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Anchorage in Orthodontics

INDIAN DENTAL ACADEMY Leader in continuing dental education

Anchorage in Fixed Appliances: 

Edgewise Appliance: Tweed Technique: “ When teeth are tipped distally as they are in anchorage preparation, osteoid tissue appears to be laid down adjacent to the mesial surface of the tooth being moved distally.” - Kaare Reitan

Tweed Technique: Anchorage Preparation: First Degree:  ANB 0º- 4º, facial esthetics are good  Mandibular terminal molars must be uprighted and maintained in a position to prevent their being elongated  Direction of intermaxillary elastic pull should not exceed 90º 

Tweed Technique: Anchorage Preparation: Second Degree:  ANB exceeds 4.5  Mandibular second molars should always be banded  Must be tipped distally so that their distal marginal ridges are at gum level  Direction of pull of intermaxillary elastics should always be > 90º 

Tweed Technique:    

Third Degree or Total Anchorage Preparation: ANB does not exceed 5º Jigs are necessary for total anchorage preparation All posterior teeth (second premolar to terminal molars) are tipped distally Distal marginal ridges of terminal molars are below gum level In difficult cases, anchorage prepared in both maxillary and mandibular arches

Tweed Technique: 

Space Closure: Class III elastics

Lower: Head gear (upper molars) Class II elastics

Upper: Head gear (lower molars)

Tweed-Merrifield Technique: 

Allows mandibular anchorage to be prepared quickly by tipping 2 teeth at a time to their anchorage prepared position by using 10 teeth as “anchorage units” to tip two teeth

Hence referred to as the Merrifield “10-2” System

Tweed-Merrifield Technique: ď Ž

Separate canine retraction with high pull Jhook headgears aided by power chains

Tweed-Merrifield Technique: ď Ž

ď Ž

Spaces closed with maxillary and mandibular closing loop arch wires Vertical support to maxillary arch with J-hook headgear; to mandibular anterior teeth with anterior vertical elastics

Tweed-Merrifield Technique: 

Sequential Mandibular Anchorage Preparation: The archwire produces an active force on only two teeth while remaining passive to the other teeth Remaining teeth act as stabilizing or anchorage units Anchorage preparation supported by high pull headgear worn distal to the mandibular central incisors

Tweed-Merrifield Technique: 

Initiated by tipping the second molar to a 15 º distal inclination After space closure, arch is checked to ensure a 15º distal tip of second molars: Readout A 10º distal tip is placed mesial to first molar brackets Compensating bend maintains 15º of terminal molar tip

Tweed-Merrifield Technique:

Tweed-Merrifield Technique: 

Final step: Place a 5º distal tip 1mm mesial to second premolar brackets In the maxillary arch, an effective 5º distal tip on the second molar is placed in the arch wire

Anchorage Considerations in Begg and Tip-Edge Techniques: Begg Technique: Very efficient in anchorage conservation in the sagittal direction. Stationary Anchorage Anchorage Control in Stage I: Sagittal anchorage: ďƒ˜ Upper Molar Anchorage: 1. Upper Class I elastics not used ď Ž

Anchorage Considerations in Begg and Tip-Edge Techniques: 2. TPA , when using power arms and palatal elastics ( also consolidating the first and second molars)

Anchorage Considerations in Begg and Tip-Edge Techniques:  1. 2.



Lower Molar Anchorage: Stiff lower wire ( 0.018” P or P+) Light (yellow) or ultra light (‘Road Runner’) elastics. Heavier elastics tax anchorage and hinder bite opening Molar stops when Class II and lower Class I elastics are used Lip bumper/lingual arch in critical anchorage cases

Anchorage Considerations in Begg and Tip-Edge Techniques: ď Ž

1. 2. 3.


Causes of anchorage loss in sagittal direction during Stage I: Insufficient resistance from anchor bends Excessively heavy elastic pull Increased resistance from anterior teeth: - incisor and/ or canine roots touching labial cortical plate - abnormal tongue or lip function High mandibular plane angle

Anchorage Considerations in Begg and Tip-Edge Techniques: ď Ž 1. 2.

Vertical Anchorage: Extrusion of molars due to anchor bends Vertical component of Class II elastics

Anchorage Considerations in Begg and Tip-Edge Techniques:    1. 2. 3. 4.

