Higher M/F for posterior teeth encourages anchorage preservation, as they resist tipping. Also, the professional should understand that unequal moments between active and reactive units generate vertical forces (Fig 4).1,2,3,8,9,10 METHODS FOR SPACE CLOSURE Orthodontic treatment planning is more than just deciding on extraction or nonextraction. Although many approaches towards space closure have been de- scribed, the biomechanical principles deining the na- ture of the force systems applied show many similarities among diverse techniques. Many details determine the tooth movement required during space closure, and it can be performed either by means of frictional or fric- tionless mechanics. Applying force by means of coil springs or power chain elastics in sliding mechanics will produce fric- tion between the bracket and the archwire, and the tooth feels less force than the orthodontist is in fact applying. Additionally, the guiding wire provides mo- ments required for prevention of tipping and rotation. In frictionless mechanics, there is no guiding wire, so there is no loss of applied force due to sliding friction. With pros and cons, each technique has its particu- larities. Simplicity is a goal of clinical practice manage- ment, and it may be at odds with the desired biome- Figure 2 - A force that does not pass through the center of resistance produc- es a rotational movement (moment of force) as well as s linear movement. chanical properties of the appliance. © 2016 Dental Press Journal of Orthodontics 117 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 special article Understanding the basis of space closure in Orthodontics for a more eicient orthodontic treatment A B C D Figure 3 - Types of tooth movement: A) Uncontrolled tipping; B) Controlled tipping; C) Bodily movement; D) Root movement. The red arrows represent the force applied to teeth and the moment of force. The blue arrows represent the force of a wire into the bracket and the moment of a couple. The green arrow is the resultant moment (moment of force minus moment of a couple). resistance to sliding has little to do with friction; instead, it is largely a binding-and-release phenomenon that does not change considerably with conventional and self-ligating brackets (Fig 5).26 As binding delays tooth movement in the active unit, the reactive unit starts to move, causing anchorage loss.27,28 Accurate control of anterior teeth during space closure in sliding mechan- ics is essential to the success of orthodontic treatment. When the line of action of force passes below the center of resistance of anterior teeth, a backward moment acts on anterior teeth, resulting in tipping and extrusion of incisors (Fig 6). The orthodontist can add power arms in the anterior segment to provide better vertical control Figure 4 - Differential moment reduces the moment/force ratio on one seg- of the anterior segment (Fig 7). When power arms are ment while increasing the moment/force ratio on another. Vertical forces occur due to difference in alpha and beta moments. lengthened, rotation of the entire dentition decreases.29 Elastic deformation of the archwire can also be a cause of rotation of anterior teeth.29 It is practically impossible for the orthodontist to Frictional mechanics know the exactly force system due to friction in the Sliding mechanics is attractive due to its simplicity. sliding mechanics. A small interbracket distance (canine However, the eiciency of this modality of space closure to second premolar, most of the times) does not allow may be compromised due to friction. Clinically, there are the clinician to apply the diferential M/F ratio. Due to numerous factors that may cause friction. These factors the very limited M/F ratio, space closure is normally include, among others, bracket slot width, bracket com- achieved by group B mechanics. Diferential space clo- position, wire size, wire composition, wire-to-slot liga- sure (i.e., group A or group C) may require additional tion method, interbracket distance, and relative interface appliances, such as headgear and miniscrews.29 motion between the bracket and the archwire.23,24,25 Bracket designs and manufacturing techniques have Frictionless mechanics improved to reduce the