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Space closure and anchorage control
Space Closure and Anchorage Control Andrew J. Kuhlberg and Derek N. Priebe The ability to close extraction spaces preferentially is an essential skill required during orthodontic treatment. Although many approaches to space closure and anchorage control have been described, the biomechanical principles defining the nature of the force systems applied show many similarities between otherwise diverse techniques. The core concept of anchorage control is the delivery of a differential force system to the anchor teeth relative to the active teeth. Specifically, anchorage is determined by applying unequal moment-to-force ratios (M/F ratios) to each unit. This implies the use of orthodontic appliances that provide either unequal forces or unequal moments. Unequal moment force systems or differential moment force systems are an excellent means of achieving anchorage control. The fundamental concepts and clinical methods of anchorage control are described. (Semin Orthod 2001;7:42-49.) Copyright© 2001 by W.B. Saunders Company
o a n c h o r is to secure firmly, to hold an object against m o v e m e n t ; anchorage is that which provides the secure hold. Specifically, orthodontic anchorage is the ability to prevent tooth m o v e m e n t of one g r o u p of teeth while moving a n o t h e r tooth or teeth. Controlling anchorage is one of the most critical elements of orthodontic treatment. O r t h o d o n t i c tooth m o v e m e n t is the result of the controlled application of mechanical forces to the teeth and periodontium. T h e stimulus that provokes the biologic activity leading to tooth m o v e m e n t is the mechanical forces exerted by orthodontic appliances. The response is b o n e r e m o d e l i n g and repositioning of teeth. From this perspective, orthodontic t r e a t m e n t can be conceived of as a stimulus-response model. Anchorage control involves the ability to create appropriate force systems (stimulus) that will provide the desired t r e a t m e n t effects (response).
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From the Department of Orthodontics, University of Connecticut, School of Dental Medicine, Fa*mington, CT. Address corresponden~ to An&vw J. Kuhlberg, DMD, MDS, Department of Orthodontics, University of Connecticut, School of Dental Medicine, l~}*~raington, CT 06030. Copyright © 2001 by W.B. Saunders Company 1073-8746/01/0701-0006535.00/0 doi:l O.1053/sodo. 200 l. 21073 42
T h e p r o b l e m of a n c h o r a g e control is rooted in Newton's third law of motion, for every action there is an equal and opposite reaction. Thus, the distal forces acting to retract anterior teeth must be o p p o s e d by equal forces acting on the anchorage units in the mesial direction. The mesial forces must be accounted for to avoid anchorage loss. In light of this, orthodontists have developed a variety o f strategies and techniques to maintain a n c h o r a g e by applying m a n y m e t h o d s to inhibit or prevent m o v e m e n t of the a n c h o r teeth. Historically, most techniques for a n c h o r a g e control were developed empirically, yet their efficacy reflects the ingenuity of their inventors. Several anchorage control m e t h o d s have b e e n developed over the last century. TM T h e contributions of such icons as Angle, Case, Tweed, Begg, and others have provided a f o u n d a t i o n for modern orthodontic m e c h a n o t h e r a p y . Alt h o u g h each of t h e m espoused different methods and philosophies, a review of their individual works shows m o r e similarities than differences. By 1907, E.H. Angle advocated 5 types of anchorage control. Occipital a n c h o r a g e dep e n d e d on the use of extraoral headgear. Intermaxillary a n c h o r a g e included the use of elastics. 1 T h e 3 r e m a i n i n g m e t h o d s were dental a n c h o r a g e techniques. Angle decribed simple,
Seminars in Orthodontics, Vol 7, No 1 (March), 2001: pp 42-49
Space Closure and Anchorage Control
reciprocal, and stationary m e t h o d s for dental anchorage. Both simple and reciprocal anchorage methods relied on c o m p e t i n g support of the dentition to effect tooth displacement. In contrast, Angle's stationary a n c h o r a g e m e t h o d s were based on his view that firm support of the a n c h o r a g e units, t h r o u g h handing multiple teeth, acted to resist tipping and thus p r o m o t e anchorage. Calvin S. Case also advocated stationary anchorage m e t h o d s despite his ideological departure f r o m Angle's "New School. ''9 Although he described the use of extraoral a n d intermaxillary forces, he too recognized that resistance to tipping movements was requisite for intraarch anchorage control. With a singular approach, Case advocated the use of firm, soldered a t t a c h m e n t of the anchorage teeth to one a n o t h e r to maintain their upright positions. Case stated that, with this strategy, "the applied force will be equally distributed over the entire mesial or distal surfaces of the alveoli for all the roots, increasing the stability of the anchorage to an incalculable degree. ''2 Approximately 20 years later, Charles Tweed advocated similar techniques. His m e t h o d of anchorage p r e p a r a t i o n was a i m e d at maintaining the anchorage teeth against unwanted tipping and extrusive side effects. ~,5,6 A series of tip back bends acted to a n c h o r the teeth like tent stakes to resist vertical and anteroposterior displacem e n t during intermaxillary elastic traction. Although Tweed r e p o r t e d that his m e t h o d s were m o r e mechanical in nature than biologic, the tip back bends were generally a further r e f i n e m e n t of Angle's and Case's stationary anchorage methods. Despite his a d h e r e n c e to the differential force theory, P.R. Begg also used a similar procedure for anchorage control. 7-9 With the use of his light wire technique, Begg regularly used tip back bends to help maintain the anteroposterior position of the anchorage teeth to effect preferential tooth movement. 4,m Additionally, he proposed tipping the anterior teeth during initial retraction, followed by an uprighting phase. All of these m e t h o d s have proven to be generally effective and well-accepted a p p r o a c h e s to orthodontic m e c h a n o t h e r a p y . Further advancements in these techniques have b e e n evolutions rather than revolutions. The c o m m o n denominator of these and subsequent techniques is that
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each aimed at controlling the type of tooth m o v e m e n t that occurred, ie, tipping versus translation. Fundamentally, advocates of m a n y of the cont e m p o r a r y orthodontic techniques have a d a p t e d their a p p r o a c h e s to different hardware designs. U n d e r s t a n d i n g the conceptual basis of biomechanics in a n c h o r a g e control permits greater latitude in t r e a t m e n t delivery and transcends the limits of any specific technique. Additionally, the c o n t e m p o r a r y shift toward compliance-independ e n t orthodontic t r e a t m e n t further requires a grasp of f u n d a m e n t a l biomechanical principles.
