Begg mechanics

CONTENTS• Introduction• Basics of biomechanics• Begg mechanics of

» Stage I» Stage II» Stage III

• Conclusion• References

26 sep '12 2

INTRODUCTION

ᵿ Biomechanics - the study of mechanics as it affects the biology of tooth movement

ᵿ Burstone deserves a lion’s share of credit for establishing biomechanics as a vital ingredient of Orthodontic Treatment.

ᵿ Quick and predictable results with a minimum of tissue damage and maximum patient comfort can only be obtained by carefully planning the application of forces and moments on the teeth

26 sep '12 3

Basics of biomechanics

Physical properties such as distance, weight, temperature and force are treated mathematically as either SCALARS or VECTORS.

SCALARS include temperature and weight, they have a definite magnitude but do not have a direction.

They are completely described by their magnitude.

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ᵿ VECTORS include force, these have both magnitude and direction.

ᵿ In case of force, along with magnitude and direction, point of application must be taken into account.

FORCE: It is defined as an act upon a body that changes or tends to

change the state of rest or motion of the body.

Force is a vector it has both magnitude and direction.

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In case of understanding the magnitude and direction of tooth movement, point of application of force is important

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Moment

ᵿ Is defined as a tendency to rotate

MOMENT is the product of the force times the perpendicular distance from the point of force application to the center of resistance.

M = F x d

It is measured in grams – millimeters.

F x d(X) = M(X)

F

d

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If a line of action does not pass through the center of resistance the force will produce some rotation. The potential for rotation is measured as moment.

The direction of a moment can be determined by continuing the line of action of the force around the center of resistance.

F x d(X) = M(X)26 sep '12 8

A MOMENT may be referred as

Rotation

Tipping

Torquing.

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MOMENT OF FORCE: When a force is applied at any point other than through the

center of resistance in addition of moving the center of resistance in direction of the force, a moment is created.

In case of tooth, since it is embedded in the alveolar bone, we cannot apply force directly on Cres, but can apply force on the exposed part of the tooth, which is at a distance from Cres.

Therefore with a single force we invariably create a moment called as moment of force.

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Moment of force is always relative to point of application. It means moment of a force will be:

low relative to a point (point of application) close to line of action

high for a point (point of application) with a large perpendicular distance to line of action.

In case of Couple moment, it is not relative to any point.

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CENTER OF ROTATION: It may be defined as a point about which a body appears to

have rotated as determined from its initial to final position.

A simple method of determining a Center of rotation - Draw the long axis of the tooth in its initial and final positions; we will see that both these lines intersect at a point.

This is the point around which the tooth rotates and is called Center of rotation.

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Center of rotation could be at the center of resistance, apical or incisal to Cres or at infinity. Its position will determine the type of tooth movement.

The moment to force ratio controls the center of rotation for the intended tooth movement.

TYPES OF TOOTH MOVEMENT

POSITION OF THE CENTER OF ROTATION

A. TRANSLATION

B. UNCONTROLLED TIPPING

C. CONTROLLED TIPPING

D. ROOT MOVEMENT OR TORQUING

LIES AT INFINITY

SLIGHTLY APICAL TO CENTER OF RESISTANCE

APEX OF ROOT

INCISAL OR OCCLUSAL EDGE

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Controlled Tipping:

In this situation, crown moves in the direction of force but the root position remains the same or get minimally displaced. Here Center of rotation lies at apex of the root.

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Uncontrolled tipping:

ᵿ In this situation, when force is applied the crown moves in one direction and root moves in the opposite direction. Here Center of rotation lies near to center of resistance.

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Translation/bodily movt.ᵿ In this situation tooth moves bodily e.g. both crown and root

portion of tooth moves bodily in the direction of force. Here Center of rotation lies at infinity.

ᵿ All the points in the tooth move by same distance in the same direction in translation.

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Root movement

In this situation, root moves in the direction of force but the crown position remains the same or get minimally displaced.

Here Center of rotation lies at incisal edge of the crown.

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COUPLE:

Two equal and opposite, non - collinear forces are called a couple.