amount of friction between Orthodontists bend closing loops in a continuous bracket and wire. Clinical studies support the view that archwire or a segmented arch with a view to deliver- © 2016 Dental Press Journal of Orthodontics 118 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 Ribeiro GLU, Jacob HB special article Figure 5 - As the canine tips distally during retraction, the orthodontic wire Figure 6 - Force system generated by a closed coil spring applying force binds against the edge of the bracket slot ("binding effect"), increasing friction. bellow de center of resistance of the segments. Due to linear distance be- tween the force application and center of resistance, moments occur, and the dumping effect with vertical forces will take part of the space closure. LOOP DESIGN Every orthodontist knows that a wire is stif, and ap- plying forces at each end will create elongation that is not detectable to the naked eye. The force-delection rate is too high and would make a useless spring. Adding bends to the wire (i.e., making loops) can dramatically reduce the force-delection rate. Over the years, diferent space closure loop conigurations have been developed. Some designs have more advantages than others.30 Stainless steel tear drop loops are the most common Figure 7 - Force system generated by a closed coil spring applying forces design due to their ease of fabrication; however, they de- at the level of the center of resistance by means of extension hooks (power arms). No moments and vertical forces occur. liver very high forces with only 1 mm of activation.7,27 Simple loops are associated with small activations and rapid force decay, including intermittent force delivery; ing forces that can perform space closure. The loops thus, having a negative impact on treatment eicien- provide the required M/F ratio with great predict- cy.28,31 Also, as shown by Burstone and Koenig,6 an error ability and versatility. Well-designed closing loops as small as 0.3 mm in the horizontal length of the com- promote a more continuous type of movement, and mon vertical loop produces large changes on the M/F there are many reasons for choosing one configura- ratio, making diference enough to change from root tion over another. Studies on force constancy sug- movement to tipping. Due to its characteristics, T-loop gest that continuous forces promote greater rates of has a high M/F ratio and delivers more constant forces tooth displacement.23,26,30 over a large deactivation span than vertical loops.1 The spring characteristics of the closing loops are Increasing wire length in the loop design, i.e., add- mainly determined by some factors, such as wire mate- ing a helix, or using metal alloys with lower modulus of rial, archwire cross-section, interbracket distance, and elasticity (i.e., beta-titanium), reduce the force delivered coniguration, and position of the loop. The moment- at the same activation.27 Due to the depth of the vestibule, to-force ratio is probably the most important charac- the orthodontist is limited to how high the loop can be teristic of a retraction archwire. Low load/delection, made. In order to overcome this problem, a wire, such as eiciency and space closure control should be preferred a T-loop, can be added horizontally, or there might be over simplicity of fabrication and delivery.30 addition of helices. © 2016 Dental Press Journal of Orthodontics 119 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 special article Understanding the basis of space closure in Orthodontics for a more eicient orthodontic treatment THE BAUSCHINGER EFFECT LOOP POSITION The Bauschinger efect is normally associated with When retracting the anterior segment, the ortho- conditions in which the strength of a metal decreases when dontist normally places closing loops immediately the direction of strain is changed. It is a general phenome- distal to the lateral or canine because this procedure non found in most polycrystalline metals.32 In other words, allows for repeated activation of the loop as the space if we have two diferent T-loop designs, when one closure closes. However, it has been shown that the loop posi- loop is activated, if all bends are bent in the same direction, tion can increase or