Vertical Anchorage: Usually adequate in low angle cases In high angle cases should be reinforced with: T.P.A. High pull headgear Posterior bite blocks Engagement of arch wire in first and second molars

Anchorage Considerations in Begg and Tip-Edge Techniques: Transverse Anchorage: Anchor bends and Class II elastics cause lingual rolling of molars To prevent: 1. Sufficiently stiff arch wires 2. Expansion of the arch wires 3. T.P.A., expanded headgear face bow, lip bumper ď Ž

Anchorage Considerations in Begg and Tip-Edge Techniques:  

Anchorage Control in Stage II: Heavy arch wires (0.018” P or P+ or 0.020” P) to maintain corrections. Also resist distobuccal rotational tendency Since anchor bends are reduced, a MAA for lingual root torque 0.010” uprighting springs on canines

Anchorage Considerations in Begg and Tip-Edge Techniques: ď Ž ďƒ˜



Anchorage Control in Stage II: Braking mechanics for protraction of posteriors: Braking springs or angulated T pins on canines and lateral incisors Torquing component on incisorscombination wires or torquing auxiliaries

Anchorage Considerations in Begg and Tip-Edge Techniques:  

 

Anchorage Control in Pre-Stage III: Upper wire: Gable bend for holding the deep bite correction and uprighting distally tipped molars Lower wire: gable and anchor bends Inversion of segments to avoid canine extrusion Ends of arch wires are bent back

Anchorage Considerations in Begg and Tip-Edge Techniques: Causes of anchorage loss in Stage III: Torquing auxiliaries and uprighting springs cause reciprocal reactions in all three planes of space: Lingual root torquing auxiliary and distal root uprighting spring: labial crown movements, extrusion of anteriors and intrusion of posteriors, buccal crown movement of posteriors

Anchorage Considerations in Begg and Tip-Edge Techniques: ď Ž

Reciprocal mesial crown moving forces resisted by cinching and use of Class II elastics

ď Ž

When mesial drag on the lower arch is greatreverse (labial) root torquing auxiliary

Anchorage Considerations in Begg and Tip-Edge Techniques: Control of Anchorage in Stage III:  Minimise need for root movements by: - careful diagnosis and planning of extractions - controlled tipping of incisors - use of brakes  Use of heavy base wires ( 0.020” P)  Lighter auxiliaries and uprighting springs  Light Class II elastics

Anchorage Considerations in Begg and Tip-Edge Techniques: Control of Anchorage in Stage III: ď Ž Reinforcement of Anchorage: In treatment of severe malocclusions, anchorage needs to be reinforced in Stage III 1. Sagittal: Reverse root torquing auxiliary, headgear or T.P.A., lip bumper 2. Vertical: High pull head gear, T.P.A. or posterior bite blocks

Anchorage Considerations in Begg and Tip-Edge Techniques: 3. Transverse: 1. 0.020� P base wires with adequate contraction and toe-in built into the wires 2. TPA or heavy overlay wires 3. Extended mouse trap or molar torquing auxiliary for buccal root torque

Anchorage Considerations in Begg and Tip-Edge Techniques:  

Arch Wires in Stage III: Cuspid circles tightly touching the cuspid brackets Posterior segments kept gingival in relation to anterior segments Contraction in the upper arch wire: 2mm for 2spur auxiliary made in 0.012” wire Molar segments of upper given a mild toe-in. Lower wire segments are in line

Anchorage Considerations in Begg and Tip-Edge Techniques:  

Arch Wires in Stage III: Gable bend in the upper and gable and anchor bends in the lower arch wire Wire ends are annealed and tightly cinched

Begg vs. Conventional Edgewise: ď Ž 1. 2.




Stationary anchorage Round wires +Light elastics Decreased friction

Near reciprocal anchorage Rectangular full size wires +Heavy forces Increased friction

Anchorage Control Using the PreAdjusted Appliance ď Ž

ď Ž

Anchorage requirements differ because of built-in adjustments which start expressing right from the beginning Initial wires being flexible, not sufficient resistance in the various planes

Anchorage Control Using the PreAdjusted Appliance  1.  

