University of Glasgow

Biomechanics in Orthodontics

Dr. Mohammed Almuzian

1/1/2013

Biomechanics in Orthodontics

Physical variables

Movement of teeth in orthodontic treatment requires application of forces and periodontal tissue response to

these forces. So to understand the biomechanics of orthodontics we need to understand physical and

biological responses to orthodontic tooth movement. Therefore it is essential to know Newton's Laws by

Isaac Newton's (1642-1727):

1. The law of inertia The law of inertia analyzes the static balance of objects. Every body in a state of

rest or uniform motion in a straight line will continue in the same state unless it is compelled to change by

the forces applied to it.

2. The law of acceleration The law of acceleration states that the change in motion is proportional to the

motive force that is applied. Ac-celeration occurs in the direction of the straight line in which the force is

applied: a= F/m, where a= acceler-ation, F= force, and m = mass.

3. The law of action and reaction The reaction of two objects toward each other is always equal and in

an opposite direction. Therefore, to every action there is always an equal and opposite reaction

Terminology

It is important the orthodontist understands the meanings of terms such as: (Smith and Burstone 1984)

1. Vector: change in the position of point from one place to other.

2. Force: is the effect that causes an object in space to change its place or its shape. It is also defined as

vector that has specific direction, duration and distribution

3. Resultants:  The resultant force is the name given to the single force representative of the two or more

vector forces acting on the tooth/teeth (this called force composition). Two component forces with a common

point of application (Smith and Burstone 1984)

Consider the two component forces to be the sides of a

parallelogram (black)

Complete the parallelogram using the dashed lines (blue)

The resultant force is the diagonal of the parallelogram (red)

The sum of multiple vectors is calculated in the same system as the calculation of two vectors.

Therefore, the third vector is added to the resultant of the first two vec-tors, and so on

4. Component: it refers to force resolution and it is the reverse of force composition, so rather than

combining two or more forces to produce a resultant force, a single force is broken up into its individual

component forces at right angles to each other, by reversing the parallelogram procedure

5. Forces or magnitude: Forces are normally expressed in units of Newtons (N) but in orthodontics they

are more commonly expressed in grams (g). The conversion factor for grams to Newtons is: 1g = 0.00981 N

1 N = 101.937 grams.

6. Center of Rotation: The center of rotation is the point around which the tooth rotates. The location of

this point is dependent on the M/F ratio. So it is not fixed point as the centre of resistance. When a couple of

force is applied on the tooth, this point is superimposed on the center of resistance (ie, the tooth rotates

around its center of resistance). In translation it becomes infinite, meaning there is no rotation.

7. Centre of resistance: The point where the line of action of the resultant force vector intersects the long

axis of the tooth, causing translation of the tooth, is defined as the center of resistance. The center of

resistance is sometimes confused with the center of mass. The center of mass is a balance point of a free

object in space under the effect of gravity. A tooth, however, is a restrained object within the periodontal and

bony structures surrounded by muscle forces. Therefore, the center of resistance must be considered a

balance point of restrained objects. The center of resistance is unique for every tooth; the location of this

point depends on the number of roots, the level of the alveolar bone crest, and the length and morphology of

the roots. Therefore, the center of resistance sometimes changes with root resorption or loss of alveolar

support because of periodontal disease. For example, in the case of loss of alveolar support, this point moves

apically."

8. Moments: Moment is the tendency for a force to produce rotation or tipping of a tooth. It is

determined by multiplying the magnitude of the force (F) by the perpendicular distance (d) from the center of

resistance to the line of action of this force: M=F x D. If single forces are applied to the crowns of teeth, it

therefore acts at a distance from the centre of resistance, producing a large moment and tooth tipping. Tooth

tipping can be overcome by applying a counter-moment, equal in magnitude and opposite in direction to the

original moment, through the use of auxiliary springs or the interaction of a rectangular archwire in a

rectangular bracket slot. Bodily tooth movement requires both a force to move the tooth in the desired

direction, and counterbalancing moments to produce the necessary counterbalancing effect that rotational

effect of the resultant moments. The heavier the force, the larger the counterbalancing moment must be to

prevent tipping and vice-versa. Additionally, increasing the magnitude of the force or the perpendicular

distance from the point of force application to the centre of resistance will increase the moment or tendency

for rotation. On the other hand the shorter the moment arm, the smaller the moment of a force and therefore

the less tipping/rotation movement and greater translation.so that removable appliance that apply very incisal

forces has more tendency to rotate teeth than lingual orthodontic forces which are closer to centre of rotation.

9. Couple: A couple is a system having two parallel forces of equal magnitude acting in opposite

directions. Every point of a body to which a couple is applied is under a rotational effect in the same

direction and magnitude. No matter where the couple is applied, the object rotates about its center of

resistance.