Anchorage from a Biomechanical Perspective The basic techniques for a n c h o r a g e control generally rely on 3 essential similarities: (1) extraoral forces on the anchorage unit (headgear), (2) intermaxillary elastics, (3) tipping movements of the active teeth while simultaneously discouraging tipping of the anchorage teeth. Patient compliance is a m a n d a t o r y r e q u i r e m e n t for h e a d g e a r and elastic wear. Without cooperation, control of tooth m o v e m e n t is lost and t r e a t m e n t o u t c o m e may be c o m p r o m i s e d . T h e a t t e m p t to maintain anchorage by promoting different types of tooth m o v e m e n t for the active teeth versus the a n c h o r units shows the biomechanical essence of a n c h o r a g e control. U n d e r s t a n d i n g how this strategy works requires an analysis of how the applied force systems d e t e r m i n e the resulting type of tooth m o v e m e n t . T h e relationship between mechanical force systems and tooth m o v e m e n t has b e e n well described and illustrates that the nature of a tooth's m o v e m e n t depends on the ratio of the applied m o m e n t relative to the applied force ( M / F ratio) at the orthodontic bracket, n T h e way a tooth moves is d e p e n d e n t on the nature of the forces (ie, the force system) imposed on it. T h e force system includes the applied force and m o m e n t s at the bracket (via elastic, coil, loop, etc), and the actual force distribution a b o u t the p e r i o d o n t i u m (stress-strain relationship). T h e force distribution is a function of the tooth's center of rotation. 11-21 Controlled tipping is tooth m o v e m e n t with the center of rotation of the tooth at the root apex. T h e resultant forces tend to be distributed at the marginal portion of the periodontal ligament
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Kuhlberg and Priebe
(PDL). The M / F ratio for controlled tipping is reported at approximately 7/1 for most teeth with normal periodontal support. Translation or bodily movement, on the other hand, maintains the axial inclination of the tooth with the center of rotation at an infinite distance from the apex. The resultant force distribution tends to be more equally distributed along the pressure side of the alveolar structures. Translation requires a M / F ratio of about 10/1. Lastly, root movem e r i t - - o r displacement of the root apex while holding the crown stationary--occurs with a M / F ratio of 12/1. Here, the applied forces tend to be concentrated along the apical ½ of the root (Fig 1). Why does this analysis show the biomechaniControlled Tipping M/F -7:1
&
i
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Figure 2. The effect of a large M/F ratio on tooth movement. A large M/F ratio produces root movement (A). A pure moment would produce only rotation, which would result in distal crown movement (B).
Translation M/F -10:1
Root Movement M/F -12:1
v
Direction of Movement
Figure 1. Tipping, translation, and root movement. The type of tooth movement depends on the M/F ratio.
cal essence of anchorage control? First, let us look at the effect of a high M / F ratio applied to the a n c h o r teeth. An applied force at the crown produces uncontrolled tipping as a result of the m o m e n t of the force. The applied m o m e n t (mom e n t of the couple) counteracts the tipping effect of the force. The applied m o m e n t acts in the opposite direction of the m o m e n t of the force. It moves the root(s) toward the extraction space. In addition, as the magnitude of the applied couple increases, the rotation of the tooth would move the crown away from the space (Fig 2). Conversely, a low M / F ratio produces tipping. With the apex remaining stationary, the crown tips toward the extraction space. Geometrically, the result is greater tooth m o v e m e n t at the occlusal plane relative to a tooth u n d e r g o i n g translation. Figure 3 shows a comparison of tipping versus translation, the center of resistance of the tooth for each example is displaced equally. The crown movement, however, is noticeably greater for the tipped tooth. This shows how tipping movements can result in greater movements of teeth from a clinical perspective. The theoretical effectiveness of differential
Space Closure and Anchorage Control
Figure 3. Tipping produces more movement at the crown or occlusal plane compared with translation. For both teeth in this illustration, the center of resistance of the tooth is displaced the same distance. M / F ratios is readily apparent. The question is, how can these force systems be p r o d u c e d clinically? For the purpose of discussion, consider the correction of a Class II malocclusion in which m a x i m u m posterior anchorage is needed. The objective is unequal applied M / F ratios: high M / F for posterior teeth, low for anterior teeth. If M/Fposterio r > M/Fante,_ior, then there must be either unequal forces or unequal moments. Unequal forces cannot be simply p r o d u c e d by a spring, loop, or chain elastic, because for every action there is an equal and opposite reaction. The retraction force a spring applies to the anterior teeth is reciprocally applied to the posterior teeth. To deliver unequal forces, external or extra-arch mechanisms must be included. Headgear and intermaxillary elastics are probably the 2 most c o m m o n means of generating these additional forces. In its simplest form, headgear acts to p r o d u c e a distal force on the anchorage teeth. By acting in opposition to the traction force from a spring or chain elastic, the headgear reduces the net force on the posterior teeth (M/Fposterio r > M/Fanterior ). Although there may be additional headgear effects, the aim conceptually is to retard the mesial forces on the posterior teeth (Fig
4A). Intermaxillary elastics, Class II elastics in this
4-5
example, increase the retraction force on the anterior teeth (M/Fposterio r > M/Fanterior ) (Fig 4B). A n o t h e r means of increasing the retraction force is the use of J - h o o k headgear applied to the anterior teeth. The applied m o m e n t is determined by the wire-bracket relationship. In the case of a straight wire, the magnitude of the moments on the anterior and posterior teeth may be presumed to be equal (see Schlegel 2u for a discussion on the effect of bracket width on the moment expressed as frictional force). For both headgear and elastics, the biomechanical effectiveness is largely a result of the generation of unequal forces applied to posterior and anterior teeth. Unfortunately, this approach depends on patient compliance for success. W h e n this is the only means of anchorage control, treatment remains at the mercy of motivational tactics and cooperative patients.