    

Specific approaches used: Ricketts: Utility arch: Buccal root torque of lower molars Tip back Toe-in bend Nance button Quad helix Headgears: cervical, combination and high pull

Anchorage Control Using the PreAdjusted Appliance 2. Alexander:  6 degrees distal tip of lower first molar  ‘Retractors’ ( Dr. Fred Schudy): Cervical, combination or high pull depending on growth pattern  5 degree labial root torque in lower anteriors  Two stage upper anterior retraction  En mass lower anterior retraction

Anchorage Control Using the PreAdjusted Appliance Roth:  Frictionless space closure with double keyhole loops  Asher facebow to retract anteriors in critical anchorage cases  Palatal arches involving second molars

Anchorage Control Using the PreAdjusted Appliance 3. Burstone: Two-tooth concept and segmental movement  Arch divided into 1 anterior and 2 posterior segments, treated as separate units  Frictionless mechanics using TMA springs; low load deflection rate  TPA/ lingual arch  Differential M/F ratios controls the anchorage

Anchorage Control Using the PreAdjusted Appliance Considerations in Loop Mechanics: The performance of a loop is determined by: 1. Spring Properties: The amount of force it delivers and the way the force changes as teeth move. Affected by wire size, wire material, leg length, configuration and interbracket distance 2. Root Paralleling Moments: Limits the amount of wire that can be incorporated to make the loop springier ď Ž

Considerations in Loop Mechanics:

Anchorage Control Using the PreAdjusted Appliance 

 1.

Location of the Loop: Extent to which it serves as a symmetric or asymmetric V bend Additionally the loop must “fail safe” : tooth movement should stop after a prescribed range of movement Different loop designs: Vertical loops:

Anchorage Control Using the PreAdjusted Appliance 2. Delta loop:  Made in 16x22 wire  Activated by opening 3. Double Keyhole Loop:  Ronald Roth  Made in 0.019x 0.026 dimension

Anchorage Control Using the PreAdjusted Appliance 4. T- loop:  Burstone  Made of 0.018/0.017 x 0.025 TMA wire  Low load deflection rate  Higher M/F ratios obtained by placing more wire length gingivally  Activation is quite sensitive and needs to be activated at 6 different places

Anchorage Control Using the PreAdjusted Appliance 5. Opus Closing Loop:  Designed by Siatkowski  Offers excellent control of forces and moments  Made in 16x22 or 18x25 steel or 17x25 TMA wire

Anchorage Control Using the PreAdjusted Appliance 6. K-SIR Loop:  .019x.025 TMA wire  Brings about simultaneous intrusion and retraction of the anterior teeth  Low load deflection rate and good range

Anchorage Control Using the PreAdjusted Appliance BENNETT AND MCLAUGHLIN: Anchorage control: ‘The maneuvers used to restrict undesirable changes during the opening phase of treatment, so that leveling and aligning is achieved without key features of the malocclusion becoming worse.’

Horizontal Anchorage Control:  

Control of Anterior Segments: Tendency for the incisors and the cuspids to tip forward when archwires are first placed To prevent anterior teeth from tipping forward, elastic force applied Opened the bite in the premolar area and deepened the bite anteriorly- Roller Coaster Effect

Horizontal Anchorage Control: 

To minimize this effect: A new system of force developed by Bennett and McLaughlin: Use of lacebacks: Initial tipping followed by a period of rebound due to levelling effect of the arch wire Bending the arch wire behind the most distally banded posterior tooth

ď Ž

Lacebacks and Bendbacks:

Horizontal Anchorage Control:  

Use of lacebacks: Study conducted by Robinson in 1989 Little additional loss of anchorage in posterior segments while a substantial gain in anchorage in anterior segments

Horizontal Anchorage Control: Control of Posterior Segments: Posterior anchorage requirements are greater in upper arch:  Upper anterior segment has larger teeth  Upper anterior brackets have greater amount of tip built into them  Upper incisors require greater torque control and bodily movement 

Horizontal Anchorage Control: Upper molars move mesially more readily  More Class II type of malocclusions encountered .˙. Extra-oral force to provide anchorage control in upper arch - High angle cases: occipital headgear - Low angle cases: cervical headgear - Supplemented with TPA 

Horizontal Anchorage Control:  

Control of Posterior Segments: Lower Arch Lingual arch and lacebacks adequate for anchorage support Class III elastics once the 0.016 round wire has been reached

Vertical Anchorage Control: ď Ž ď ś

Incisor Vertical Control: Distally tipped canines cause extrusion of the incisors- avoided by not bracketing the incisors or not tying the arch wire into incisor brackets