10. Couple moment: The calculation of the moment of a couple can be performed by multiplying the

magnitude of one of the forces by the perpendicular distance between the lines of action.

11. Centre of resistance: The centre of resistance is the point in a body at which resistance to movement

can be considered concentrated, for mathematical analysis. The centre of resistance is determined by:

o The mass,

o Shape

o Form,

o The characteristics of the supporting structures, the bone and the periodontal ligament

(Pryputniewicz and Burstone 1979). The greater the loss in periodontal support, as seen in patients with

periodontal disease, the more apically positioned the centre of resistance becomes (Melsen 1988).

The location of the centre of resistance of a single rooted tooth is at the approximate midpoint of the

embedded portion of the root on its long axis i.e. about half way between the root apex and the crest of the

alveolar bone (Burstone and Pryputniewicz 1980). For a multi-rooted tooth, the centre of resistance is

estimated to be at the furcation area or 1-2 mm apical to the furcation, assuming that the periodontal support

is intact (Burstone et al. 1981)

12. Centre of rotation: defined as a point about which a body appears to have rotated, as determined from

its initial and final positions. The centre of rotation can however be positioned at variable points on or off the

body and in orthodontics this is controlled by varying the moment to force ratio at the bracket/archwire

interface.

13. Friction that exists before one of the objects starts to move is called static frictional force. Static

friction is the amount of force necessary to start movement of an object in a static state.

14. Kinetic friction (or dynamic friction) is the friction that exists during the movement of the object, and

it is the amount of force that the object must overcome to continue moving. Theoretically, kinetic friction has

lower values than static friction.

Forces related variables

Orthodontic forces and movement depends on a variety of factors including:

1. Magnitude

Magnitude and optimal force: Quinn and Yoshikawa (1985) reviewed 4 hypotheses:

Theory (A) - once the magnitude of force exceeds the minimum force threshold required for tooth

movement a fixed rate of tooth movement is observed and increasing the magnitude of force further does not

increase the rate of tooth movement. This theory is supported by evidence from studies by Owman-Moll et

al. (1996) and Iwasaki et al. (2000).

Theory (B) - once the magnitude of force exceeds the minimum force threshold required for tooth

movement the rate of tooth movement increases linearly with force magnitude. Studies supporting this theory

include those by Andreasen and Johnson (1967).

Theory (C) - once the force magnitude exceeds the minimum force threshold the rate of tooth

movement increases with force magnitude up to a point, after which the rate plateaus and then decreases or

ceases as the force levels continue to increase. There is therefore an optimal force for maximal tooth

movement. Lee (1995) has published evidence supporting this theory.

Theory (D) - the rate of tooth movement increases linearly with force up to a point where the

response is constant despite further increases in force magnitude. This theory is support by evidence put

forward by Boester and Johnston (1974) and King et al. (1991) and Samuel studies (1998) (The strongest

theory)

More recently, Ren et al. (2003) systematically reviewed the literature concerning the optimal force or range

of forces for orthodontic tooth movement. They found that there was neither universal consensus nor sound

scientific evidence regarding specific numeric values of optimal force magnitude.

Ren et al. (2004) again stated that the rate of tooth movement increases linearly with force and then a small

plateau is reached representing the optimum force magnitude to obtain the maximum rate of tooth movement.

Then increasing the force beyond that would cease the movement. Similar to theory D but in a form of a

curve.

Optimal forces are those that result in minimal discomfort, mobility and lag period. Rate of tooth movement is not a good indicator as heavy forces can result in rapid tooth movement.

Time (days)

Toot

h m

ovem

ent (

mm

)

1

2

7 14 21

light force

heavy force

The reasons for a high tendency of tooth movement in children (Mitchell 2001)

o Physiological tooth movement is greatest.

o The periodontal ligament is more cellular.

o The alveolar bone has a greater proportion of osteoclasts

o The cellular response is quicker

o The width of the periodontal ligament is increased in newly erupted teeth, and so a greater force can

be applied before constriction of the blood vessels occurs

o Growth can be utilised

The advantages of optimal force

o Reduced discomfort

o More efficient movement because there is no delays in the differentiation and activation of bone cells

o Reduced tooth mobility

o Reduced root resorption

o Reduced pulpal damages

o Less anchorage demanding

Magnitude and type of tooth movement:

o Tipping: The forces used to tip teeth must be kept low (35-60g) as the pressure in the two areas where

it is concentrated is high in relation to the force applied to the crown. 

o Bodily movement:  100-150g force to achieve and optimal PDL stress (a moment to force ratio of at

least 8:1 is also required at the bracket wire interface to overcome the undesirable tipping effect)

o Torque: It describes the differential movement of one part of a tooth, usually the root, whilst

physically restraining any movement of the crown. It is achieved by applying a force couple to the crown of

the tooth, only in this instance the moment to force ratio must be greater than 8:1.

o Rotation: The objective being to rotate the tooth around its long axis. However, rotational vectors

invariably result in some tipping and forces should therefore be limited to 35-60g

o Intrusion and Extrusion: extrusive forces applied to buccal attachments will result in tipping and

stress concentrations in areas of the periodontal ligament. Therefore, forces need to be light, 35-60g.

