Indian Dental Academy - Retraction Mechanics in SWA

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RETRACTION
MECHANICS IN
SWA


INTRODUCTION


Mechanics is the discipline that
describes the effects of forces on
bodies

Biomechanics refers to the science of
mechanics in relation to biologic system.


MECHANICAL PRINCIPLES IN
ORTHODONTICS

STRESS- internal distribution of the load
defined as force per unit area
STRAIN- internal distortion produced by the load
deflection per unit length


STRENGTH- maximal load that the material can resist
measured in stress units( gm/cm2)


STIFFNESS- inverse of springiness
given by the slope of the stress strain
curve
RANGE- distance that the wire will bend elastically
before permanent deformation occurs
measured in mm


STRENGTH = STIFFNESS X RANGE
RESILIENCE- energy storage capacity
area under the stress strain curve
upto the proportional limit
FORMABILITY- amt of permanent deformation
that a wire can withstand without
failing


SOME BIOMECHANICAL TERMS
FORCE- load applied to an object that will tend to
move it to a different position in space
F = ma
units are newton,gms or ounces


Center of mass
Each body has a point on
its mass , which behaves as
if the whole mass is
concentrated at that single
point. We call it the center
of mass in a gravity free
environment.
Center of gravity
The same is called the
centre of gravity in an
environment when gravity is
present.

CENTER OF MASS-(of a free body) is the point
through which an applied force must pass to move it
linearly without any rotation. This center of mass is
the free objects “Balance Point”

CENTER OF RESISTANCE- is the equivalent balance
point of a restrained body.


Center of resistance
of 2 teeth

Center of resistance of maxilla

Center of resistance of
Maxillary molar


AJO DO 90: 29-36, 1986

Center of resistance depending upon the level of alveolar bone.


Center of resistance during anterior teeth
retraction
BURSTONE et al in 1987
BURSTONE et al in 1991
TURK et al in 2005


Center of rotation
defined as a point about which a body appears to have
rotated, as determined from its initial and final positions.


A simple method for determining a
center of rotation is to take any
two points on the tooth and
connect the before and after
positions of each point with a line.
The intersection of the
perpendicular bisectors of these
lines is the center of rotation


AJO DO 85(4):294-307,1984

Moment of the force :It is the tendency of a force to produce rotation.
The force is not acting through the Cres
It is determined by multiplying the magnitude of force by the
perpendicular distance of the line of action to the center of
resistance.
Unit– Newton . mm ( Gm. mm)


The direction of moment of force can be determined by continuing
the line of action around the Cres


Couple
A couple consists of two forces of equal magnitude, with parallel but
noncolinear lines of action and opposite senses.

1000gm.mm


Moment of a couple
The tendency of a couple to produce pure rotation around the Cres
The magnitude of a couple is calculated by multiplying the magnitude
of forces by the distance between them
Unit :- Newton . mm (Gm . mm)

Cres


In orthodontics depending up on the plane in which the couple is acting
they are called as

Rotation-1st order

Tipping- 2nd order


Torque- 3rd order

Systems Equivalent force
A useful method for predicting the type of tooth movement that will
occur with the appliance activation is to determine the “ equivalent
force system at tooth’s center of resistance.
It’s done in three steps
First- Forces are replaced at the Cres maintaining its magnitude and
direction
Second- The moment of force is also placed at the Cres.
Third- Applied moment ( moment of couple in bracket wire combination)
is also placed at Cres.