Force
B
Force
Figure 4. The effect of changing the force magnitude on the M/F ratio. Headgear is a means of decreasing the mesial force to the posterior teeth (A). Intermaxillary elastics (Class II elastics) increase the distal force to the anterior teeth (B).
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T h e inequality, M/Fposterio r > M/Fanterior, indicates the n e e d for an alternative approach. Rather than varying the forces, unequal moments may be applied. Increasing the m o m e n t on the posterior teeth a n d / o r decreasing the m o m e n t on the anterior teeth serves as a n o t h e r option toward creating differential M / F ratios. The horizontal force on the anterior teeth equals the horizontal force on the posterior teeth. T h e m o m e n t s or couples created by the bracket/wire-spring combination generate a greater m o m e n t to the a n c h o r a g e teeth. Simultaneously, a lower m o m e n t acts on the anterior teeth. For the Class I I / u p p e r anterior retraction challenge, the M / F ratio on the posterior teeth will p r o d u c e translation or root m o v e m e n t , while the low M / F ratio on the anterior teeth will show controlled tipping. T h e large posterior m o m e n t s encourage anchorage preservation as they resist tipping. Also, a very large posterior m o m e n t would actually cause distal crown movement, effectively increasing the size of the extraction space! T h e application of unequal m o m e n t s must also satisfy Newton's laws. Because the m o m e n t s on each end of the spring are unequal, the total force system must have additional effects. Vertical forces, intrusive to the anterior and extrusive to the posterior, are also acting. T h e vertical force m a g n i t u d e d e p e n d s on the difference in the 2 m o m e n t s and the distance between anterior and posterior a t t a c h m e n t points (Fig 5). In addition to the potential side effects created by the vertical forces, this a p p r o a c h to space
J Figure 5. The force system from differential moment orthodontic appliance designs for space closure.
closure frequently results in occlusal plane discrepancies between the anterior a n d posterior teeth. T h e posterior teeth may be positioned with the crowns distally tipped a n d the roots mesially oriented. T h e canines c o m m o n l y have a root-mesial axial inclination and the incisors are excessively upright. This situation is a natural consequence of the force system used but may also be an advantage given a p p r o p r i a t e malocclusions (ie, anterior protrusion with excessive dentoalveolar height and gingival display). An a p p r o p r i a t e stage of root correction after space closure prepares the occlusion for orthodontic finishing details. In comparison with the use of elastics or headgear, a differential m o m e n t a p p r o a c h to a n c h o r a g e control reduces the influence of compliance on t r e a t m e n t outcome. Because the force system is g e n e r a t e d by the intraoral appliance, elastics or h e a d g e a r b e c o m e less critical. In extremely difficult cases, h e a d g e a r or elastics may be used to further s u p p l e m e n t anchorage. Several orthodontic springs, loops, and devices have b e e n designed using this a p p r o a c h to anchorage control. 23-26 T h e wide variety of designs reflects the b r e a d t h of the options available to the clinician for i m p l e m e n t i n g this strategy for anchorage control in patient care. The imp o r t a n t issue is not the specific spring, it is the force system the spring applies to the dentition.
Biologic Considerations A n o t h e r factor in a n c h o r a g e control is the relative rates of tooth m o v e m e n t for tipping, translation, and root m o v e m e n t . T h e stress distribution within the periodontal support is different for each type of tooth m o v e m e n t . T h e stresses on the PDL are greatest at the cervix of the tooth for controlled tipping and a p p r o a c h zero at the apex. Conversely, the greatest stresses are at the apex for root m o v e m e n t . Translation applies a u n i f o r m stress along the root surface. The rates of tooth m o v e m e n t for each of these stress-strain relationships may also affect a n c h o r a g e control. T o o t h displacement rates have often b e e n evaluated on the basis o f force magnitude. Smith and Storey 7 r e p o r t e d that the m a n i p u l a t i o n of force magnitudes has an impact on relative rates of tooth displacement and thus anchorage control. Unfortunately their conclusions have not b e e n s u p p o r t e d by others. 27-s2 It is suggested,
Space Closure and Anchorage Control
however, that the stress distribution a b o u t the periodontal ligament, rather than the absolute magnitude of the force, has a greater impact on rates of displacement. ~S Histologic studies have shown that tipping produces localized regions of high stress, whereas translation results in a m o r e diffuse stress distribution. 34-36 Thus, a simple force applied at the bracket will be concentrated at the apical and marginal regions of the PDL and effectively increase the stress in these areas. If force magnitude, specifically the stress magnitude within the PDL, determines the rate of displacement, m,29,:~1 then tipping m o v e m e n t s occur faster because of the higher localized stresses. Storey r e p o r t e d that tipping m o v e m e n t s occurred m o r e rapidly than translational movem e n t s Y Although there is still some question regarding the effects of force magnitude on rates o f tooth displacement, the c o m b i n a t i o n o f these biologic concepts with the geometric advantage of tipping m o v e m e n t s over translation (Fig 3) may help explain the effectiveness of differential m o m e n t strategies for a n c h o r a g e control.
