BIOMECHANICS OF TOOTH MOVEMENT

CONTENTS

Introduction

What is Biomechanics  Center of gravity  Center of resistance  Center of rotation Various Terminologies and laws FORCE MOMENT COUPLE MOMENT TO FORCE RATIO STATEOF EQUILIBRIUM 

Begg Mechanotherapy  INTRODUCTION  Objectives of Stage-I Biomechanics of incisor intrusion Degree of anchor bend Role of Class II elastics 

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o

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Biomechanics of Incisor Tipping  Objectives of Stage-II Biomechanics of space closure  Conclusion  Bibliography www.indiandentalacademy.com

The literature on orthodontic biomechanics usually concerns either specific applications of interest to clinicians or basic questions primarily of interest to researchers. Few articles have attempted to explain biomechanical principles by an approach that would allow the clinician without a background in engineering to understand the concepts and their potential for clinical relevance. In this article, we attempt to review for the clinician the basic relationships between forces and tooth movement.

BIOMECHANICS

Biomechanics is the study of mechanics as it affects the biologic systems. It is the application of mechanics to the biology of tooth movement. Biology + Mechanics = 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.

VECTORS include force, these have both magnitude and direction. In case of force, along with magnitude and direction, point of application must be taken into account.

Various terminologies and laws: FORCE MOMENT COUPLE MOMENT TO FORCE RATIO

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.

The forces are indicated by straight arrows

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

CENTER OF MASS Each body has a point in its mass, which behaves as if the whole mass is concentrated at that single point, which we call the CENTER OF MASS in a gravity free environment.

Center of Gravity: The same is called center of Gravity in an environment where gravity is present.

The center of gravity of the tooth is located more towards the crown of the tooth as the mass of the tooth is concentrated more coronally

Since the tooth is partially restrained as its root is embedded in bone its center of gravity moves apically and this is known as CENTER OF RESISTANCE (Cres)

Center of Resistance

Center of Resistance Center of Gravity

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In case of single rooted tooth center of resistance is on the long axis of tooth between one third and one half of the root length apical to alveolar crest.

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For a multirooted root, the center of resistance is probably between the roots 1-2 mm apical to furcation.

Center of Resistance Varies (Cres): Length of root: Maxillary canine have long root than maxillary lateral incisor. Thus center of resistance of canine will be more apically placed as compared with center of resistance of lateral incisor. Alveolar bone height: Center of resistance shifts apically as with the alveolar bone loss.

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Periodontal status: The center of resistance shifts apically in periodontally compromised patients. Size and shape of the crown and root.

The center of resistance for a single rooted tooth estimated by different authors as; At 50% of root length – Proffit, Nikoli  Between 50% to 30% of root length – Smith and Burstone.  At 33% of root length – Burstone  Between 25% to 33% root length – Nanda 

Moment Is defined as a tendency to rotate

Moments can be symbolized by curved arrows.

MOMENT is the product of the force times the perpendicular distance from the point of force application to the center of resistance. M=Fxd It is measured in grams â&#x20AC;&#x201C; millimeters.

F x d(X) = M(X)

F

MOMENT OF FORCE: Moment is a measure of the turning tendency produced by a 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. www.indiandentalacademy.com

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.

A MOMENT may be referred as Rotation Tipping Torquing.

Rotation  Tipping  Torquing 

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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 www.indiandentalacademy.com x d(X) = M(X)

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. www.indiandentalacademy.com

Center of Rotation

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 MOVEMENT

TOOTH

POSITION OF THE CENTER OF ROTATION

A.

Translation

Lies at infinity

B.

Uncontrolled tipping

Slightly apical to center of resistance

C.

Controlled tipping

Apex of root

D.

Root movement or Torquing

Incisal or occlusal edge

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Uncontrolled tipping: 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. This is referred as uncontrolled tipping.

Uncontrolled tipping

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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.

Controlled tipping

ď&#x192;&#x2DC; Translation

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

Bodily Movement

Center of Rotation at infinity

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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.

Root Movement

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.