Vertical Anchorage Control: ď ś

Avoid early engagement of high labially placed canines

Vertical Anchorage Control:  

 

Molar Vertical Control: Upper second molars generally not initially banded; step placed behind the first molar Attempt to achieve bodily movement during expansion Palatal bars In high angle cases, highpull or combination pull headgear Upper or lower posterior bite plate

Lateral Anchorage Control: ď Ž

Intercanine Width: Should be maintained

ď Ž

Molar Crossbites: Avoid correction by tipping movements

Anchorage Control Using the PreAdjusted Appliance ď Ž

ď Ž

During space closure, heavy forces avoided by the use of active tiebacks Once completed, passive tiebacks used to maintain the correction

Inverse Anchorage Technique:  

José Carrière: Mandible is a preferred point of reference for diagnosis and treatment planning, while maxilla is better suited to accepting orthodontic correction Mandible is subjected to considerable movement and hence a variable reference point. Actively influenced by muscles surrounding it

Inverse Anchorage Technique: 

Maxilla bears a fixed anatomical relationship to the skull. Less influenced by vectors and forces generated by the surrounding muscles Histological difference between maxilla and mandible ; maxilla has more plasticity of response Treatment starts from the distal segments and moves sectionally towards the mesial part (distomesial sequence)

Inverse Anchorage Technique: Inverse Anchorage Equation: C - Dc/2 – R1 = 0 where, C= horizontal distance b/w the cusp tip of the upper canine and the end of the distal ridge of the lower canine Dc= arch length discrepancy of the mandibular arch, measured from distal of both lower canines R1= amount in mm which the anterior limit of the lower incisors should be moved in the cephalogram for the correction of a case ď Ž

Inverse Anchorage Technique:

Inverse Anchorage Technique: 

 

On knowing both the variables, it is possible to deduce the distance to which the upper canines have to be distalised C= Dc/2 + R1 If C > Dc/2 + R1; amount of anchorage prepared is greater than needed If C < Dc/2 + R1; a loss of anchorage has occured

Inverse Anchorage Technique: ď Ž

1. 2. 3.

Through this equation, we are able to: Prescribe the amount of anchorage required Control the condition of the anchorage Ideal results

Inverse Anchorage Technique:

Inverse Anchorage Technique: Stages: ď Ž Maxillary stage: Treatment started in the maxilla with posterior leveling, canine retraction, anterior leveling and anterior retraction ď Ž Mandibular stage: same sequence

IMPLANTS : Boucher: ‘Implants are alloplastic devices which are surgically inserted into or onto jaw bone.’ Why implants? Limitations of fixed orthodontic therapy:  Headgear compliance  Reactive forces from dental anchors 


Anchorage Source: Orthopedic anchorage: - maxillary expansion - headgear like effects Dental anchorage: - space closure - intrusion ( anterior and posterior) - distalization

IMPLANTS :      

Implant designs for orthodontic usage: Onplant Impacted titanium post Mini-implant Micro-implant Skeletal anchorage system

IMPLANTS : Implants for intrusion of teeth:  Creekmore ( 1983)  Vitallium bone screw

IMPLANTS : ď&#x201A;§ Implants for space closure: Eugene Roberts: use of retromolar implants for anchorage Size of implant: 3.8mm width and 6.9mm length


Onplant: Block and Hoffman (1995) Titanium disc- coated with hydroxyapatite on one side and threaded hole on the other Inserted subperiosteally

IMPLANTS : Impacted titanium posts: Bousquet and Mauran (1996) Post impacted between upper right first molar and second premolar extraction space on labial surface of alveolar process

ď Ž

IMPLANTS : Mini-implant: Ryuzo Kanomi ( 1997) Small titanium screws 1.2mm diameter and 6mm length Initially used for incisor intrusion

ď Ž

IMPLANTS : Skeletal anchorage system (SAS): Sugawara and Umemori (1999) Titanium miniplates Placement in key ridge for upper molar and ramus for lower molar intrusion Uses: - molar intrusion - Molar intrusion and distalisation - Incisor intrusion - Molar protraction ď Ž


Micro-implants: For retracting the maxillary anteriors & uprighting the mandibular molars No side effects on the anterior teeth