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has a similar effect. Because wire stiffness is inversely related to the third power of the length, an off-centered or asymmetrically positioned spring will deliver greater m o m e n t s to the teeth that it approximates (Fig 6). 39 A n o t h e r m e t h o d of anterior retraction that uses a differential m o m e n t strategy for anchorage control is c o m b i n e d incisor intrusion and retraction. This simple yet effective appliance uses the tip back m o m e n t of the intrusion arch for creating the large posterior M / F ratio. 42A3 The retraction force is applied with either coil springs or elastic chain (Fig 7). By carefully controlling the intrusive and retraction forces, the overbite and overjet can be simultaneously corrected. Careful m o n i t o r i n g is crucial for successful anchorage control during space closure. A sys-
Clinical Techniques Using Differential Moments for Anchorage Control A n u m b e r of springs have b e e n designed that use the differential m o m e n t strategy for anchorage control. 2-~-u6,:~s,:~-~T h e selection of one spring or a n o t h e r depends largely on individual preferences. T h e T-loop spring described by Burstone and subsequently refined or modified is a simple yet effective device for controlled space closure. 23,ss-4° Although most frequently presented as a s e g m e n t e d spring, it can also be effective within a continuous wire. 41 With correct application, however, most retraction springs may be effective at closing spaces while simultaneously providing anchorage control. The core principle of loop design for all of these springs is increased stiffness of the wire on the anchorage side of the spring. All other factors being equal, an increase in wire stiffness has the effect of establishing greater m o m e n t s at the engaged teeth. Increases in stiffness may be accomplished by using composite springs with the incorporation of wires showing different moduli of elasticity, with the stiffer section engaging the anchorage units. Conversely, asymmetric positioning of the loop toward the anchorage teeth
J la
? I
Figure 6. Anchorage control with a differential moment strategy through the use of a T-loop spring. A T-loop positioned toward the posterior attachment increases the moment to the posterior teeth and decreases the moment to the anterior teeth (A). The expected tooth movements, the anterior teeth are expected to tip distally while the posterior teeth show root correction (B).
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Kuhlberg and Priebe
B
Figure 7. C o m b i n e d anterior retraction and d e e p overbite correction with posterior a n c h o r a g e control. An intrusion arch is used to create the m o m e n t on the posterior s e g m e n t with the c o n c u r r e n t intrusive force on the anterior teeth and extrusive force on the posterior teeth. A chain elastic or coil spring is used to create the retraction force (A). The anticipated tooth m o v e m e n t s would be intrusion and retraction of the anterior teeth following the line of action of the resultant force and m o l a r tip back which aids in anchorage presei-vation (B).
tematic evaluation of treatment progress identifies t h e n e c e s s a r y a d j u s t m e n t s f o r e a c h p a t i e n t visit. T h e a m o u n t a n d t y p e o f t o o t h m o v e m e n t o f t h e a c t i v e a n d a n c h o r t e e t h n e e d to b e assessed. S u b s e q u e n t appliance adjustments should be based on treatment progress. Specific s p r i n g a n d / o r w i r e a c t i v a t i o n s c a n b e m a d e tail o r e d to t h e i n d i v i d u a l p a t i e n t ' s t r e a t m e n t o b j e c tives. A f r e q u e n t l y o v e r l o o k e d c o n s i d e r a t i o n i n anc h o r a g e c o n t r o l is t h e f i r s t - o r d e r side effects o f space closure. The mesially directed, buccally l o c a t e d f o r c e o n t h e m o l a r will t e n d to p r o d u c e a m e s i a l l y i n w a r d r o t a t i o n . T h i s r o t a t i o n gives t h e a p p e a r a n c e o f a n c h o r a g e loss w h e n v i e w e d f r o m t h e b u c c a l p e r s p e c t i v e . H o w e v e r , distalization of the molar may not be necessary, a mesia l l y - o u t w a r d f i r s t - o r d e r r o t a t i o n m a y b e all t h a t is n e e d e d f o r r e g a i n i n g t h e d e s i r e d m o l a r posi-
tion. A transpalatal arch provides an excellent means for preventing this side effect or actively correcting it. 44,45 Few studies have investigated effectiveness of differential m o m e n t strategies for anchorage control. H a r t et a146 f o u n d adequate anchorage control with differential torque mechanics for extraction space closure in 18 Class I malocclusions a n d 12 Class II, Division 1 malocclusions. 46 Rajcich and Sadowsky47 showed minimal anchorage loss with a differential m o m e n t a p p r o a c h for a n c h o r a g e control using intra-arch mechanics. Well-controlled clinical studies of explicit orthodontic t r e a t m e n t strategies are difficult because of the great n u m b e r of c o n f o u n d i n g variables associated with orthodontic treatment. The differences a m o n g patients and the specific objectives of their treatments complicate the analysis of the effectiveness of particular treatm e n t mechanisms. However, the studies that have b e e n c o m p l e t e d provide support for a differential m o m e n t strategy for anchorage control.