Couple consists of two forces of equal magnitude, which are parallel to each other but not coincident and they face in opposite direction.

The moment of this couple is equal to the magnitude of one of the forces multiplied by the perpendicular distance between the two lines of action of force.

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It seems that type of movement exhibited by a tooth is determined by the ratio of the counter-balancing moment produced to the net force that is applied to a tooth .

This is called as the moment to force ratio .

In terms of direction, the counter-balancing moment is always going to be in the direction opposite the moment of force.

26 sep '12 19

M/F Ratio values1. M/F ratio less than 5:1 causes uncontrolled tipping in

which the crown and the root apex move in opposite directions.

2. M/F ratio between 5:1 and 8:1 causes controlled tipping in which the root apex remains stationary and only the crown moves.

3. M/F ratio of 10:1 causes translation. The crown and the root apex move to same extent in the same direction of force.

4. M/F ratio of 12:1 causes root movement. The crown remains stationary while only the root moves.

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Moment of force

Force

Counter-balancing moment

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STATE OF EQUILIBRIUM

ᵿ When an appliance is fitted in the mouth, it assumes a state of equilibrium.

ᵿ The active elements in the appliance generate certain forces or moments.

ᵿ Other forces or moments arise automatically in the system to balance these forces or moments. Some of them may be beneficial while others may be undesirable.

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ᵿ For example, tip back bend (like the bite opening bend in Begg appliance) generates a moment which tends to tip the molar tooth crown distally.

ᵿ This is balanced by an automatic creation of another moment in the overall system in opposite direction comprising of two forces an intrusive force at the anterior end and on extrusive force on the molar.

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Begg Mechanics

There are three basic movements in the Begg mechanotherapy

Incisor intrusion - intrusive force magnitude and direction. Tipping of teeth Root uprighting. basic of M/F ratio.

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Stage I

ᵿ Open the anterior biteᵿ Eliminate anterior crowdingᵿ Close anterior spacesᵿ Over correct rotated cuspids and bicuspidsᵿ Over correct the mesiodistal relationship of the buccal

segments

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Open the anterior bite : Proper amount of bite opening bends or curves in the arch wire. Continuous wearing of Class II (intermaxillary) elastics as

required.

Eliminate anterior crowding : Vertical loops between crowded anterior teeth, with bracket

areas modified for desired overcorrection.

Close anterior spaces : Plain arch wire with latex elastic or elastomeric chain from

cuspid to cuspid.

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Over correct rotated cuspids and bicuspids : Rotating springs Elastomeric traction into the arch wire

Over correct the mesiodistal relationship of the buccal segments

Continuous wearing of class II elastics.

Proper bite opening bends in both upper and lower arch wires.

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Mechanics in Stage I

ᵿ The orthodontic environment created during stage I is conducive to rapid movement of anterior teeth under the light forces generated by the arch wires and intermaxillary elastics

Stage I arch wire

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Intrusion

ᵿ All the six anterior teeth are intruded together in Begg practice.

ᵿ The round archwire derives its bite opening force from the anchor bends.

ᵿ This force acts on the teeth through the brackets which are placed on the labial surfaces of the incisors, i.e. away from the long axis of the teeth on which the CRes. of the individual teeth are located.

26 sep '12 30

ᵿ Depending on the direction of the intrusive force in relation to the long axis of the tooth, the tooth would undergo varying amounts of intrusion (translation) and labial crown-lingual root tipping (rotation).

ᵿ Such rotational displacement is generally undesirable (the exception being lingually inclined incisors as in Cl. II div. 2 cases),

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ᵿ resisted in the case of upper incisors by using Cl. II elastics during stage I.

ᵿ However, the Cl II force not only has a horizontal component for providing this resistance, it also has a vertical component which reduces the magnitude of the intrusive force of the wire.

ᵿ Further, the horizontal component of the elastic force affects the direction of the net resultant force.

ᵿ Thus, the interplay between the wire generated intrusive force and the elastic force determines both the magnitude and direction of the net resultant force acting on the teeth.