Zygoma Ligatures: An Alternative Form of Maxillary Anchorage Brite Melson Jens Kolsen Peterson Antonio Costa JCO/ MARCH 1998 ď Ž

ď Ž

Indicated in patients without sufficient posterior anchorage in whom other forms of anchorage have been ruled out Best bone quality is found in the zygomatic arch and infrazygomatic crest in a partially edentulous patient

Zygoma Ligatures: An Alternative Form of Maxillary Anchorage  

Surgical Technique: A horizontal bony canal drilled in the region of infrazygomatic crest A double twisted 0.012 wire is pulled through this canal Wire covered by a thin polyethylene catheter to protect the mucosa

Zygoma Ligatures: An Alternative Form of Maxillary Anchorage

Zygoma Ligatures: An Alternative Form of Maxillary Anchorage  

Orthodontic Technique: A coil spring is extended from the zygoma ligature to the point of force application Center of resistance determines point of force application Prosthesis should be constructed immediately after removal of the appliance Zygomatic wires are removed by pulling at one end

Zygoma Ligatures: An Alternative Form of Maxillary Anchorage

Zygoma Ligatures: An Alternative Form of Maxillary Anchorage

Zygoma Ligatures: An Alternative Form of Maxillary Anchorage

Rapid orthodontic tooth movement into newly distracted bone after mandibular distraction osteogenesis in a canine model Eric Jein-Wein Liou Alvaro A. Figueroa John W. Polly AJO, April 2000

‘Distraction osteogenesis is a process of growing new bone by mechanically stretching preexisting vascularised bone tissue.’

 Purpose of the Study: To determine the feasibility, timing and rate of orthodontic tooth movement into the fibrous bone recently formed through distraction osteogenesis in the canine mandible

  

Material and Methods: Four mature beagle dogs A custom-made intraoral distraction device using an orthodontic palatal expander

 Surgical Procedure:  

Mandibular body osteotomy Care taken to preserve 0.5 to 1.0mm thickness of alveolar bone Distraction device fixed with bone screws

  

Distraction Procedures: 7 day latency period Distraction device activated 1mm each day for 14 days

 Orthodontic Tooth Movement: 

Calibrated elastic threads with 50g of orthodontic force applied to mandibular fourth premolars for 5 weeks

On one side, premolar moved simultaneously with the distraction procedure and on the other after the completion of distraction Distraction device and orthodontic appliances left in place for another 4 months before the dogs were sacrificed

 Results: 

Tooth movement at the same time as distraction- 6mm in 7 weeks

Tooth movement immediately after cessation of distraction- 6mm in 5 weeks Fourth premolars moved with distraction- horizontal bone loss. No native alveolar bone identified Radiographically, extruded and tipped forward Fourth premolars moved after distraction- mild to no alveolar bone loss Native alveolar bone preserved

 1. 

Discussion: Osteogenesis in rapid tooth movement: Average rate of tooth movement: 0.3 mm per week In the study, rate of tooth movement: 1.2 mm per week The process of osteogenesis on the tension side; a form of distraction osteogenesis No infrabony defect on tension side

2. Less bone resistance, faster tooth movement: 

Typical rate of tooth movement with 100g of tipping force: 1.5 mm in 5 weeks In this study, with 50g of tipping force: 6mm in 5 weeks Teeth moved into fibrous immature bone tissues

3. Timing to initiate rapid orthodontic tooth movement: ď&#x192;&#x2DC; Theoretically, during the first few days after distraction ď&#x192;&#x2DC; Transient burst of localized osteoclastic activity results in resorption of alveolar ď&#x192;&#x2DC; Native alveolar bone adjacent to fourth premolar moved simultaneously with distraction disappeared completely


Fourth premolars moved after distraction: native crestal alveolar bone preserved and brought into the distraction space

4. Pulp Vitality: ď&#x192;&#x2DC; Maintained in all teeth Conclusion: The best time to initiate tooth movement was immediately after the end of distraction

Ongoing Innovations in Biomechanics and Materials for the New Millennium Robert P. Kusy Angle Orthodontist, 2000

    

Glossary of Terms: FR: classical friction µ: coefficient of friction N: normal or ligation force θ: second order angulation of an arch wire relative to a bracket θc: critical contact angle or second order angulation after which binding (BI) occurs θz: second order angulation after which binding(BI) ends and physical notching(NO) begins