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four-fold increased orthodontic force magnitude on tooth movement and root resorptions. An intra-individual study in adolescents. EurJ Orthod 1996;18:287-294. Pilon~J, Kuijpers-Jagtman AM, MalthaJC. Magnitude of orthodontic forces and rate of bodily tooth movement. An experimental study. Am J Orthod Dentofacial Orthop 1996;110:16-23. Burstone C. Application of bioengineering to clinical orthodontics, in Graber T, Vanarsdall R, (eds): Orthodontics: Current Principles and Techniques. St. Louis, MO, Mosby, 2000. Reitan K. Some factors determining the evaluation of forces in orthodontics. Am J Orthod 1957;43:3245. Reitan K. Tissue behavior during orthodontic tooth movement. Am J Orthod 1960;46:881-900. Thilander B, Rygh P, Reitan K. Tissue reactions in orthodontics, in Graber T, Vanarsdall RL (eds): Orthodontics: Current Principles and Techniques. St. Louis, MO, Mosby, 2000, pp. 117-191. Storey E. The nature of tooth movement. Am J Orthod 1973;63:292-314. Burstone CJ. The segmented arch approach to space closure. Am J Orthod 1982;82:361-378. Kuhlberg AJ, Burstone CJ. T-loop position and anchorage control. Am J Orthod Dentofacial Orthop 1997;112: 12-18. Manhartsberger C, Morton JY, Burstone CJ. Space closure in adult patients using the segmented arch technique. Angle Orthod 1989;59:205-210. Nanda R, Kuhlberg AJ. Biomechanics of extraction space closure, in Nanda R (ed): Biomechanics in Clinical Orthodontics. Philadelphia, PA, Saunders, 1997. Shroff B, Lindauer SJ, Burstone CJ, et al. Segmented approach to simultaneous intrusion and space closure: Biomechanics of the three-piece base arch appliance. Am J Orthod Dentofacial Orthop 1995;107:136-143. Shroff B, Yoon WM, Lindauer SJ, et al. Simultaneous intrusion and retraction using a three-piece base arch. Angle Orthod 1997;67:455461. Burstone C, Manhartsberger C. Precision lingual arches. Passive applications. J Clin Orthod 1988;22:444-451. Burstone C. Precision lingual arches. Active applications. J Clin Orthod 1989;23:101-109. Hart A, Taft L, Greenberg SN. The effectiveness of differential moments in establishing and maintaining anchorage. A m J Orthod Dentofacial Orthop 1992;102: 434-442. Rajcich MM, Sadowsky C. Efficacy of intraarch mechanics using differential moments for achieving anchorage control in extraction cases. Am J Orthod Dentofacial Orthop 1997;112:441-448.
o a n c h o r is to secure firmly, to hold an object against m o v e m e n t ; anchorage is that which provides the secure hold. Specifically, orthodontic anchorage is the ability to prevent tooth m o v e m e n t of one g r o u p of teeth while moving a n o t h e r tooth or teeth. Controlling anchorage is one of the most critical elements of orthodontic treatment. O r t h o d o n t i c tooth m o v e m e n t is the result of the controlled application of mechanical forces to the teeth and periodontium. T h e stimulus that provokes the biologic activity leading to tooth m o v e m e n t is the mechanical forces exerted by orthodontic appliances. The response is b o n e r e m o d e l i n g and repositioning of teeth. From this perspective, orthodontic t r e a t m e n t can be conceived of as a stimulus-response model. Anchorage control involves the ability to create appropriate force systems (stimulus) that will provide the desired t r e a t m e n t effects (response).
T
From the Department of Orthodontics, University of Connecticut, School of Dental Medicine, Fa*mington, CT. Address corresponden~ to An&vw J. Kuhlberg, DMD, MDS, Department of Orthodontics, University of Connecticut, School of Dental Medicine, l~}*~raington, CT 06030. Copyright © 2001 by W.B. Saunders Company 1073-8746/01/0701-0006535.00/0 doi:l O.1053/sodo. 200 l. 21073 42
T h e p r o b l e m of a n c h o r a g e control is rooted in Newton's third law of motion, for every action there is an equal and opposite reaction. Thus, the distal forces acting to retract anterior teeth must be o p p o s e d by equal forces acting on the anchorage units in the mesial direction. The mesial forces must be accounted for to avoid anchorage loss. In light of this, orthodontists have developed a variety o f strategies and techniques to maintain a n c h o r a g e by applying m a n y m e t h o d s to inhibit or prevent m o v e m e n t of the a n c h o r teeth. Historically, most techniques for a n c h o r a g e control were developed empirically, yet their efficacy reflects the ingenuity of their inventors. Several anchorage control m e t h o d s have b e e n developed over the last century. TM T h e contributions of such icons as Angle, Case, Tweed, Begg, and others have provided a f o u n d a t i o n for modern orthodontic m e c h a n o t h e r a p y . Alt h o u g h each of t h e m espoused different methods and philosophies, a review of their individual works shows m o r e similarities than differences. By 1907, E.H. Angle advocated 5 types of anchorage control. Occipital a n c h o r a g e dep e n d e d on the use of extraoral headgear. Intermaxillary a n c h o r a g e included the use of elastics. 1 T h e 3 r e m a i n i n g m e t h o d s were dental a n c h o r a g e techniques. Angle decribed simple,
Seminars in Orthodontics, Vol 7, No 1 (March), 2001: pp 42-49
Space Closure and Anchorage Control
reciprocal, and stationary m e t h o d s for dental anchorage. Both simple and reciprocal anchorage methods relied on c o m p e t i n g support of the dentition to effect tooth displacement. In contrast, Angle's stationary a n c h o r a g e m e t h o d s were based on his view that firm support of the a n c h o r a g e units, t h r o u g h handing multiple teeth, acted to resist tipping and thus p r o m o t e anchorage. Calvin S. Case also advocated stationary anchorage m e t h o d s despite his ideological departure f r o m Angle's "New School. ''9 Although he described the use of extraoral a n d intermaxillary forces, he too recognized that resistance to tipping movements was requisite for intraarch anchorage control. With a singular approach, Case advocated the use of firm, soldered a t t a c h m e n t of the anchorage teeth to one a n o t h e r to maintain their upright positions. Case stated that, with this strategy, "the applied force will be equally distributed over the entire mesial or distal surfaces of the alveoli for all the roots, increasing the stability of the anchorage to an incalculable degree. ''2 Approximately 20 years later, Charles Tweed advocated similar techniques. His m e t h o d of anchorage p r e p a r a t i o n was a i m e d at maintaining the anchorage teeth against unwanted tipping and extrusive side effects. ~,5,6 A series of tip back bends acted to a n c h o r the teeth like tent stakes to resist vertical and anteroposterior displacem e n t during intermaxillary elastic traction. Although Tweed r e p o r t e d that his m e t h o d s were m o r e mechanical in nature than biologic, the tip back bends were generally a further r e f i n e m e n t of Angle's and Case's stationary anchorage methods. Despite his a d h e r e n c e to the differential force theory, P.R. Begg also used a similar procedure for anchorage control. 7-9 With the use of his light wire technique, Begg regularly used tip back bends to help maintain the anteroposterior position of the anchorage teeth to effect preferential tooth movement. 4,m Additionally, he proposed tipping the anterior teeth during initial retraction, followed by an uprighting phase. All of these m e t h o d s have proven to be generally effective and well-accepted a p p r o a c h e s to orthodontic m e c h a n o t h e r a p y . Further advancements in these techniques have b e e n evolutions rather than revolutions. The c o m m o n denominator of these and subsequent techniques is that
43
each aimed at controlling the type of tooth m o v e m e n t that occurred, ie, tipping versus translation. Fundamentally, advocates of m a n y of the cont e m p o r a r y orthodontic techniques have a d a p t e d their a p p r o a c h e s to different hardware designs. U n d e r s t a n d i n g the conceptual basis of biomechanics in a n c h o r a g e control permits greater latitude in t r e a t m e n t delivery and transcends the limits of any specific technique. Additionally, the c o n t e m p o r a r y shift toward compliance-independ e n t orthodontic t r e a t m e n t further requires a grasp of f u n d a m e n t a l biomechanical principles.