If the two forces of the couple act on opposite sides of the center of resistance, their effect is additive. However, if they are on the same side of the center of resistance, their effect is subtractive

F2

d

+ F1

M1= F1Xd

M2=F2Xd

F1 F2

D1

-

D2

M1=F1XD1

M2=F2XD2

M= F X (D1-D2) Subtractive www.indiandentalacademy.com

DIFFERENCE BETWEEN THE MOMENT OF A FORCE AND MOMENT OF COUPLE:

Moment is a measure of the turning tendency produced by a force. ď&#x192;&#x2DC; 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 and high for a point (point of application) with a large perpendicular distance to line of action. ď&#x192;&#x2DC; In case of Couple moment, it is not relative to any point. www.indiandentalacademy.com

MOMENT TO FORCE RATIO:

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 counterbalancing moment is always going to be in the direction opposite the moment of force.

Counter-balancing moment

Moment of force

Force

The ratio of the counter-balancing moment to the force applied determines the type of tooth displacement, brought about by the combined application of a force and counter-balancing moment. As the counter-balancing moment increases, the center of rotation moves apically. www.indiandentalacademy.com

At one specific level of M/F the moment which arises from the force and the applied counter-balancing moment cancel out each other i.e. there is no rotational component, and hence only a translation takes place under the effect of force .

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M/F Ratio values normally quoted of various types of displacements are M/F ratio less than 5:1 causes uncontrolled tipping in which the crown and the root apex move in opposite directions. M/F ratio between 5:1 and 8:1 causes controlled tipping in which the root apex remains stationary and only the crown moves. www.indiandentalacademy.com

M/F ratio of 10:1 causes translation. The crown and the root apex move to same extent in the same direction of force. M/F ratio of 12:1 causes root movement. The crown remains stationary while only the root moves.

It is important to note that the differences between the M/F Raito for controlled tipping, translation and root movement are small. In other words, even small alterations in the magnitude of the applied force or the counter-balancing moment will alter the type of tooth movement brought about. www.indiandentalacademy.com

STATE OF EQUILIBRIUM

When an appliance is fitted in the mouth, it assumes a state of equilibrium. The active elements in the appliance generate certain forces or moments. 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.

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. 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. www.indiandentalacademy.com

BEGG MECHANOTHERAPY

Begg mechanotherapy is very efficient in opening the deep anterior overbites. It is generally agreed that Begg mechanics bring about bite opening by a combination of molar extrusion (especially of lower molars) and some intrusion of lower anteriors. Upper anteriors may not change in their position in vertical direction (i.e. they are prevented from erupting) or may intrude slightly or may even extrude slightly. www.indiandentalacademy.com

There are three basic movements in the Begg mechanotherapy Incisor intrusion  Tipping of teeth  Root uprighting. 

The mechanism of intrusion is understood by considering the net intrusive force magnitude and direction. While tipping of teeth and root uprighting is explained on the basic of M/F ratio.

OBJECTIVES OF STAGE I:

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. ď&#x192;&#x2DC; Eliminate anterior crowding : Vertical loops between crowded anterior teeth, with bracket areas modified for desired overcorrection. ď&#x192;&#x2DC;

Close anterior spaces : Plain arch wire with latex elastic or elastomeric chain from cuspid to cuspid. ď&#x192;&#x2DC; Over correct rotated cuspids and bicuspids : Rotating springs Elastomeric traction into the arch wire ď&#x192;&#x2DC;

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. ď&#x192;&#x2DC;

BIOMECHANICS OF STAGE I

As we understand today the Begg appliance is a good example of single couple system. Stage I arch wire

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

MECHANISM OF INTRUSION:

Lack of true intrusion of the maxillary incisors was one of the major weaknesses of traditional Begg. Bite opening occurred mainly on account of molar extrusion and some intrusion of the lower incisors.

Stage I arch-wire

Whether the upper incisors intruded is a debated issue. The round archwire derives bite opening force from the anchor bends.