decrease the amount of posterior it provides more resistance to permanent deformation than anchorage loss.24,31 If the closing loop is placed of- if all bends are bent in the opposite direction (Fig 8). centered between the anterior and posterior units, the Wire bends should be in the same direction during shorter section creates greater moments, encouraging the processes of forming and activation. Due to some root tipping (increasing anchorage), while the longer designs, the orthodontist should overbend the wire, fol- section creates smaller moments, encouraging trans- lowing it by a reversal in the direction of the bending, lation.6,15,18 Moreover, asymmetrical placement of the so as to reach the inal shape. As a result, the direction loop between brackets not only results in unequal mo- of the last bend is correct and provides favorable residual ments, but also generates vertical forces.33,34 The verti- stress during activation. This overbend will provide re- cal forces could lead to a deep overbite relationship. sistance to permanent deformation, thereby increasing This can be detrimental when a loop is placed closer to the range of activation. The orthodontist may heat-treat anterior teeth due to extrusion (Fig 9). (stress relief) a stainless steel archwire when loop form- ing does not provide favorable residual stress. Figure 8 - A) Closing loop with bends in the winding-direction. This configuration presents more resistance to permanent deformation dur- ing activation; B) Closing loop with bends in A B unwinding-direction. Figure 9 - Tear drop loop asymmetrically placed (closer to anterior than posterior segments) pro- vides a very low moment/force ratio with inad- equate root control. The advantage of this loop position is the possibility of numerous activations on the same wire as the space closes. © 2016 Dental Press Journal of Orthodontics 120 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 Ribeiro GLU, Jacob HB special article ANGLED BENDS AND THE NEUTRAL POSITION understanding of the gable effects helps clinicians to Orthodontists have learned that, in order to achieve desired clinical results, such as increased an- achieve bodily movement, an attraction spring (clos- chorage control. ing loop) must produce a counter-moment, and the The orthodontist needs to understand that gable M/F ratio will determine the type of movement (i.e., bends produce angulation, but when the springs are translation or uncontrolled tipping).19-22 By ensuring placed only at the occlusal portion, the vertical arms that the ideal force system is produced, orthodon- will cross one on top of the other, causing some hori- tists can place second-order bends (V-bends or gable zontal force. This will cause more horizontal activation bends) to increase root control. These preactivation than what is anticipated by the clinician, leading to ei- loads are capable of keeping teeth upright during de- ther permanent deformation or high forces.34 activation. Adding gable bends is a common means to The so-called neutral position has no horizontal forc- adjust the M/F ratio in the anteroposterior direction, es, although some vertical forces may be present. Neutral thus avoiding dumping of teeth as the space closes.35 position is an important concept of a speciic shape. The Gable bends adjust the moment-force ratio to a level starting position (neutral position) for a zero horizontal that produces the desired unit movement, for the force is with vertical arms crossed (when occlusal bends most part of the loop configurations are insufficient are present). The orthodontist cannot assume that zero to prevent uncontrolled tipping.5,13 Having a better force is present, if the vertical arms are just touching. A B C Figure 10 - Space closure in a clinical case with non-extraction treatment: A) Initial phase; B) Beginning of the space closure phase; C) End of treatment. A B C D Figure 11 - Space closure in a clinical case with extraction treatment: A) Initial phase; B) Beginning of the space closure phase; C) Gable bends: D) End of treatment. © 2016 Dental Press Journal of Orthodontics 121 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 special article Understanding the basis of space closure in Orthodontics for a more