Intrusive forces concentrate stress at the root apex. As this is of very small surface area the forces used need

to be very light, 10-20g.

2. Direction of force

The direction of the applied force is important as it will determine the resultant force and subsequently the

type of movement.

3. Root surface area

For a given force application, the magnitude of force transmitted to the surrounding cells in the case of a

large multi-rooted tooth is less than that for a small single rooted tooth, in which the force is concentrated

over a smaller surface area, so the type of movement might be affected. 

4. Duration

A. Orthodontic force duration classification (constancy of force)

Continuous - where forces are maintained between appliance activation appointments. For example,

the force ap-plied by nickel titanium (NiTi) open coil springs is a continuous force.

Interrupted - where force levels decline to zero between activations. The best example of an ac-tive

element that applies interrupted force is the rapid expansion screw.

Intermittent - where force levels decline rapidly to zero intermittently e.g. when a removable

appliance is removed or intermaxillary elastics are removed or break. The intermittent force can also become

interrupted between appliance activations.

B. The relationship between continuity of force and tooth movement

It suggests that there is a threshold for force duration in humans of 4-8 hours, and that increasingly

effective tooth movement is produced if forces are maintained for longer durations (Proffit and Fields 2000).

Evidence from the literature would suggest that using continuous forces results in more rapid tooth

movement (Samuels et al. 1998, Dixon et al. 2002)

There may be an increased risk of root resorption (Weiland 2003) this may be related to the fact that

without a period of rest during tooth movement there is less chance of repair if root resorption has already

taken place.

C. The relationship between continuity/magnitude and tooth movement

i. An optimal force

An optimal force is considered one that produces stress within the periodontal ligament that does not

exceed the capillary blood pressure (~ 30mmHg).

When such a force is applied, blood flow is decreased but continues through the partially compressed

periodontal ligament, while the periodontal ligament cells and fibres are mechanically distorted.

Within a few days osteoclasts migrate in from direct or frontal resorption.

On the tension side the periodontal fibres are stretched, and proliferation of fibroblasts and

osteoblasts occurred.

As these changes are mediated by cells derived from the blood supply, the latter is an important

prerequisite for tooth movement.

It must be remembered that irregularities in the periodontal ligament space, mean that a theoretically

optimal force may result in small areas of excessive compression and hyalinisation. In clinical practice,

reactivation of an appliance should be at intervals of more than three weeks apart to allow these areas to

repair fully and reduce the risk of root resorption.

ii. Continuous excessive force

Sufficient stresses within the ligament space applied and occlude the blood supply.

A sterile avascular necrosis, known as hyalinisation

Indirect resorption then takes place deep to the hyalinised area. This is known as undermining

resorption, as the attack is from the underside of the lamina dura.

Delays tooth movement due to the increased time required to allow for the differentiation and

activation of cells from the marrow spaces .

Cellular events in the tension areas are no different to those described in cases where an optimal light

force is used.

5. Other variables that related to force

a) Occlusal interferences

b) Bracket/wire interactions: Mechanical and biological factors affecting friction at the bracket/wire

interface include: (Downing et al 1994.)

o Brackets (Material, width, Bracket/archwire angulation)

o Archwires (Material, roughness, cross section, size, Torque)

o Ligation (material, force of ligation)

o Biological (Saliva, Plaque/acquired pellicle)

c) Drug Effects on the response to Orthodontic Force

I. bisphosphonates used in the treatment of osteoporosis, which is a condition mainly confined to older

patients and bisphosphonates used in its treatment act as specific inhibitors of osteoclast mediated bone

resorption. Oestrogen is an alternative drug treatment option for females and has little or no impact on

orthodontic tooth movement.

II. Prostaglandins, formed from arachidonic acid play an important role in the signalling system that

leads to tooth movement. Corticosteroids reduce prostaglandin synthesis by inhibiting the formation of

arachidonic acid, while NSAIDs inhibit the conversion of arachidonic acid to prostaglandins. NSAIDs used

at dose levels sufficient to relieve pain associated with orthodontic treatment have little or no inhibiting effect

on actual tooth movement.