Anchorage from a Biomechanical Perspective The basic techniques for a n c h o r a g e control generally rely on 3 essential similarities: (1) extraoral forces on the anchorage unit (headgear), (2) intermaxillary elastics, (3) tipping movements of the active teeth while simultaneously discouraging tipping of the anchorage teeth. Patient compliance is a m a n d a t o r y r e q u i r e m e n t for h e a d g e a r and elastic wear. Without cooperation, control of tooth m o v e m e n t is lost and t r e a t m e n t o u t c o m e may be c o m p r o m i s e d . T h e a t t e m p t to maintain anchorage by promoting different types of tooth m o v e m e n t for the active teeth versus the a n c h o r units shows the biomechanical essence of a n c h o r a g e control. U n d e r s t a n d i n g how this strategy works requires an analysis of how the applied force systems d e t e r m i n e the resulting type of tooth m o v e m e n t . T h e relationship between mechanical force systems and tooth m o v e m e n t has b e e n well described and illustrates that the nature of a tooth's m o v e m e n t depends on the ratio of the applied m o m e n t relative to the applied force ( M / F ratio) at the orthodontic bracket, n T h e way a tooth moves is d e p e n d e n t on the nature of the forces (ie, the force system) imposed on it. T h e force system includes the applied force and m o m e n t s at the bracket (via elastic, coil, loop, etc), and the actual force distribution a b o u t the p e r i o d o n t i u m (stress-strain relationship). T h e force distribution is a function of the tooth's center of rotation. 11-21 Controlled tipping is tooth m o v e m e n t with the center of rotation of the tooth at the root apex. T h e resultant forces tend to be distributed at the marginal portion of the periodontal ligament
44
Kuhlberg and Priebe
(PDL). The M / F ratio for controlled tipping is reported at approximately 7/1 for most teeth with normal periodontal support. Translation or bodily movement, on the other hand, maintains the axial inclination of the tooth with the center of rotation at an infinite distance from the apex. The resultant force distribution tends to be more equally distributed along the pressure side of the alveolar structures. Translation requires a M / F ratio of about 10/1. Lastly, root movem e r i t - - o r displacement of the root apex while holding the crown stationary--occurs with a M / F ratio of 12/1. Here, the applied forces tend to be concentrated along the apical ½ of the root (Fig 1). Why does this analysis show the biomechaniControlled Tipping M/F -7:1
&
i
C
Figure 2. The effect of a large M/F ratio on tooth movement. A large M/F ratio produces root movement (A). A pure moment would produce only rotation, which would result in distal crown movement (B).
Translation M/F -10:1
Root Movement M/F -12:1
v
Direction of Movement
Figure 1. Tipping, translation, and root movement. The type of tooth movement depends on the M/F ratio.