eicient orthodontic treatment ONE-PHASE (EN-MASSE) VERSUS TWO-PHASE incisors without flatting them. There is no reason RETRACTION (SINGLE CANINE RETRACTION) to retract the anterior segment in two phases, unless Classically, it has been believed that separated canine crowding is present. Additionally, two phases can retraction followed by four incisors retraction would be unesthetic due to a more anterior gap, in addi- preserve posterior anchorage. The reason to believe tion to increasing treatment time. Another factor can so is because lighter forces could be used at each stage. be a more significant number of side effects, such as Maybe this could work, if low magnitude of force were extrusion of incisors due to tipping back the canine used, retracting the anterior segment and not being crown, especially during sliding mechanics.36,37 enough to move the posterior segment. Clinical studies In sliding mechanics, the orthodontist uses a guide have shown that there is no diference in anchorage loss wire. To retract canines, a stainless steel round-base arch- between the two types of retraction.36 wire is used to slide canines distally. Normally, the canine Normally, separate canine retraction is indicated is retracted with the use of 0.016-in and 0.018-in stainless to crowding cases or midline discrepancy cases. The steel wires in 0.018-in and 0.022-in slots, respectively. mechanics (friction or frictionless) is practically the The reason is that the wire should be stif enough for re- same. The orthodontist should bear in mind that us- traction, but should have delection to ight against a po- ing forces applied away from the center of resistance tential tipping tendency. Rotation is another side efect will result in tipping and rotation. Canine retraction that occurs as a result of sliding mechanics, and ligatures can be carried out little enough to create space for ties need to be used.38,39 A B C Figure 12 - Clinical case with maxillary first premolar extractions and congenitally missing mandibular second premolars. A) End of the alignment and leveling phase; B) Beginning of space closure; C) End of treatment. A B C D E F Figure 13 - Clinical case with all four first premolar extractions. A) Initial; B) Partial canine retraction; C) Beginning of space closure using a T-loop design; D) Prog- ress of space closure; E) Management of canine relationship; F) End of the case. © 2016 Dental Press Journal of Orthodontics 122 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 Ribeiro GLU, Jacob HB special article A B C D Figure 14 - Management of space closure in a surgical case. A) Initial phase; B) Space closure phase; C) Class III elastics to create a differential anchorage control and decompensation of the incisors; D) End of treatment. A B C D E Figure 15 - Clinical case with maxillary and mandibular first premolar extractions. A) Initial phase; B) Beginning of space closure; C) Headgear to provide greater anchorage on maxillary molars; D) Frictionless mechanics on maxilla and friction mechanics associated with miniscrew anchorage on the man- dible; E) End of treatment. A B Figure 16 - Clinical case without extraction. A) Space closure using miniscrew as anchorage in the max- illa; B) End of the space closure phase. © 2016 Dental Press Journal of Orthodontics 123 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 special article Understanding the basis of space closure in Orthodontics for a more eicient orthodontic treatment A F B G C H D I Figure 17 - Most common space closure loop designs used by orthodontists: A) reverse verti- cal loop, B) open vertical loop, C) closed vertical loop, D) bull loop, E) reverse vertical loop with E J helix, F) open vertical loop with helix, G) closed vertical loop with helix, H) tear drop loop, I) heli- cal loop, J) T-loop. CONTROL OF MECHANICAL SIDE EFFECTS Adding third order bends can be ineffective for Because the forces are not passing through the center several reasons. A full-size wire should be used to of resistance, an additional moment should be provided provide less play between wire and bracket. High- when no rotation is necessary. A lingual attachment can torque activation requires a very small amount of acti- be bonded, adding force on the lingual