III. Other classes of drugs that affect prostaglandin levels include:

Tricyclic antidepressants

Phenytoin

Anti-arrhythmic agents

Anti-malarial drugs

Tetracycline

Moment-to-force (M/F) Ratios and Types of movement

It can be seen that the type of movement exhibited by a tooth is determined by the ratio between:

The magnitude of the moment from the applied couple, and

The force applied to the tooth (Burstone and Pryputniewicz 1980)

The moment of the force applied to the tooth is the force magnitude applied at the bracket times the

perpendicular distance from line of force to the centre of resistance. For most teeth this is 8-10 mm. The

moment of the force will therefore be 8 to 10 times the force. A force of 100gm applied to a tooth will,

therefore, require an anti-rotational/counterbalancing moment of 800-1000gm/mm to obtain bodily

movement/translation of that tooth

Moment-to-force (M/F) Ratios required for various types of tooth movement: In this equation the moment

refers to the counter moment not the original moment (Smith and Burstone 1984, Lindauer 2001)

If single force causes movements of the crown and apex in opposite directions. It is called

uncontrolled tipping, and it is usually clinically undesirable. In this movement, the M/F ratio can vary but

less than 1:5. If a light, counter-clockwise moment (M2; torque) is added to the system with a rectangular

wire while the single distal force is still being applied, the tooth tips distally in what is called controlled

tipping, which is clinically desirable. In this movement, the center of rotation moves apically, and the tooth

tips around a circle of a greater radius. In controlled tipping, the M/F ratio is from approximately 6:1 to 9:1.

When the counterclockwise moment (M2; torque) is increased to equal the moment of force (M1), the

moments neutralize each other, and there is no rotation in the system. In this case, the center of rotation no

longer exists (it is infinite) and the tooth undergoes translation, or bodily movement. In translation, the M/F

ratio is approximately 10:1 to 12:1. Clinically, translation is a desirable movement, but it is hard to achieve

and maintain.

If the counterclockwise moment (M2; torque) is increased even more to an M/F ratio of ap-

proximately 14:1, then the moment becomes greater than Ml, and the tooth undergoes root movement. In root

movement, the center of rotation is located at the crown (root torque).

Everything explained above is also valid in the trans-verse plane. A canine moving distally with a

segmented arch acting on the bracket at a point away from the cen-ter of resistance rotates distolingually.

This rotation can be controlled with an antirotation bend. In this plane, the M/F ratio is also equal to the

distance between the center of resistance and the line of action of the force. This is why rotation control in

self-ligation is difficult. This is particularly important in the treatment of adult patients, who often have

periodontal problems. To obtain a higher M/F ratio, two options can be considered: 1. Place the bracket

gingivally. If this is done, the bracket base may no longer adapt well to the tooth surface! And an adaptive

step-up bend may be needed on the archwire, but this might affect the precision of alignment. 2. Custom

made bracket with gingival position. 3. Increase the moment, decrease the force, or a combination of both.

It is important to remember that the centre of resistance moves apically in PD compromised teeth and

this means that the distance to the centre of resistance increases which mean more counter moment is

required to control tipping. This makes bodily movement more difficult.

It is important to know that adding loops has a direct correlation with the F/M ratio. More loops or

using flexible loops means low the resultant force and subsequently the resultant moment. The later,

indicates that the resistance of the bracket slot (counter moment) would be sufficient to clear off the moment.

Therefore, more controlled movement would be expected. It has been reported by Burstone et al 1987, that

when the loop is full activated by bending, it would initially produce the highest amount of force that

resulting in an uncontrolled tipping. However over the time, as the loop gradually deactivated, the force

reduces and more controlled tipping results. At the end of the activation cycle, the force reaches its

bottommost level; subsequently the F/M rises resulting in translational bodily movement. Accordingly, it is

advisable to use coiled loop, NiTi or TMA loop and definitively allow the loop to express itself entirely

without interruption as at this stage, the tooth upright itself.

Summary: By varying the ratio of moment to force applied to a tooth, the type of tooth movement produced

can be regulated by the orthodontist

Bracket dimensions and Moments

As can be seen from the diagram below, the

moment of the couple produced at (A) is greater than

that produced at (B) due to the greater

perpendicular distance between the two forces

at (A). So that, Siamese brackets with good

bracket width offer greater mesiodistal control of root

position versus single wing brackets that often

require auxiliary springs in a vertical slot to

deliver second order prescription.

Type of force system 1) A   statically determinate force system   is one where it is possible to calculate the applied forces and

moments, and therefore, predict to a certain extent the resulting tooth movement. This is done by considering

the force system at one specific time point and by assuming that it is in static equilibrium at that time. It is

also called One-couple statically determinate systems: A one couple statically determinate force system is

where an appliance is inserted into a bracket or tube at one end, where both a couple and force are created,

and is tied to a single point of contact at the other, where a simple force is applied without a couple. There is

normally a long inter-bracket span between both points of attachment. Examples of such appliances include:

i. Extrusion springs: Extrusion springs are used to bring severely displaced or impacted teeth into the line of

the arch, such as maxillary canines. The diagram below demonstrates that as the extrusion spring is activated

a couple is generated in the molar tube along with an intrusive force, while an extrusive force is applied to

the displaced tooth. As the sum of the extrusive and intrusive forces, which are equal in magnitude and

opposite in direction, is zero and the moment produced by the extrusive and intrusive forces is equal in

magnitude and opposite in direction to the couple

generated in the molar tube, the force system is said to be

in static equilibrium.