cal essence of anchorage control? First, let us look at the effect of a high M / F ratio applied to the a n c h o r teeth. An applied force at the crown produces uncontrolled tipping as a result of the m o m e n t of the force. The applied m o m e n t (mom e n t of the couple) counteracts the tipping effect of the force. The applied m o m e n t acts in the opposite direction of the m o m e n t of the force. It moves the root(s) toward the extraction space. In addition, as the magnitude of the applied couple increases, the rotation of the tooth would move the crown away from the space (Fig 2). Conversely, a low M / F ratio produces tipping. With the apex remaining stationary, the crown tips toward the extraction space. Geometrically, the result is greater tooth m o v e m e n t at the occlusal plane relative to a tooth u n d e r g o i n g translation. Figure 3 shows a comparison of tipping versus translation, the center of resistance of the tooth for each example is displaced equally. The crown movement, however, is noticeably greater for the tipped tooth. This shows how tipping movements can result in greater movements of teeth from a clinical perspective. The theoretical effectiveness of differential
Space Closure and Anchorage Control
Figure 3. Tipping produces more movement at the crown or occlusal plane compared with translation. For both teeth in this illustration, the center of resistance of the tooth is displaced the same distance. M / F ratios is readily apparent. The question is, how can these force systems be p r o d u c e d clinically? For the purpose of discussion, consider the correction of a Class II malocclusion in which m a x i m u m posterior anchorage is needed. The objective is unequal applied M / F ratios: high M / F for posterior teeth, low for anterior teeth. If M/Fposterio r > M/Fante,_ior, then there must be either unequal forces or unequal moments. Unequal forces cannot be simply p r o d u c e d by a spring, loop, or chain elastic, because for every action there is an equal and opposite reaction. The retraction force a spring applies to the anterior teeth is reciprocally applied to the posterior teeth. To deliver unequal forces, external or extra-arch mechanisms must be included. Headgear and intermaxillary elastics are probably the 2 most c o m m o n means of generating these additional forces. In its simplest form, headgear acts to p r o d u c e a distal force on the anchorage teeth. By acting in opposition to the traction force from a spring or chain elastic, the headgear reduces the net force on the posterior teeth (M/Fposterio r > M/Fanterior ). Although there may be additional headgear effects, the aim conceptually is to retard the mesial forces on the posterior teeth (Fig
4A). Intermaxillary elastics, Class II elastics in this
4-5
example, increase the retraction force on the anterior teeth (M/Fposterio r > M/Fanterior ) (Fig 4B). A n o t h e r means of increasing the retraction force is the use of J - h o o k headgear applied to the anterior teeth. The applied m o m e n t is determined by the wire-bracket relationship. In the case of a straight wire, the magnitude of the moments on the anterior and posterior teeth may be presumed to be equal (see Schlegel 2u for a discussion on the effect of bracket width on the moment expressed as frictional force). For both headgear and elastics, the biomechanical effectiveness is largely a result of the generation of unequal forces applied to posterior and anterior teeth. Unfortunately, this approach depends on patient compliance for success. W h e n this is the only means of anchorage control, treatment remains at the mercy of motivational tactics and cooperative patients.
Force
B
Force
Figure 4. The effect of changing the force magnitude on the M/F ratio. Headgear is a means of decreasing the mesial force to the posterior teeth (A). Intermaxillary elastics (Class II elastics) increase the distal force to the anterior teeth (B).
46
Kuhlberg and Priebe
T h e inequality, M/Fposterio r > M/Fanterior, indicates the n e e d for an alternative approach. Rather than varying the forces, unequal moments may be applied. Increasing the m o m e n t on the posterior teeth a n d / o r decreasing the m o m e n t on the anterior teeth serves as a n o t h e r option toward creating differential M / F ratios. The horizontal force on the anterior teeth equals the horizontal force on the posterior teeth. T h e m o m e n t s or couples created by the bracket/wire-spring combination generate a greater m o m e n t to the a n c h o r a g e teeth. Simultaneously, a lower m o m e n t acts on the anterior teeth. For the Class I I / u p p e r anterior retraction challenge, the M / F ratio on the posterior teeth will p r o d u c e translation or root m o v e m e n t , while the low M / F ratio on the anterior teeth will show controlled tipping. T h e large posterior m o m e n t s encourage anchorage preservation as they resist tipping. Also, a very large posterior m o m e n t would actually cause distal crown movement, effectively increasing the size of the extraction space! T h e application of unequal m o m e n t s must also satisfy Newton's laws. Because the m o m e n t s on each end of the spring are unequal, the total force system must have additional effects. Vertical forces, intrusive to the anterior and extrusive to the posterior, are also acting. T h e vertical force m a g n i t u d e d e p e n d s on the difference in the 2 m o m e n t s and the distance between anterior and posterior a t t a c h m e n t points (Fig 5). In addition to the potential side effects created by the vertical forces, this a p p r o a c h to space
J Figure 5. The force system from differential moment orthodontic appliance designs for space closure.
closure frequently results in occlusal plane discrepancies between the anterior a n d posterior teeth. T h e posterior teeth may be positioned with the crowns distally tipped a n d the roots mesially oriented. T h e canines c o m m o n l y have a root-mesial axial inclination and the incisors are excessively upright. This situation is a natural consequence of the force system used but may also be an advantage given a p p r o p r i a t e malocclusions (ie, anterior protrusion with excessive dentoalveolar height and gingival display). An a p p r o p r i a t e stage of root correction after space closure prepares the occlusion for orthodontic finishing details. In comparison with the use of elastics or headgear, a differential m o m e n t a p p r o a c h to a n c h o r a g e control reduces the influence of compliance on t r e a t m e n t outcome. Because the force system is g e n e r a t e d by the intraoral appliance, elastics or h e a d g e a r b e c o m e less critical. In extremely difficult cases, h e a d g e a r or elastics may be used to further s u p p l e m e n t anchorage. Several orthodontic springs, loops, and devices have b e e n designed using this a p p r o a c h to anchorage control. 23-26 T h e wide variety of designs reflects the b r e a d t h of the options available to the clinician for i m p l e m e n t i n g this strategy for anchorage control in patient care. The imp o r t a n t issue is not the specific spring, it is the force system the spring applies to the dentition.
Biologic Considerations A n o t h e r factor in a n c h o r a g e control is the relative rates of tooth m o v e m e n t for tipping, translation, and root m o v e m e n t . T h e stress distribution within the periodontal support is different for each type of tooth m o v e m e n t . T h e stresses on the PDL are greatest at the cervix of the tooth for controlled tipping and a p p r o a c h zero at the apex. Conversely, the greatest stresses are at the apex for root m o v e m e n t . Translation applies a u n i f o r m stress along the root surface. The rates of tooth m o v e m e n t for each of these stress-strain relationships may also affect a n c h o r a g e control. T o o t h displacement rates have often b e e n evaluated on the basis o f force magnitude. Smith and Storey 7 r e p o r t e d that the m a n i p u l a t i o n of force magnitudes has an impact on relative rates of tooth displacement and thus anchorage control. Unfortunately their conclusions have not b e e n s u p p o r t e d by others. 27-s2 It is suggested,
Space Closure and Anchorage Control
however, that the stress distribution a b o u t the periodontal ligament, rather than the absolute magnitude of the force, has a greater impact on rates of displacement. ~S Histologic studies have shown that tipping produces localized regions of high stress, whereas translation results in a m o r e diffuse stress distribution. 34-36 Thus, a simple force applied at the bracket will be concentrated at the apical and marginal regions of the PDL and effectively increase the stress in these areas. If force magnitude, specifically the stress magnitude within the PDL, determines the rate of displacement, m,29,:~1 then tipping m o v e m e n t s occur faster because of the higher localized stresses. Storey r e p o r t e d that tipping m o v e m e n t s occurred m o r e rapidly than translational movem e n t s Y Although there is still some question regarding the effects of force magnitude on rates o f tooth displacement, the c o m b i n a t i o n o f these biologic concepts with the geometric advantage of tipping m o v e m e n t s over translation (Fig 3) may help explain the effectiveness of differential m o m e n t strategies for a n c h o r a g e control.