 

Glossary of Terms: BI: elastic binding caused by exceeding θc but less than θz

NO: physical notching caused by exceeding θz

Bracket Index: Width/Slot Clearance Index: 1Engagement Index Engagement Index: Size/Slot

Introduction: Biomechanics and materials complement one another; yet are presented as though they are independent of each other Biomechanics as a Science: For each arch-wire bracket combination a critical contact angle (θc ) exists given by the relationship: θc = 57.3( Clearance Index) (Bracket Index)

θc = 57.3( 1- Engagement Index) (Bracket Index)  Once binding occurs, it can assume two forms:  Elastic Deformation  Plastic Deformation (physical notching)  Overall resistance to sliding: RS = FR+BI+NO  FR occurs because of the ligation or normal force (N)

 

Elastic binding (BI) occurs once the wire contacts the diagonal tiewings of a bracket Physical notching: plastic deformation occurs at the diagonal tie-wings or the opposing wire contacts For optimal sliding θ ≈ θc Sliding at θ < θc results in increased treatment time Sliding at θc < θ <θz : amount of binding and the treatment time increases

Using Biomechanics to Innovate New Materials To reduce FR, 2 options exist: Decrease µ or decrease N  Reducing FR by decreasing µ for θ < θc Improving surface chemistry  Reducing FR by decreasing N for θ < θc Two methods: 1. Use of self ligating brackets 2. Development of stress relaxed ligatures 

Using Biomechanics to Innovate New Materials 

 

Use of self ligating brackets: Minimize N When θ < θc FR is low

BI behaves similar to conventional brackets  Perhaps the overstatement of their capabilities promoted practitioners to slide teeth when θ > θc 

Using Biomechanics to Innovate New Materials ď Ž ď&#x192;&#x2DC;


Development of stress relaxed ligatures: Short term forces resisted by elastic, high strength material; long term forces accommodated by stress relaxation and an accompanying decrease in N Formed from acrylic monomer n-butyl methacrylate and drawn polyethylene fibers by use of the photo-pultrusion process

Using Biomechanics to Innovate New Materials   1. 2.  

Stabilizing θ at θ ≈ θc 2 means are available: Power arms Composite arch wires Power arms A force that passes through the center of resistance generates no moment Once a tooth moves, the point of force application shifts away from the center of resistance

Using Biomechanics to Innovate New Materials  

Use of composite arch wires: To slide teeth a clinician chooses from among several archwire- bracket combinations By integrating two classes of materials (a ceramic and a polymer), a composite archwire can be fabricated. Mechanical properties differ, overall crosssectional area remains constant

Use of composite arch wires: 

Manufactured by the photo-pultrusion process using ceramic glass fiber yarns and acrylic monomers For 3 levels of fiber loading (49, 59 and 70% v/v) the values of µ and θc remained constant This constancy should be advantageous

Using Biomechanics to Innovate New Materials 

Reducing BI for θc < θ <θz : If θ exceeds θc , some binding occurs In the past, practitioners chose archwire bracket combinations that represent a compromise between binding and control

Reducing BI for θc < θ <θz : 

With increasing stiffness, decreasing interbracket distance, or both, binding increases In recent work, binding has been reduced by materials having high resiliencies and high yield strength- resistance to deformation and physical notching Use of composite wires made from ceramic glass fibers and a BIS-GMA-TEGMA matrix

Photo-pultrusion: 

Fibers are drawn into a chamber: spread, tensioned and coated with monomer Reconstituted into a profile of specific dimensions via a die As photons of light polymerize the structure into a composite Any shrinkage voids are replenished by a gravity fed monomer

Photo-pultrusion: 

If further shaping is required, composite is only partially cured (α staged) Further processed using a second die and β staged into final form

Conclusions: 

Sliding mechanics should occur only at values of angulation (θ) that are in close proximity to the critical contact angle (θc)

Material innovations can reduce FR at θ < θc by reducing the coefficient of friction, the normal force of ligation or both, among which various surface treatments and stress relaxed ligatures are 2 means

Conclusions: 

Composite materials can stabilize θ at θ ≈ θc by maintaining the same archwire bracket clearance while permitting the force deflection characteristics to vary Decreasing wire stiffness or increasing interbracket distance can reduce RS at θc < θ <θz, independent of the material used

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