Some undesirable effects of One-couple statically

determinate systems

The tendency to rotate the canine tooth

palatally as the point of force application (extrusive) is buccal to its centre of resistance.

The tendency to rotate the molar tooth buccally as the point of force application (intrusive) is buccal

to its centre of resistance. However, where the canine tooth lies palatal to the molar tooth in the frontal plane,

as the spring is activated it will be rotated palatally, creating a moment to rotate the crown of the molar tooth

palatally.

Segmented arch in the standard edgewise technique: an antitip bend (13 degrees in the example) must be placed in the wire to achieve the de-sired controlled tipping. To increase this M/F ratio, either the degree of the antitip bend can be in-creased or the magnitude of the force can be decreased. With this mo-ment, the crown tends to move mesially and the root distall

On the other hand, when a straight wire is placed in a straight-wire bracket having a 13-degree angulation, the same 1,050-g-mm positive moment occurs (Fig 3-17b). To distalize this tooth with controlled tipping, making an extra bend is not necessary because the antitip an-gulation is already built into the bracket.

ii. Laceback : it is useful to control distally tipped canine and might be used to retract canines.

iii. Midline springs

iv. Anterior Burstone intrusion arches: An anterior intrusion arch is probably the most common

application of a one couple force system where it is used to intrude the upper labial segment

teeth. Originally described by Burstone in 1977, this appliance consists of an archwire inserted

into tubes on the right and left molar teeth (the anchorage unit) at one end and is then tied to a

single point of contact on the labial segment teeth. When the wire is passive it lies apical to the

brackets on the labial segment teeth. It is activated by pulling the anterior segment of the wire

incisally and tying it at the level of the incisor brackets. As it is not engaged into an orthodontic

bracket, the end that is tied as a point contact cannot produce a couple but only a simple force

(Isaacson et al. 1993). The end which is engaged in the bracket slot produces both a force and a

couple. The labial segment teeth are normally tied together with a base archwire to which the

intrusion arch is attached at any point. This base wire helps to maintain the vertical positions of

the labial segment teeth relative to each other as they intrude. An extrusive force acts on the

molar teeth as does a couple tending to tip the crowns of the molar teeth distally and the roots

mesially. Tip back of the upper molar teeth may be a favourable outcome in Class II cases as it

will help improve the buccal segment relationships

Some undesirable effects of this force system include:

o Rotation of the labial segment teeth labially as they intrude, increasing the arch

length. This occurs if the line of action of the intrusive force is labial to their centre of resistance.

It can be overcome by tying the intrusion arch behind the lateral incisor brackets such that the

intrusive force is through the centre of resistance of the labial segment teeth, thereby reducing

the moment to rotate these teeth labially. Cinching the archwire back behind the molar tubes so

the wire cannot slide forwards, also restrains labial movement of these teeth the effect being

lingual root torque instead (Isaacson et al. 1993b).

o The extrusive force at the molar teeth is acting buccal to their centre of resistance

resulting in a tendency for these teeth to tip buccally as a result of the moment of that force.

Placing a transpalatal arch will help stabilise the molar teeth. Use of high pull headgear will

counteract the extrusive force if it is undesirable.

o The magnitude of force used with an intrusion arch is approximately 60g for four

upper incisors, 15-20g per tooth (Burstone 2001) and 50g for four lower incisors, 12.5g per tooth

(Bishara 2001). Heavier forces than these will increase the tendency for molar extrusion

v. Anterior extrusion arches: An anterior extrusion arch, which is used for the closure of anterior

open bites, is simply an inverted intrusion arch with all of its force systems inverted.

