biomechanics in orthodontics by almuzian

University of Glasgow

Biomechanics in Orthodontics

Dr. Mohammed Almuzian

1/1/2013

Biomechanics in Orthodontics

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.

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

to indirect/undermining resorption reaching the periodontal ligament.

Orthodontic forces factors

Orthodontic tooth movement depends on a variety of factors including:

1. Magnitude

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).

Mohammed Almuzian, University of Glasgow, 2013 Page 1

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.

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

2001)

1. Physiological tooth movement is greatest.

2. The periodontal ligament is more cellular.

3. The alveolar bone has a greater proportion of osteoclasts

4. The cellular response is quicker

5. 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

6. Growth can be utilised

The advantages of optimal force

1. Reduced discomfort

2. More efficient movement because there is no delays in the differentiation and

activation of bone cells

3. Reduced tooth mobility

4. Reduced root resorption


5. Reduced pulpal damages

6. Less anchorage demanding

2. Direction of force

The direction of the applied force is important as it will affect the amount of force

being applied to a particular area of the root and periodontal ligament. There are

five basic types of tooth movement:

1. 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.

2. 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)

3. 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.

4. 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

5. 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.


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.

4. Duration

I. Continuity of force

A. 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.

B. 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.

II. Orthodontic force duration classification

Continuous - where forces are maintained between appliance activation

appointments

Interrupted - where force levels decline to zero between activations


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.

III. Clinical experience

a) 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).

b) Evidence from the literature would suggest that using continuous forces results in

more rapid tooth movement (Samuels et al. 1998, Dixon et al. 2002)

c) 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

5. Other

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

Mechanics of Tooth Movement

It is important the orthodontist understands the meanings of terms such as: (Smith

and Burstone 1984)

a) Forces: 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.

b) Moments: 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 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. This is called

couple moments. 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 negating the rotational effect of the resultant moments.

The heavier the force, the larger the counterbalancing moment must be to prevent

tipping and vice-versa. Moments: it try to rotate the tooth. The magnitude of the

moment is equal to the magnitude of the force multiplied by the perpendicular

distance from the point of force application to the centre of resistance. 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/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.

c) Resultants: The resultant force is the name given to the single force representative

of the individual component 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)

d) Vectors: Force resolution 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


C) 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)

D) 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

(discussed later).

Types of movement and the Position of centre of rotation

Root movement-Incisal (occlusal) edge

Controlled tipping- Closer to apex


Uncontrolled tipping- At or slightly apical to the centre of resistance

Translation- Infinity

Intrusion/Extrusion-Perpendicular to the long axis of the tooth

E) Couples: is the resultant or the net of parallel forces opposite in direction applied to

a body.

F) Moment-to-force (M/F) Ratios

Following on from the descriptions and definitions discussed already 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 ratio of applied force, to the anti-rotational/counterbalancing moment at the

bracket of a tooth, is often referred to as the moment to force ratio. The


counterbalancing moment is usually the moment of a couple, created by the

interaction between the archwire and the bracket slot in a fixed appliance system.

In terms of direction, the moment of the couple is almost always opposite to that of

the moment of the force relative to the centre of resistance.

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

(Smith and Burstone 1984, Lindauer 2001)

M/F = 0 - when only a force is applied at the bracket of a tooth (no

counterbalancing moment) tooth movement will be uncontrolled tipping with the

centre of rotation at or just apical to the centre of resistance.

M/F is less than 8/1 - by increasing the moment to force ratio the centre of

rotation moves progressively closer to the root apex, increasing the

counterbalancing moment, and reducing the tendency of the tooth crown to tip in

the direction of the force, but not negate it completely. The resulting tooth

movement is controlled tipping.

M/F 8/1 to 10/1 - with an average distance of 10mm from the bracket to the centre

of resistance, the centre of rotation will approach infinity as the M/F ratio reaches

10:1, resulting in bodily movement/translation (equal movement of crown and

root).


M/F is 10/1 - 12/1 or 13/1 the moment of the couple is now greater than the

moment from the applied force which will put the centre of rotation nearer the

incisal edge, resulting in the root apex moving further than the crown in the

direction of the applied force (root torque).

M/F = 12/1 or 13/1 - the centre of rotation will be at the incisal edge resulting in

mainly root movement (root torque).

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.

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.

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.

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:

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 this force system include:

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.


Midline springs

Anterior 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


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.

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

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.

Two-couple statically indeterminate systems

A two-couple statically indeterminate force system is where an appliance is

inserted into a bracket or tube at both ends of the dental arch creating two couples.

Such a complex system makes it difficult to evaluate precisely all the forces and

moments at work. Examples of such appliance systems include:

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.


1. 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)

2. There is an extrusive force acting on the molar teeth which is buccal to their centre

of resistance tending to roll these teeth lingually 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.

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

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 magnitude of the extrusive force and

couple on the molar teeth, possibly tipping the balance of tooth movement towards

extrusion of the posterior teeth.

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.

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.

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

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;

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.

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.

Mesiodistal molar tipping where the molar teeth require uprighting.

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

on the side where no molar extrusion is required

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


biomechanics in orthodontics by almuzian

Health & Medicine