MC-MF

F

F

MC

MF


Moment to force ratio & types of tooth movement
The type of movement exhibited by a tooth is determined by the
ratio between the magnitude of the couple (M) and the force (F)
applied at the bracket.
The ratio of the two has units of millimeters


Tipping
-Greater movement of crown of the tooth than of the root

Uncontrolled tipping:
-Movement of the root apex and crown in opposite direction
-Crot – Between Cres and apex
-Mc/F ratio 0:1 to 5:1
-0<Mc/MF<1

Controlled tipping:
-Movement of the crown only
- Crot – At the root apex
-Mc/F ratio 7:1
-0<Mc/MF<1
JCO13:676-683,1979


AJO 85(4):294-307,1984

Translation
-Bodily moment occurs
-Crot – At infinity
-Mc/F ratio 10:1
-Mc/MF=1

Root movement
-Root movement occurs with the crown being stationary
-Crot – at the incisal edge or the bracket
-Mc/F ratio 12:1 - Mc/MF>1

Pure rotational movement
-Root & crown move equally in opposite direction
- Crot – Just incisal to Cres
- Mc/F ratio 20:1 - Mc/MF>1
JCO13:676-683,1979

AJO 85(4):294-307,1984

Newton’s Laws :
First Law: The Law Of Inertia
Every body continues in its state of rest or uniform motion in a
straight line unless it is compelled to change by the forces impressed
on it.
Second Law :The Law Of Acceleration
The change in motion is proportional to the motive force impressed
& is made in the direction of straight line in which the force is
impressed.
Third Law :The Law Of Action & Reaction
To every action there is always opposing & equal reaction.
When a wire is deflected or activated in order to insert it into
poorly aligned brackets the 1st & 3rd laws are apparent.

Static Equilibrium

Σ Horizontal forces = 0
Σ Vertical forces = 0
Σ Transverse forces = 0
AND
Σ Moments ( Horizontal axis ) = 0
Σ Moments ( Vertical axis )= 0
Σ Moments ( Transverse axis ) = 0


Sign Conventions
A universal sign convention is available for forces & moments in
dentistry & orthodontics.
Forces are positive when they are in :
-Anterior direction
-Lateral direction
-Mesial direction
-Buccal direction
-Extrusive forces
Moments are positive when they move the crown in a mesial,
buccal or labial direction.

RESULTANTS AND COMPONENTS OF ORTHODONTIC
FORCE SYSTEMS
Teeth are often acted upon by more than one force. Since the
movement of a tooth (or any object) is determined by the net effect
of all forces on it, it is necessary to combine applied forces to
determine a single net force, or resultant.
At other times there may be a force on a tooth that we wish to
break up into components. For example, a cervical headgear to
maxillary molars will move the molars in both the occlusal and distal
directions. It may be useful to resolve the headgear force into the
components that are parallel and perpendicular to the occlusal plane, in
order to determine the magnitude of force in each of these directions.


h
a
ø
b
sin ø= a/h
cos ø = b/h

a = h sin ø
b = h cos ø


Resultant of forces

F1

F1
ø

F

2

F2

F1 cos ø + F2 cos ø

The parallelogram method of determining the resultant of 2
forces having common point of application


Components of a force
F sin ø
F

ø

F cos ø


The resultant of 2 force with different point of
application can be determined by extending the line of
action to construct a common point of application

Centered ‘V’ bend


AJO DO 98(4):333-339 1990

Off Centered ‘V’ Bend


AJO DO 98(4):333-339 1990

RETRACTION MECHANICS

FRICTION

CONTINUOUS

FRICTIONLESS

SEGMENTAL

CONTINUOUS


SEGMENTAL

FRICTION MECHANICS


ROLE OF FRICTION

When one moving object contacts another
tangentially friction at the interface resists the
movement .
Consequently , orthodontists have to apply more
force to overcome the frictional force to achieve
the desirable result, due to which there is more
patient discomfort and pain and also increases
anchorage demands.


Factors effecting frictional resistance during tooth
movement.
PHYSICAL
1. Arch wire
Material
cross section size and shape
surface texture
stiffness
2. ligation of arch wire and bracket
ligture wire
elastomerics
method of ligation
3. Bracket
material
Manufacturing process
Slot width and depth
Design of bracket
Second order angulation
Third order bend


4. Orthodontic appliance
interbracket span
level of bracket slots b/w adjacent teeth
forces applied for retraction
BIOLOGICAL
saliva
Plaque
corrosion


Components of resistance to sliding (RS)
1 st component – classical friction (FR)

is a product of co –efficient of friction (µ) and normal
force.