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Consideration of the magnitude of intrusive force

Optimum intrusive force:ᵿ Many authors have suggested optimum intrusive force values

ranging from 15-30 g per upper incisor and slightly higher values for upper canines.

ᵿ Begg did not specify the precise force values in the Begg bite opening mechanics.

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ᵿ Later, Kesling (1985) stated that the upper and lower bite opening bends generate intrusive forces of approximately 1.5 oz and 1.2 oz magnitude respectively at the upper and lower midlines.

ᵿ The extrusive component of the light Cl. II elastics on the upper incisors is approximately 1 oz.

ᵿ Hence the net intrusive force on the upper incisors is approximately 0.5 oz.

26 sep '12 36

Role of light Class II elasticsᵿ A net intrusive force of 60 gm can be obtained by a

combination of 75 gm intrusive force , as follows :ᵿ Jayade-By using light elastic force for longer periods (from 2

to 5 days), a very light Cl. II force is provided most of the time, since the elastic force diminishes rapidly in the oral environment. Such very low force values do not adversely affect concomitant retraction, because forces in the vicinity of 5 gm are known to be capable of achieving tipping movements.

ᵿ Sims has suggested the use of 3/8 ultra light elastics (e.g., “road-runner elastics” of M/s. Ormco) instead of the routinely used 5/16 light elastics (e.g. T.P. yellow elastics). He goes to the extent of continuing the same elastics for 4-5 days, till they break.

26 sep '12 37

Consideration of the direction of the resultant force

ᵿ Hocevar- teeth respond only to the resultant of the forces, and not to the individual components of the force system.

ᵿ The anterior teeth would respond to a resultant of the wire generated intrusive force and the elastic generated retractive force.

ᵿ This resultant force should ideally pass through the center of resistance of the upper incisors (which is very difficult to achieve), or at least should lie very close to and directed as much parallel to the long axis of the teeth as possible.

26 sep '12 38

The direction and the magnitude of the resultant force both depend upon the interplay between

1. The magnitude of the intrusive force – its direction being almost constant i.e. tangential to the arc which the anterior segment of the archwire would subscribe if released from the brackets.

2. The magnitude and direction both of the elastic force.

26 sep '12 39

ᵿ in case of severely proclined upper anteriors a low magnitude of intrusive force along with light class II force would give a desired resultant force, passing palatal to Cres, this will help correcting the proclination of incisors .

ᵿ Once the inclination of upper incisors is corrected then the class II elastics force is reduced helping in keeping the resultant force close to Cres .

45gms

60gms

60 gms

30gms26 sep '12 40

ᵿ In Class II Division 2 cases , where the upper centrals are retroclined , only intrusive force should be used (Avoiding the Class II elastics) The intrusive force acts labial to Cres and corrects the retroclination. Once the inclination is corrected then we can use Class II elastics .

50gms

40gms

20gms26 sep '12 41

ᵿ Modifying the force system to achieve simultaneous intrusion and retraction using Class I elastic instead of Class II elastics was first illustrated by Shin Yang Liu (1981).

In this arrangement the vectors are in the same direction as the elastic pull and the archwire force are unidirectional and hence synergistic

26 sep '12 42

Arch wire design

VARIOUS TYPES OF BITE OPENING BENDS: The Anchor bend the conventional bite opening bend causes

more intrusion of canines while the lateral and central incisors progressively lag behind.

A Gable bend causes a progressively more intrusion of central and lateral incisor, as compared to canine

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Swain modification: Mild gingival curve is incorporated in the anterior section, from mesial of cuspid to mesial of other side cuspid.

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Mechanics of tipping

ᵿ Reitan. -Generally, uncontrolled tipping is undesirable because it leads to root resorption.There is more resorption when uncontrolled tipping is in labio-lingual direction.

ᵿ Intrusion and tipping are intimately related not only because they are carried out simultaneously but also, when both are balanced judiciously it help in overcoming uncontrolled tipping of incisors.

26 sep '12 45

ᵿ This is achieved by manipulating the intrusive force generated by wire and retractive component of force from the Class II elastics.

ᵿ Both the anchor bend in the wire and class ii elastics produce moments in the same labio-lingual plane but act in opposite directions.