A anticlockwise moment generated by the anchor bend in the molar tube (upper) is automatically balanced by the generation of clockwise moment in the anterior segment along with intrusive force on the anterior and extrusive force on the molars in order to establish state of equilibrium. www.indiandentalacademy.com

This flaring tendency of upper incisors can be resisted by using Class II elastics during stage I. But class II force along with horizontal component have vertical component of force which reduces the magnitude of the intrusive force of the arch wire on the upper anteriors.

vertical problem

Thus the interplay between the intrusive force from the archwire and the retractive force from the elastics determines both the magnitude and direction of the net resultant force acting on anterior teeth.

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.

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A Gable bend causes a progressively more intrusion of central and lateral incisor, as compared to canine Mollenhouer’s bite opening curve – Mollenhouers especially recommends it with use of 0.018 wire.

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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.

CONSIDERATION OF THE MAGNITUDE OF INTRUSIVE FORCE.

OPTIMAL INTRUSIVE FORCE VALUE:

Many authors have suggested optimum intrusive force values ranging from 15-30 grams per upper incisor and slightly higher values for upper canines.

For active intrusion the upper anteriors should receive approximately 60 grams net force in the midline, after negating the extrusive component of Class II elastics.

ROLE OF LIGHT CLASS II ELASTICS:

Hocevar stated that 120 grams of archwire generated intrusive force in conjunction with 60 grams of Class II elastics pull on either side is â&#x20AC;&#x153;efficient for intrusionâ&#x20AC;?

According to Dr.Jayade net intrusive force of 60 grams can be obtained by a combination of 75 grams of intrusive force generated by arch wire and some modification in wearing of elastics that is by using light elastic forces for longer periods from 2-5 days. Very light Class II force is delivered as the elastic force diminishes rapidly in oral environment. www.indiandentalacademy.com

Sims states the use of 3/8â&#x20AC;? ultra light elastics instead of routinely used 5/10â&#x20AC;? light elastics. He said continue the same elastic for 4-5 days till they break.

Role of Class I Elastic Forces

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).

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In pure begg technique the direction of the intrusive vector of the maxillary arch wire and the extrusive vector of the class II elastics are opposite . This accounts for the difficulty in obtaining anterior maxillary teeth intrusion.

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In this technique modification, of using Class I elastics , it solve the problem of lack of intrusion of the maxillary anteriors.

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

Dr. Jyothindra Kumar introduced concept of power arms as a point of attachment high up in the vestibule for the engagement of Class I elastics.

CLA SS IE

LAS TI

CF ORC E

Dr. Jayade has been using Class I elastics, which were worn from transpalatal arch (TPA) to the canine hooks/loops.

CLA SS IE

LAS TI

CF ORC E

It is impossible to precisely calculate the required intrusive force every time, for every patient, since it is dependent on various variables. ď&#x192;&#x2DC; Different root sizes and tooth inclination. Different arch sizes, which affect the length of the wire spans and stretch of the elastics.

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Individual biomechanical response

Difference in the archwire sizes. Normally .018” wire will produce more intrusive force as compared to 0.016” wire when some degree of anchor bend is given. 

THE CONCLUSION IS, “TO USE HIGHER INTRUSIVE FORCES IN COMBINATION WITH VERY LIGHT CLASS II ELASTIC FORCES FOR ACTIVE UPPER INCISOR INTRUSION”

CONSIDERATION OF THE DIRECTION OF THE RESULTANT FORCE:

Teeth respond only to the resultant of the forces which are applied and not to the individual components of the force system.

During Stage I, the upper anteriors are subjected to two forces i.e. the retractive force of class II elastics and the intrusive force generated by the anchor bend in the arch wire. The resultant of these two will determine how the upper anterior teeth respond to the intrusion.

THE INTERPLAY BETWEEN THE ANCHOR BEND AND CLASS II ELASTICS

INTRUSION FORC

IC T S LA

E C R FO

IE I SS A L Cwww.indiandentalacademy.com

The direction and magnitude of resultant force both depend upon the interplay between. ď&#x192;&#x2DC; Magnitude of Intrusive Force: Whose direction remains constant i.e. tangential to the arc that the anterior segment of the archwire would subscribe, if released from the brackets. ď&#x192;&#x2DC; Magnitude and the direction of the elastic force. www.indiandentalacademy.com

Different inclinations of the anterior teeth would require different combinations on of the intrusive and elastic forces. Hocevar states, that the teeth are not affected by the magnitudes of various components of force systems, they experience only the total resultant force www.indiandentalacademy.com

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

60 gms

45gms

30gms

60gms

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 .