Co –eff of frictionit is the objects frictonal proportionality constant. i.e
surface roughness of the material.
Nis the amount of force acting perpendicular to the surface
of the object such as ligation force.on the bracket.


2 nd component – Binding
SECOND ORDER ANGULATON –
it is the angle b/w base Of The wire (vertical dimension
of wire) and the bracket.{θ}.
Critical contact angle –
the level where the wire contacts both the ends of the
bracket slot. .{θc}.
When the second order angulation increases to critical angle
binding occurs .






Passive configuration- FR
exsists has an only
component when the arch
wire and bracket have
clearance, in this angulation
b/w arch wire and bracket
is less than critical
angulation.
Active configuration- when
clearance is absent and
interferance occurs (θ = θ
c) binding occurs. Under
these conditions two forces
exsists i.e. N and binding
force(BI).


Factors determining critical contact angle








Slot size
Bracket width
Arch wire size

Engagement index – size/ slot
Bracket index – WIDTH / SLOT


Bracket
width

Wire
size

Slot size


3rd component - notching


Influence of arch wire and bracket dimensions on
sliding mechanics : derivations and determinations of
the critical contact angles for binding
( robert .p. kusy and whitley -1999)

Derived an equation

size/ slot = width/ slot(sin θc)+cos θc.
In this equation size/slot defines the engagement index .This index
defines the fraction of the bracket slot filled by the arch wire .
width/ slot defines the bracket index – the number of times the
bracket width is more than slot dimension.
Together , these two dimensionless indices define all that is
necessary to determine θc as the point at which the binding starts.
This study derived the maximum and minimum engagement and bracket
indices possible,


For maximum bracket index - large bkt width/ small bkt slot =
size= 250 mil/18 = 13.9
For minimum bracket index - small bkt width/ large bkt slot
size=125mil/22=5.7
The range bracket index is 5.7 to 13.9
For maxi engagement index – large wire size/ small bkt slot=
16/18=.86
For mini engagement index – small wire size/ large bkt slot=
14x22=.64
The range for engagement index is .5 to1
When the nominal parameters of arch wire and bracket used in
sliding mechanics were estimated for critical contact angle
three important conclusions were drawn


1) Narrow bracket showed θc double the value when
compared to the wider brackets.
2) Smaller bracket slot showed decreased θc
value .Hence, more precise aligning and leveling is
required before retraction.
3)Smallest wires used for retraction i.e. 16 size wire
in 22 slot, 125mil width . θc =2.8 degrees.
Same wire in 18 slot showed θc =0.9 degrees.
Even in the best scenario the practitionar must
align and level so that the angulation b/w wire and
Bracket is within the range of 1-4 degrees or else
binding increases and sliding ceases.
To accomplish the best scenario most easily
within the strength and stiffness requirements.
The bracket width and wire size should be small
and bracket slot should be larger.

INFUENCE OF BINDING OF THIRD ORDER
TORQUE TO SECOND ORDER ANGULATION
(ROBERT P. KUSY 2004)
As base dimensions of arch wire increases, bracket width
decreases, bracket slot size decreases the critical contact
angle for binding decreases.
But when torque is incorporated into the wire ,the height of
the wire is also considered. ( depth of the wire).
As the torque angle is increased, clearance b/w arch wire
and bracket decreases reducing the critical contact angle.
Thus, increasing the chances of binding.


stainless steel brackets






These are the most popular brackets till today.
Friction is minimum in these brackets due to
smoother surface.
Sintered stainless steel brackets had low friction
then cast stainless steel brackets due to more
smoother surface texture.