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THE INTERPLAY BETWEEN THE ANCHOR BEND AND CLASS II ELASTICS

CLASS II ELASTIC FORCE

INT

RU

SIO

N F

OR

C

26 sep '12 47

ᵿ The intrusive force produces crown labial-root lingual moment e.g.. anticlockwise moment on the upper anteriors.

ᵿ While the retractive force produced the Class II elastics generates clockwise moment e.g. crown lingual-root labial moment

The moment from the intrusive force can act as the counter balance moment against the moment produced by the elastic force.

The ratio of the former to the retraction component of the elastic force is the M/F ratio which governs the type of tipping while retracting the anterior teeth.

26 sep '12 48

ᵿ The most important consideration is to keep light Class II elastic and use adequate amount of intrusive force so that correct M/F ratio (8:1) is obtained to have a controlled tipping.

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PREVENTING UNCONTROLLED TIPPING OF

LOWER INCISORS The flaring can be avoided by two means;

1. Minimizing the clockwise force moment by reducing the intrusive force or by placing the brakets much gingivally.

2. Secondly, cinching tightly the distal ends of the arch wire.

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ᵿ In case of severely lingually tipped lower anteriors, Cres will be lying buccal to the point of application of the intrusive force generated by the anchor bend so there is more chances to tip the lower anteriors more lingually.

ᵿ So in that case we give a By pass arch wire in order to upright the lower incisors .26 sep '12 52

26 sep '12 53

BEGG STAGE II

The sole or main purpose of II stage is closure of extraction spaces.

ᵿ The extraction space can be closed by either retraction of the anteriors or protraction of the posteriors or combination of both.

During Stage II all the corrections achieved during Stage I should be maintained

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Maintain Edge to Edge relationship of anterior teeth:

Reduce the anchor bend in arch wire and wear intermaxillary elastics as required

Maintain anterior space closure :

To give cuspid ties either by elastomeric rings or steel ligatures.

To maintain overcorrected or normal mesiodistal molar relationship :

Keep wearing of intermaxillary elastics as required during posterior space closure.

26 sep '12 55

BIOMECHANICS OF STAGE II

ᵿ The anchor bend should be sufficient as to produce a counter clockwise moment greater than the clockwise moment produced by the Class I and Class II elastics in upper arch.

ᵿ The M/F ratio should be sufficient or around 8/1 so as to have a controlled tipping movement.

If anticlockwise moment is less than clockwise moment produce by Class I and Class II elastics on upper anterior, then M / F ratio will less and it will uncontrolled tipping of upper anterior teeth.

26 sep '12 56

“Class I Elastic” Forces

CLASS I ELASTIC FORCE

INT

RU

SIO

N F

OR

C

At the end of Stage II26 sep '12 57

ᵿ in lower arch the clockwise moment should be greater than anticlockwise moment produced by Class I elastics. So as to have controlled tipping movement

ᵿ Normally 0.016 upper and lower arch wires with reduced bite opening bends are used.

ᵿ Some authors say use of heavy arch wire 0.020” as it will function as retainers to maintain arch form and bite opening achieved during stage I.

26 sep '12 58

ᵿ Dr. Swain advocated the use of lingual attachments on molars and cuspids to allow the use of lingual space closing elastics to aid the traditionally used buccal vector of intra maxillary elastic force during stage II known as half strength elastics.

Two distinct advantages It gives a better positional control over the anchor molar thus

obviating the need for a mandatory compensate toe in bend when using elastic force only from buccal side.

Closure of extraction spaces becomes easier.

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BRAKING MECHANICSᵿ When further retraction of anterior teeth into the remaining

extraction space is deemed undesirable clinically , then the posterior teeth are brought forward, that is posterior teeth are mesialized.

ᵿ Mostly in extraction of 5’s cases

ᵿ To achieve mesialization of posterior teeth heavy elastic forces are required with concurrent use of brakes in the anterior region.