47
has a similar effect. Because wire stiffness is inversely related to the third power of the length, an off-centered or asymmetrically positioned spring will deliver greater m o m e n t s to the teeth that it approximates (Fig 6). 39 A n o t h e r m e t h o d of anterior retraction that uses a differential m o m e n t strategy for anchorage control is c o m b i n e d incisor intrusion and retraction. This simple yet effective appliance uses the tip back m o m e n t of the intrusion arch for creating the large posterior M / F ratio. 42A3 The retraction force is applied with either coil springs or elastic chain (Fig 7). By carefully controlling the intrusive and retraction forces, the overbite and overjet can be simultaneously corrected. Careful m o n i t o r i n g is crucial for successful anchorage control during space closure. A sys-
Clinical Techniques Using Differential Moments for Anchorage Control A n u m b e r of springs have b e e n designed that use the differential m o m e n t strategy for anchorage control. 2-~-u6,:~s,:~-~T h e selection of one spring or a n o t h e r depends largely on individual preferences. T h e T-loop spring described by Burstone and subsequently refined or modified is a simple yet effective device for controlled space closure. 23,ss-4° Although most frequently presented as a s e g m e n t e d spring, it can also be effective within a continuous wire. 41 With correct application, however, most retraction springs may be effective at closing spaces while simultaneously providing anchorage control. The core principle of loop design for all of these springs is increased stiffness of the wire on the anchorage side of the spring. All other factors being equal, an increase in wire stiffness has the effect of establishing greater m o m e n t s at the engaged teeth. Increases in stiffness may be accomplished by using composite springs with the incorporation of wires showing different moduli of elasticity, with the stiffer section engaging the anchorage units. Conversely, asymmetric positioning of the loop toward the anchorage teeth
J la
? I
Figure 6. Anchorage control with a differential moment strategy through the use of a T-loop spring. A T-loop positioned toward the posterior attachment increases the moment to the posterior teeth and decreases the moment to the anterior teeth (A). The expected tooth movements, the anterior teeth are expected to tip distally while the posterior teeth show root correction (B).
48
Kuhlberg and Priebe
B
Figure 7. C o m b i n e d anterior retraction and d e e p overbite correction with posterior a n c h o r a g e control. An intrusion arch is used to create the m o m e n t on the posterior s e g m e n t with the c o n c u r r e n t intrusive force on the anterior teeth and extrusive force on the posterior teeth. A chain elastic or coil spring is used to create the retraction force (A). The anticipated tooth m o v e m e n t s would be intrusion and retraction of the anterior teeth following the line of action of the resultant force and m o l a r tip back which aids in anchorage presei-vation (B).
tematic evaluation of treatment progress identifies t h e n e c e s s a r y a d j u s t m e n t s f o r e a c h p a t i e n t visit. T h e a m o u n t a n d t y p e o f t o o t h m o v e m e n t o f t h e a c t i v e a n d a n c h o r t e e t h n e e d to b e assessed. S u b s e q u e n t appliance adjustments should be based on treatment progress. Specific s p r i n g a n d / o r w i r e a c t i v a t i o n s c a n b e m a d e tail o r e d to t h e i n d i v i d u a l p a t i e n t ' s t r e a t m e n t o b j e c tives. A f r e q u e n t l y o v e r l o o k e d c o n s i d e r a t i o n i n anc h o r a g e c o n t r o l is t h e f i r s t - o r d e r side effects o f space closure. The mesially directed, buccally l o c a t e d f o r c e o n t h e m o l a r will t e n d to p r o d u c e a m e s i a l l y i n w a r d r o t a t i o n . T h i s r o t a t i o n gives t h e a p p e a r a n c e o f a n c h o r a g e loss w h e n v i e w e d f r o m t h e b u c c a l p e r s p e c t i v e . H o w e v e r , distalization of the molar may not be necessary, a mesia l l y - o u t w a r d f i r s t - o r d e r r o t a t i o n m a y b e all t h a t is n e e d e d f o r r e g a i n i n g t h e d e s i r e d m o l a r posi-
tion. A transpalatal arch provides an excellent means for preventing this side effect or actively correcting it. 44,45 Few studies have investigated effectiveness of differential m o m e n t strategies for anchorage control. H a r t et a146 f o u n d adequate anchorage control with differential torque mechanics for extraction space closure in 18 Class I malocclusions a n d 12 Class II, Division 1 malocclusions. 46 Rajcich and Sadowsky47 showed minimal anchorage loss with a differential m o m e n t a p p r o a c h for a n c h o r a g e control using intra-arch mechanics. Well-controlled clinical studies of explicit orthodontic t r e a t m e n t strategies are difficult because of the great n u m b e r of c o n f o u n d i n g variables associated with orthodontic treatment. The differences a m o n g patients and the specific objectives of their treatments complicate the analysis of the effectiveness of particular treatm e n t mechanisms. However, the studies that have b e e n c o m p l e t e d provide support for a differential m o m e n t strategy for anchorage control.
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