2) A   statically indeterminate force system   on the other hand is where the moments and forces are

too complex for precise measurement and evaluation. Such a situation exists where continuous

wire mechanics is used. Here the forces and moments acting on each tooth will interact with the

force systems on the adjacent teeth making it extremely difficult to evaluate the resulting net

forces and moments. It is also called Two-couple statically indeterminate systems. Examples of

such appliance systems include:

Mohammed Almuzian, University of Glasgow, 2013 Page 1

i. The utility arch (Ricketts 1976, Ricketts et al. 1979): Ricketts utility intrusion arch has been used

with much success to level an increased Curve of Spee by intrusion of the labial segment teeth

(Engel et al. 1980, Dake and Sinclair 1989). It consists of a rectangular archwire, which engages

the brackets of the incisor teeth anteriorly, and the molar teeth posteriorly. The molar teeth act as

the anchorage unit. It does not engage the premolar or canine teeth and is stepped in an apical

direction in this region. Placing tip back bends mesial to the molar tubes activates the wire such

that when it is passive the anterior aspect of the archwire lies apical to the labial segment

brackets. It is a classic example of a two-couple force system. Raising the anterior aspect of the

archwire, which is tied into the labial segment brackets, results in an intrusive force on the labial

segment teeth and a couple, while there is an extrusive force of the same magnitude on the

posterior teeth as well as a couple. The moment of the couple will tend to tip the crowns distally.

Some undesirable effects of this force system include:

o As the line of action of the intrusive force on the labial segment teeth is facial to their centre of

resistance there is a tendency for a moment to tip the crowns facially. This line of action cannot

be varied as the archwire is tied into the bracket slots (unlike the case with an intrusion arch). It

must also be remembered that there is an additional moment created by the couple within the

brackets of the incisor teeth. The moment of this couple cannot be known (indeterminate) but is

important as it affects the magnitude of the intrusive force on the incisor segment. The direction

and magnitude of this moment being dependent on the location of the activation bend and the

properties of the wire (Davidovitch and Rebellato 1995)

o There is an extrusive force acting on the molar teeth which is buccal to their centre of resistance

tending to roll these teeth buccally and tip them distally. Any adverse molar tooth movement can

however be minimised by using buccal stabilising sections, but does not always work to ones

advantage as illustrated in the photograph below.

o Preventing the labial tipping of the crowns of the incisor teeth can be achieved by:

o Incorporating lingual crown torque into the anterior segment of the utility arch, which will create

a moment of the same direction as that acting at the molars. This will however increase the

magnitude of the intrusive force on the labial segment teeth while at the same time increase the

Mohammed Almuzian, University of Glasgow, 2013 Page 2

magnitude of the extrusive force and couple on the molar teeth, possibly tipping the balance of

tooth movement towards extrusion of the posterior teeth.

o Applying a force to retract the incisors by cinching the archwire, thereby creating a lingual force

at the incisor brackets restraining labial tipping of the incisor teeth. The incisor inclination will

continue to increase, due to lingual root movement, as the intrusive force is still acting labial to

the centre of resistance of the incisor teeth. Cinching the archwire will also create a force that

tends tip and move the molar tooth mesially, a movement that is normally undesirable.

o It is also normal to place buccal root torque in the archwire where it is tied into the molar tubes.

This places the roots of the molar teeth in contact with the buccal cortical plates thereby

increasing the anchorage value of these teeth in resisting unwanted mesial movement.

ii. Torquing arches: The torquing arch is an appliance system designed to place simultaneous, same

directional third order (torque) couples on one or more incisors, while treating all of these teeth

as one big tooth and one big bracket. The second couple is created where the appliance is

inserted into the molar tubes posteriorly. It is an effective system for delivering anterior root

torque

iii. Transpalatal arch: It is another example of a two-couple statically indeterminate force system as

the molar sheaths effectively behave as a two bracket system. Other tooth movements possible

with a removable transpalatal arch include;

o Unilateral distal movement of an upper molar using a unilateral toe-in bend in the occlusal plane

on the side where no distal molar movement is required. This can be useful in correcting a

unilateral Class II buccal segment relationship and is most effective where there is no tooth

present distal to the tooth being moved.

o Bilateral or unilateral mesiolingual molar rotation which is useful where there is an excess of

space remaining in the upper buccal segments due to a tooth size discrepancy or in upper arch

only extraction cases.

o Mesiodistal molar tipping where the molar teeth require uprighting.

o Unilateral molar extrusion, by placing a unilateral toe-in bend in the frontal plane on the side

where no molar extrusion is required

Mohammed Almuzian, University of Glasgow, 2013 Page 3

iv. A 2 x 6 appliance : A 2 x 6 appliance is an example of a partially bracketed, two couple statically

indeterminate appliance system, consisting of a rectangular archwire engaged into brackets

attached to the six anterior teeth (canine to canine) and both first molars. The appliance can be

activated in the transverse dimension, resulting in constriction or expansion of intermolar width

and first order molar rotations (Rebellato 1995b). The system is useful in that both symmetric

and asymmetric expansion and constriction can be achieved with minimal movement of the

anterior teeth (Burstone 1962, 1966).

Using this system the anterior teeth provide the anchorage unit, while the archwire itself should

ideally bypass the premolars. This provides a long span of free wire with low load deflection

properties and a large range of activation, while facilitating the desired force levels and moments

required for molar tooth movement.