40gms 50gms

20gms

MECHANICS OF BEGG TIPPING:

The concept of tipping back the teeth in the first stage & further in stage II â&#x20AC;Ś

INTRUSION FORC

ST A L II E

IC

RC O F

E

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

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.

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

BOTH THE ANCHOR BEND IN THE WIRE AND CLASS II ELASTICS PRODUCE MOMENTS IN THE SAME LABIO-LINGUAL PLANE BUT ACT IN OPPOSITE DIRECTIONS.

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

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.

PREVENTING UNCONTROLLED TIPPING OF UPPER INCISORS

In the refined Begg mechanics, use of MAA which provides a moment in the labio-lingual plane by creating a couple. This couple moment is an anti-clockwise moment.

SS A CL

TIC S LA E II

F

CE R O

Once the bite is opened in the first stage, the intrusive force level is reduced which inturn reduces M/F ratio. This leads to greater likelihood of uncontrolled tipping of upper anterior teeth during later part of the first stage and whole of second stage. Thus the anticlockwise moment produced by anchor bend on anterior is supplemented by with the moment of couple produced by MAA www.indiandentalacademy.com

Flaring occurs as lower incisors are subjected to crown labial root-lingual moment from the intrusive force generated in arch wire, while there is no restraining force on these teeth as similar to Class II elastic force on Upper incisors.

PREVENTING UNCONTROLLED TIPPING OF LOWER INCISORS:

The flaring can be avoided by two means; Minimizing the clockwise force moment by reducing the intrusive force. Secondly, cinching tightly the distal ends of the arch wire. ď&#x192;&#x2DC;

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Lastly by producing counter moment using a MAA for labial root torque or a reverse torquing auxiliary (Udder arch)

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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.

So in that case we give a By pass arch wire in order to upright the lower incisors .

BEGG STAGE II

Amongest the traditionally described stages of Begg technique, the second stage of treatment involves closure of extraction spaces. This is thought to be the easiest phase of treatment

During Stage II all the corrections achieved during Stage I should be maintained. ď&#x192;&#x2DC;

Maintain Edge to Edge relationship of anterior teeth: Reduce the anchor bend in arch wire and wear intermaxillary elastics as required .

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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. www.indiandentalacademy.com

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In addition to the above, the stage II of the refined Begg aims are Controlled tipping of the incisors, when space closure is to be mainly achieved by the anterior retraction.

OBJECTIVES OF STAGE II:

When all the objectives of Stage I are met stage II mechanics can be instituted. The sole or main purpose of II stage is closure of extraction spaces.

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

BIOMECHANICS OF STAGE II

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.

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.

Class I Elastic Forces

INTRUSION FORC

CLASS I ELASTIC FORCE

At the end of Stage II www.indiandentalacademy.com

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

Normally 0.016 upper and lower arch wires with reduced bite opening bends are used. Some authors say use of heavy arch wire 0.020â&#x20AC;? as it will function as retainers to maintain arch form and bite opening achieved during stage I.

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 in using intra maxillary (Half strength) space closing elastics ď&#x192;&#x2DC; 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. ď&#x192;&#x2DC; Closure of extraction spaces becomes easier. www.indiandentalacademy.com

USE OF BRAKING MECHANICS

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.

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

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

Passive Uprighting Springs

UDDER ARCH

T PINS

The brakes reverse the anchorage site from the posterior to anterior segment by allowing bodily movement rather than the tipping of anterior teeth, this bodily movement provides more resistance hence acting as a anchorage.

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He summarized that the direction of resultant force should pass through the center of resistance of anterior teeth (or close to it). ď&#x192;&#x2DC; 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. www.indiandentalacademy.com

Stage I arch-wire