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ᵿ The brakes- reverse the anchorage site- from posterior to anterior segment

ᵿ Permitting only the bodily movement of anterior teeth, instead of allowing them the freedom of tipping

ᵿ the direction of resultant force should pass through the center of resistance of anterior teeth (or close to it).

ᵿ Therefore, substituting Class II elastic forces by Class I elastic forces would orient the resultant force more vertically passing nearer to the center of resistance of anterior teeth.

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Various brakes are: Breaking springs (passive uprighting springs) Reverse torque to incisor roots (Udder arch and MAA) Using Angulated-T pins

Passive Uprighting Springs

UDDER ARCH

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Stage III BEGG

ᵿ The third stage of Begg treatment involves predominantly root movements in a labiolingual or mesiodistal direction.

ᵿ A doubt is expressed by some edgewise operators as to how it is possible to obtain a high M/F ratio required for the root movements using the Begg torquing auxiliary and uprighting springs.

ᵿ However, a careful scrutiny of the forces generated by the torquing auxiliary and the uprighting springs in relation to the light Cl.II elastic force will help in dispelling this apprehension.

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Objectives of stage III

1.Maintaining all the corrections achieved during first and second stages.

2.Achieve desired axial inclinations of all the teeth.

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Stage III arch-wire

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1. Maintaining all the corrections achieved during stages I & II.

Mesiodistal molar relationship maintained through the wearing of class II or class III elastics as required.

Original spaces between anterior teeth are prevented from recurring by tying intermaxillry circles to the cuspid brackets with steel ligature wire.

Over corrections of cuspids are maintained by engaging the brackets which have been offset on the teeth.

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Over corrections of bicuspids are held by replacing elastic threads with steel ligature ties.

Over corrections of central and lateral incisors are maintained through the continued use of bayonet bends in the arch wires.

Opening of a deep anterior overbite is maintained through the continued use of bite-opening bends and class II or class III elastics.

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The correction of posterior crossbites is maintained by modifying the archwire or by wearing of cross elastics as necessary.

Posterior spaces kept closed by bending the distal ends of the arch wire around the buccal tubes.

Arch form and overbite correction maintained by using heavier (0.018 to 0.025) main archwire.

26 sep '12 69

2. Achieve desired axial inclinations of the teeth.

Changes in the mesiodistal inclinations of teeth are accomplished by the use of individual root-tipping springs.

Lingual or labial root torque is applied to anterior teeth through the application of torqueing auxilaries.

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Auxiliaries used during stage III

The two main auxiliaries:ᵿ Individual Root Springs or Mesio distal uprighting Springs.ᵿ Torqueing auxiliaries.

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Torqueing Auxiliaries

ᵿ To torque roots of the maxillary anterior teeth lingually.

ᵿ Torqueing is nearly always necessary (especially with upper incisors) in mild discrepancy cases that require extraction of the four first premolars i,e in cases having only a mild excess of tooth substance relative to jaw size.

ᵿ This is because crowns of the incisors tipped back a long way lingually to close the extraction spaces.

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Spring - Pin

ᵿ A problem inherent in all uprighting springs is that, when engaged and under tension, the coil presses against the gingival edge of the beacket.

ᵿ If arch wire is not safely tied into the slot of the bracket, this force from the coils can cause the bracket to move away from the arch wire, with a subsequent elongation of the tooth.

26 sep '12 73

ᵿ As a solution to this problem authors have invented, Spring Pin.

ᵿ A Combination of a Lock Pin and an Uprighting Spring.ᵿ The leg of the pin portion passes lingual to the arch wire and

the tail fits labial to it in the space in the bracket that normaly accepts the lock pin.

26 sep '12 74

Mechanics of stage III

ᵿ The torquing auxiliary - labio-lingual root movements and ᵿ the uprighting springs - mesiodistal root movement generate

…..reciprocal reaction in all the three planes of space which when not properly controlled, result in complication:

1. The lingual root-torquing auxiliary also tends to cause labial crown movements, extrusion of the anteriors and intrusion of posteriors, and buccal crown movement of posteriors.

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2. The labial root torquing auxiliary will have effect in opposite direction. ᵿ The uprighting springs for distal root movement also have

similar effects as the lingual root-torquing auxiliary in all the three directions. The vertical and sagittal reactions are easily appreciated.