An outward bend a few millimetres behind the canine bracket results in expansion of the molar

with little or no rotation. An outward bend behind the canine combined with a toe-in bend at the

molar will allow expansion and mesial out rotation of the molar tooth

Two-Bracket Geometries

When an arch wire is placed in a set of brackets in the mouth, a complex force system is

produced along the arch. To aid in understanding this force system, it is helpful to simplify it into

a series of two-tooth segments, which can then be summed to estimate the force system at each

tooth. Utilizing the laws of statics, Burstone and Koenig describe in detail the initial force system

produced by placing a wire into two nonaligned brackets.

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For simplification, if the wire passes above the bracket reference line it will cause extrusion and

vice versa.

The force system for step bend is identical to that produced by a straight wire engaged into two

parallel stepped brackets is similar to Class I geometry.

With regard to the V bend, the location of the bend is crucial in determining the resultant effect

as shown below. This is the principle for intrusion effect in Begg appliance and should be

considered during closing retraction loop as well. If the anti-tip is required on molar, it should be

placed immediately before the molar to produce the maximum moment on molar to tip it distally,

but if intrusion bend is planned to intrude the incisors with minimum protrusion of incisors, it

should be place one third from molar. If the gable bend is place in the mid-distance, then incisor

would intrude and procline and the molars will extrude and tip distally, all is good in Class II D2.

When a V-bend is made in a wire halfway between two teeth with equal anchorage (eg,

premolar and ca-nine) and placed in the premolar bracket, the mesial end of the wire will lie

gingival to the canine bracket. In this case, the wire is passive (no force sys-tem); therefore, no

movement is expected. When the mesial end of the wire is inserted into the canine bracket slot, a

force system consisting of two teeth and an arch-wire is created. Because the anchorages are

equal, the center of resistance of the system is located at the midpoint of the centers of resistance

of the teeth. This V-bend archwire delivers a clockwise moment to the premolar bracket and a

counterclockwise mo-ment to the canine bracket. The sum of all forces acting on the force

system and the sum of all the moments around a point must equal zero (see the previous section

on statically determinate force systems). With the effect of equal and opposite moments, the

teeth will tip around their centers of resistance in a way that their crowns will move away from

each other. When the wire becomes totally passive as the force on the brackets drops to zero, the

system will be statically balanced. If the crowns are ligated to each other, the roots will move

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toward each other around the center of rotations located on the crowns. When the wire be-comes

passive, the axial inclinations of the teeth will also be corrected . This modification, used in the

edgewise technique, is called a gable bend.'

For simplification, if the wire passes above the bracket reference line it will cause extrusion and

vice versa. The same applied to artistic and toe in bend,

Physical properties

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o Stress described as Force/Area and determined by Pascals (N/m2). When force is applied to a material, the distance between the atoms changes, depending on the nature of the force, which is called stress. The movement of the force strains the material until it changes in size and becomes deformed. When the stress on the material is a pulling force, the distance between the atoms increases and the material expands. This process is called tension. When the stress is a pushing force, the distance between the atoms is reduced and the size of the material decreases. This process is called compression. When a pair of equal and opposite forces, called a couple, is applied to the material from different planes, a third kind of deformation occurs.2 This process is called shear. Tension, compression, and shear are the forms of stress that can be applied to a material

o Strain Described as the change in length of a material relative to its original length after an

applied force. It may recover or remain deformed.

o Elastic materials: material under stress absorbs energy from the force and returns it when the stress is removed. Materials that can return the absorbed energy completely, regaining their original size when the stress is removed, are called elastic materials.

o Plastic materials: Materials unable to return to their orig-inal size are called plastic materials.

o Viscoelastic materials can show elastic and plastic behaviors at the same time. Examples of these

materials are human skin, muscles, veins, nerves, and fibers.

o Proportional or Elastic Limit This is the maximum value of stress before permanent deformation

occurs.

o Yield strength: This is the value of stress at which 0.1% deformation occur.

o Ultimate strength: This is the value of stress at which permanent deformation occur

o Failure point: This is the value of stress at which breakage occur.