surface of the ca- vation and frequent wire adjustment. Also, it is almost nine, so that the resultant force (buccal and lingual com- impossible to determine the amount of third-order bined) passes through the center of resistance. Moreover, bend providing enough M/F ratio. Adjacent bracket antirotation bends can be placed to prevent rotation dur- side effect can receive equal and opposite moments. ing canine retraction by means of loops.23,39,40 A torquing arch can be an alternative to produce Ater leveling canine retraction, side efects, such as ideal incisor torque. The force system produced by a reverse curve of Spee, can be generated. Uprighting of torquing arch (i.e., 0.017 x 0.025-in TMA) results in canines can produce mesial crown movement and cre- adequate correction of incisor roots. A small amount ate space between canines and premolars. Tie-back or of force as well as a high and continuous moment are power chain elastics can be used while uprighting of produced because of the large arm. The incisors will canines is performed. Also, a canine bypass is used to receive the desired moment while undesired vertical prevent side efects on adjacent teeth. force should be avoided using a stabilizing archwire. This system has the advantage of allowing easy visu- EVALUATION OF SPACE CLOSURE AND CLINICAL alization and measurement of torsional activations.41 CONSIDERATIONS In summary, there is no such thing as the best One of the most common problems ater space clo- method of space closure. Some situations will require sure is incisor torque. Round wire or undersized wire some techniques over others, and the orthodontist can lead to lingual tipping of the crown. Several methods might have his or her own preferences. Regardless of are suggested to correct the undesired incisor torque, the method to be used, a good understanding of bio- such as twisting the wire or using special springs. mechanics is essential. © 2016 Dental Press Journal of Orthodontics 124 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25 Ribeiro GLU, Jacob HB special article REFERENCES 1. Burstone CJ. The segmented arch approach to space closure. Am J Orthod. 23. Iwasaki LR, Haack JE, Nickel JC, Morton J. Human tooth movement in 1982 Nov;82(5):361-78. response to continuous stress of low magnitude. Am J Orthod Dentofacial 2. Burstone CJ, Koenig HA. Optimizing anterior and canine retraction. Orthop. 2000 Feb;117(2):175-83. Am J Orthod. 1976 Juy;70(1):1-19. 24. Kuhlberg AJ, Burstone CJ. T-loop position and anchorage control. 3. Kuhlberg AJ, Priebe DN. Space closure and anchorage control. Semin Am J Orthod Dentofacial Orthop. 1997 July;112(1):12-8. Orthod. 2001 Mar;7(1):42-9. 25. Burstone CJ, Koenig HA. Force systems from an ideal arch. Am J Orthod. 4. Monini AC, Gandini LG Jr, Santos-Pinto A, Maia LG, Rodrigues WC. 1974 Mar;65(3):270-89. Procedures adopted by orthodontists for space closure and Anchorage 26. Articolo LC, Kusy RP. Inluence of angulation on the resistance to sliding in control. Dental Press J Orthod. 2013 Nov-Dec;18(6):86-92. ixed appliance. Am J Orthod Dentofacial Orthop. 1999 Jan;115(1):39-51. 5. Burstone CJ. Rationale of the segmented arch. Am J Orthod. 1962 27. Fok J, Toogood RW, Badawi H, Carey JP, Major PW. Analysis of maxillary Nov;48:805-22. arch force/couple systems for a simulated high canine malocclusion: Part 1. 6. Burstone CJ, Koenig HA. Optimizing anterior and canine retraction. Passive ligation. Angle Orthod. 2011 Nov;81(6):953-9. Am J Orthod. 1976 July;70(1):1-19. 28. Queiroz GV, Rino Neto J, Paiva JB, Rossi JL, Ballester RY. Comparative study 7. Faulkner MG, Lipsett AW, el-Rayes K, Haberstock DL. On the use of vertical of classic friction among diferent arch wire ligation systems. Dental Press J loops in retraction systems. Am J Orthod Dentofacial Orthop. 1991 Orthod. 2012 May-Jun;17(3):64-70. Apr;99(4):328-36. 29. Kusy RP, Whitley JQ. Friction between diferent wire-bracket conigurations 8. Gjessing P. Biomechanical design and clinical evaluation of a new canine and materials. Semin Orthod. 1997 Sept;3(3):166-77. retraction spring. Am J Orthod. 1985 May;87(5):353-62. 30. Siatkowski RE. Continuous arch wire closing loop design, optimization, 9. Zeigler P, Ingervall B. A clinical study of maxillary canine retraction with and veriication. Part I. Am J Orthod Dentofacial Orthop. 