ᵿ Reactions in the transverse direction arise because of the vertical forces acting away from the centre of resistance of posterior teeth.

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ᵿ The sagittal forces are easily appreciated.

ᵿ The uprighting springs on the anterior teeth for distal root movement and the torquing auxiliary for palatal root torque, both have an extrusive effect on the anteriors and an intrusive effect on the molars.

ᵿ The intrusive effect on the molars is responsible for a transverse buccal rolling action on the molars. Such undesired reactions should be carefully monitored and neutralized.

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ᵿ The reciprocal mesial crown moving forces are commonly reisted by:

1. Cinching the distal ends of archwires

2. Class II elastics

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Forces generated (in grams) by the commonly used four spur and two spur torquing auxiliaries with 5 mm spur

length. Wire Horizontal Vertical

Lateral Ce

ntr

al

010 14 18 11

4 Spurs 012 26 30 19

014 48 53 23

016 96 103 77

010 22 14

2 Spurs 012 42 28

014 64 28

016 112 78

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ᵿ The auxiliary commonly used is the one made in 0.012 premium plus wire.

ᵿ Although the forces produced by this auxiliary are low, the moments generated by these forces are sufficient because the moment arm is much greater in a torquing auxiliary than in a rectangular archwire twisted for torquing effect.

26 sep '12 80

The forces generated by the uprighting springs made from

different wires Activation 75o 60o 45o 25o

Minispring 142.5 97.5 72.5 < 37.5

0.000 (s) 137.5 82.5 52.5 < 37.5

0.010 (s) 157.5 97.5 57.5 < 37.5

0.012 (s) 282.5 162.5 112.5 57.5

0.012 (p) 257.5 157.5 107.5 57.5

0.014 (sp+) 387.5 297.5 197.5 97.5

0.016 (p) 437.5 307.5 207.5 107.5

Spring pin 787.5 637.5 487.5 287.5

26 sep '12 81

ᵿ As Nikolai has pointed out, greater moments are required for the mesio-distal root movements than for the bucco-lingual root movements, since holding force for the former is greater due to the mesio-distal crown contact.

ᵿ Thus the forces produced by the torquing auxiliary are smaller than the forces generated by the uprighting springs for the same individual teeth.

26 sep '12 82

Some other torquing auxiliary design

ᵿ Single root torquing auxiliary proposed by Keslingᵿ Reciprocal torquing auxiliary (SPEC) designᵿ Reverse torquing auxiliary for controlling the roots of canines

or premolars ᵿ Buccal root torque on molars ᵿ Labial root torque only on lateral incisor

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Conclusion ᵿ A common misconception is that the application of

biomechanical properties would make the begg technique too cumbersome. On the contrary, biomechanically designed appliance gives a predictable tooth movement, optimal biologic tissue response and minimal side effects.

ᵿ In the lighthearted note - One can say that on the average, an orthodontist spends half the treatment time on problems presented by the patient and other half on problems resulting from treatment side effects

ᵿ Orthodontics could be in our hand if we use efficient biomechanics

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ᵿ Vijay P.Jayade. Refined Begg for modern times.ᵿ Nanda Ravindra. Biomechanics in clinical orthodontics.Philadelphia: W.B

Saunders Company ;1997 ᵿ Begg, P. R.: Begg orthodontic theory and technique, Philadelphia, 1965, W.

B. Saunders Company.ᵿ Swain, B. F., and Ackerman, J. L.: An evaluation of the Begg technique,

AM. J. ORTHOD. 55: 668-687, 1969.ᵿ Hocevar RA: Orthodontic force systems: Technical refinements for

increased efficiency. AM J ORTHOD 81: 1-11, 1982.ᵿ Hocevar RA: Understanding, planning, and managing tooth movement:

Orthodontic force system theory. AM J ORTHOD 80: 457-477, 1981.ᵿ Reitan K: Tissue behavior during orthodontic tooth movement. AM J

ORTHOD 46: 881-900, 1960.

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References