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o Strength: The ability of a material to resist stress without fracture. The stress at the point of

fracture determines the strength of the material.

o Modulus of Elasticity: Calculated on the slope of the stress/strain diagram (the red one) i.e.

defined as stress/strain. This can also be expressed as the rigidity of the material, with a high

modulus indicating an increased rigidity.

o Hook law, which states "the strain is proportional to the stress applied on the material up to the

elastic limit."

o Range (or minimum elastic radius) : Describes the amount a wire can be displaced(on the

diagram described as linear amount on horizontal direction) without permanent deformation.

o Springback: Describes the amount a wire can be displaced with only 0.1% deformation (on the

diagram described as linear amount on horizontal direction).

o Ductility or formability: The amount of energy absorbed before failure of fracture of an

orthodontic wire (area under the slop from yield point to failure point).

o Toughness : The amount of energy a material can absorb before fracturing.(in the diagram is the

area under the curve from failure point. It is equal to Resilience + Ductility). A material with low

toughness is described as being brittle. The toughness of a material can be illustrated as the area

under a stress/strain diagram.

o Fatigue is the weakening (reduction of elasticity) of ma-terials under repeated stress

o Work hardening or steel hardening: it is a process of repeated application of force that pass the

yield strength but less than the ultimate strength. This will cause a repeated deformation of 0.1%.

as a result the distance between the yield strength point and the failure point will be decreased on

the stress strain curve which means that the ductility or the formability will be reduced leading to

fracture. The crystal will be stressed in this situation. Annealing is the process of reducing the

crystal stress and improves the ductility again.

o Corrosion is the change in mechanical properties and the metal's loss of weight under the effects

of various chemical agents. There are various types of corrosion:

1) Uniform The metal surfaces of orthodontic appliances are uniformly exposed to corrosion.

Uniform corrosion is rarely seen on orthodontic attachments themselves, as these materials do

not frequently come in contact with corrosive agents.

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2) Pitting Pitting corrosion is the most common type seen on orthodontic attachments. The

mechanical characteristics and appearance of the materials are affected more than its weight.

This type of corrosion is noticed mostly on materials that have welded or soldered joints and are

not well polished. Parts that are not suitably manufactured or materials containing substances

that compromise their purity are more prone to becoming corroded. the chloride from salt ions is

particularly responsible for this kind of corrosion

3) Crevicular Crevicular corrosion is another common defect found on orthodontic attachments. It

occurs especially in the presence of chlorides when the attachments are in contact with materials

such as adhesives, acrylic, and elastics."'" SS is considered to be especially sensitive to this kind

of corrosion."

4) Intergranular The appearance of the metal and its weight do not change during intergranular

corrosion, but there is a loss of its mechanical characteristics, and failure may even occur. This

insidious attack starts from inside and can reach the grains of the metal."

5) Microbiologic The surfaces not in contact with air, such as the bracket base, may be affected by

microbiologic corrosion.° Various microorganisms such as Desulfovib-rio desulfuricans and

Desulfotomaculum; oxidants such as Thiobacillus ferroxidans and Beggiatoa; and Thiothrix,

Aer-obacter, and Flavobacterium; produce sticky and humid matter, which affects the iron in SS.

There are also iron-consuming microorganisms such as Sphaerotilus, Hypho-mi crobium, and

Gallionella.'6

6) Electrochemical Saliva serves as a good medium for electrolytic reaction between metals. There

is constant friction between the wire and the bracket slot, and this causes fretting corrosion on

the metal surfaces in con-tact and possible appliance breakage. As a result of cor-rosion, heavy

metals such as nickel, cobalt, and chromium deteriorate in the oral environment. This is

particularly important for patients with sensitivity to nickel. To over-come the predisposition of

metal alloys to corrode, ti-tanium brackets and wires have been introduced.

o Resilience: This is the amount of energy absorbed before plastic deformation occurs. On a

stress/strain diagram it is described as the area under the slope up until the elastic limit.

Resilence of the wire depend on:

1. Size In round wires, the force applied by the wire is directly proportional to the fourth power of

the change in wire size. For example, when the wire size is doubled, the force applied increases

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16 times. However, in rectangular wires, however, the force applied by the wire is directly

proportional to the width (ie, the "edgewise" dimension) of the wire in making first-order bends

and to the cube of its thickness (ie, the vertical dimension) in making second-order bends. This

means that a wire of twice the width will deliver twice the force. A wire of twice the thickness

will deliver eight times the force.

2. Length A force applied by a wire is indirectly propor-tional to the cube of the wire's length. This

means that if the length of the wire is doubled, the force is reduced one-eighth; if the length of

the wire is halved, the de-livered force will be eight times as much.

3. Material The third factor that defines stiffness in a wire is the material from which it is made.

Phases of the orthodontic tooth movement

Burstone (1962) divided orthodontic tooth movement into three phases:

1. The initial phase characterised by rapid tooth movement that lasts 2-3 days. It occurs due

to displacement within the periodontal ligament space and possible alveolar bone bending.

2. The lag phase, where the rate of tooth movement is slow and may be due to areas of

periodontal ligament hyalinisation in response to excessive forces being used or irregularity of

the socket wall (Burstone et al 1982). higher forces could be expected to cause increased hyalinisation

and prolonged lag phase followed by a more rapid post lag phase.

3. The post lag phase where the rate of tooth movement again increases in response to

indirect/undermining resorption reaching the periodontal ligament.

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