1997 a retraction spring and with sliding mechanics. Am J Orthod Dentofacial Oct;112(4):393-402. Orthop. 1989 Feb;95(2):99-106. 31. Siatkowski RE. Continuous arch wire closing loop design, optimization, 10. Haskell BS, Spencer WA, Day M. Auxiliary springs in continuous arch and veriication. Part II. Am J Orthod Dentofacial Orthop. 1997 treatment: Part 1. An analytical study employing the inite-element method. Nov;112(5):487-95. Am J Orthod Dentofacial Orthop. 1990 Nov;98(5):387-97. 32. Sowerby R, Uko DK , Tomita Y. On the Bauschinger efect and its inluence 11. Haskell BS, Spencer WA, Day M. Auxiliary springs in continuous arch on U.O.E. pipe making process. Int J Mech Sci. 1977;19(6):351-9. treatment: Part 2. Appliance use and case reports. Am J Orthod Dentofacial 33. Thiesen G, Shimizu RH, Valle CVM, Valle-Corotti KM, Pereira JR, Orthop. 1990 Dec;98(6):488-98. Conti PCR. Determination of the force systems produced by diferent 12. Sachdeva RC. A study of force systems produced by TMA '91T' loop conigurations of tear drop orthodontic loops. Dental Press J Orthod. retraction springs. [masters thesis.] Farmington (CT): The University of 2013 Mar-Apr;18(2):19.e1-18. Connecticut School of Dental Medicine; 1985. 34. Shimizu RH, Sakima T, Santos-Pinto A, Spinelli D, Shimizu IA. 13. Manhartsberger C, Morton JY, Burstone CJ. Space closure in adult patients Comportamento mecânico da alça Bull modiicada durante o fechamento using the segmented arch technique. Angle Orthod. 1989 Fall;59(3):205-10. de espaços em ortodontia. Rev Dental Press Ortod Ortop Facial. 2002 Jan- 14. Smith R, Burstone C. Mechanics of tooth movement. Am J Orthod. 1984 Fev;7(2):13-24. Apr;85(4):294-307. 35. Burstone CJ, Koenig HA. Creative wire bending--the force system from step 15. Brodsky JF, Caputo AA, Furstman LL. Root tipping: a photoelastic- and V bends. Am J Orthod Dentofacial Orthop. 1988 Jan;93(1):59-67. histopathologic correlation. Am J Orthod. 1975 Jan;67(1):1-10. 36. Heo W, Nahm DS, Baek SH. En masse retraction and two-step retraction of 16. Baeten LR. Canine retraction: a photoelastic study. Am J Orthod. maxillary anterior teeth in adult Class I women. A comparison of anchorage 1975 Jan;67(1):11-23. loss. Angle Orthod. 2007 Nov;77(6):973-8. 17. Pryputniewicz RJ, Burstone CJ. The efect of time and force magnitude on 37. Owman-Moll P, Kurol J, Lundgren D. Continuous versus interrupted orthodontic tooth movement. J Dent Res. 1979 Aug;58(8):1754-64. continuous orthodontic force related to early tooth movement and root 18. Burstone CJ, Pryputniewicz RJ. Holographic determination of centers resorption. Angle Orthod. 1995;65(6):395-401; discussion 401-2. of rotation produced by orthodontic forces. Am J Orthod. 1980 38. Frank CA, Nikolai RJ. A comparative study of frictional resistances between Apr;77(4):396-409. orthodontic bracket and arch wire. Am J Orthod. 1980 Dec;78(6):593-609. 19. Tanne K, Sakuda M, Burstone CJ. Three-dimensional inite element analysis 39. Yamaguchi K, Nanda R, Morimoto N, Yoshihito O. A study of force for stress in the periodontal tissue by orthodontic forces. Am J Orthod application, amount of retarding force, and bracket width in sliding Dentofacial Orthop. 1987 Dec;92(6):499-505. mechanics. Am J Orthod Dentofacial Orthop. 1996 Jan;109(1):50-6. 20. Tanne K, Koenig HA, Burstone CJ. Moment to force ratios and the center of 40. Kojima Y, Kawamura J, Fukui H. Finite element analysis of the efect of force rotation. Am J Orthod Dentofacial Orthop. 1988 Nov;94(5):426-31. directions on tooth movement in extraction space closure with miniscrew 21. Kusy RP, Tulloch JF. Analysis of moment/force ratio in the mechanics of sliding mechanics. Am J Orthod Dentofacial Orthop. 2012 Oct;142(4):501-8. tooth movement. Am J Orthod Dentofacial Orthop. 1986 Aug;90(2):127-31. 41. Isaacson RJ, Rebellato J. Two-couple orthodontic appliance systems: 22. Burstone CJ, Pryputniewicz RJ. Holographic determination of centers torquing arches. Semin Orthod. 1995 Mar;1(1):31-6. of rotation produced by orthodontic forces. Am J Orthod. 1980 Apr;77(4):396-409. © 2016 Dental Press Journal of Orthodontics 125 Dental Press J Orthod. 2016 Mar-Apr;21(2):115-25