CERAMIC BRACKETS

demonstrated significantly
higher frictional forces than ss
brackets.highly magnified views
revealed numerous small
indentations in ceramic
brackets.
monocrystalline alumina
brackets had smoother surface
than polycrytalline bracket,but
their frictional characteristics
are comparable.
since ,greater forces are
required to slide the teeth.
Caution in preserving anchorage
must be exerted in such
situations.
ceramic brackets with metal
slots showed decreased friction
as wire is contacting the
smoother metal slot.

Zincornia brackets


Zincornia brackets has been offered as an
alternative to the ceramic brackets since surface
hardening treatments to increase fracture
toughness are available for zincornium oxide .
However, the frictional co-efficients for these
brackets were found to be greater than or equal
to polycrystalline brackets in both wet and dry
states. Surface changes consisting of wire debris
and surface damage in zincornia brackets after
sliding of wires were observed.


Titanium brackets
Introduced in response to reports of the corrosion
of stainless steel brackets and increased
sensitivity to nickel content of the alloy.
It is proven to be biocompatible.
It is very rough as the titanium content of the
alloy is increased.
More chance of cold weld formation with the
titanium brackets at bracket wire interface which
increases resistance to sliding.


Plastic brackets
In an attempt to make a esthetic bracket with low
frictional resistance and easier debonding
features than ceramic ,a wide variety of new
ceramic reinforced plastic brackets with or without
metal slots were introduced.
several studies showed that when these brackets
were tightly ligated with steel ligatures deformed
slightly to squeeze the bracket slot thereby
increasing friction.


WIRES
Specular reflectance studies have shown that
stainless steel wire have smoothest surface
followed by co –cr, beta–ti, niti in the order of
inceasing surface roughness.
Beta titanium wires may form micro-welds in dry
states and further increase the frictional forces.
frank and nicoli found that stainless steel wires
had least friction at non binding sites ,but as
angulation increased and binding was present , the
reverse was true.


MECHANICAL AND SURFACE CHARACTERISTICS
OF 3 ARCH WIRE ALLOYS. ( VINOD KRISHNAN
AND JYOTHINDRA KUMAR 2002 ).
SEM of STAINLESS STEEL
SS IS STRONG , HAS
SMOOTH SURFACE
SEM of BETA TITANIUM
BETTER LOAD DEFLECTON,
LESS STIFFNESS THAN
SS,ROUGH SURFACE
SEM of TIMOLIUM
IT IS A α AND BETA
TITANIUM, HAS
INTERMEDIATE
PROPERTIES TO SS AND
BETA TITANIUM.


Co-efficient of friction and surface roughness
Kusy et al used laser spectroscopy to study
surface roughness of orthodontic wires . Among
the four wire alloy types that are commonly used
in orthodontics , stainless steel appeared to be
lowest followed by cobalt chromium, beta titanium
and nickel titanium.
kusy and whiteley were the first to look at the
effect surface roughness on friction co-efficient .
The results showed that low surface roughness was
not sufficient condition for low friction co
efficient.
For ex: beta titanium has decreased roughness
than niti wires but frictional force resistance is
more for beta titanium.

Ion implantation
Gas ions like nitrogen and oxygen are implanted
into the wire surface, resulting in a surface that
is hard and creates a considerable compressive
force at atomic level.
This improves the surface characteristics and
reduce co=-efficient of friction.
Burstone and farzin –nia demonstrated that ion
implanted beta titanium wires produced the same
level friction as stainless steel,

Round vs rectangular wires.
Several studies have found that an increase in wire
size increase bracket wire friction.
Rectangular wires produce more friction than round
wires.
At non binding sites contact area between arch
wire and bracket is an important factor in friction
hence more friction with rectangular wires.
At binding sites with rectangular wire the force is
distributed over a large surface area resulting in
less pressure and less resistance to movement.
At binding sites with round wires the bracket slot
can bite the wire causing indentations resulting in
more friction.

Ligation techniques.
Normal ligation force ranges from 50 to 300 grams.
Edward et al in 1995 compared the frictional forces
produced elastomeric modules applied conventionally or figure
of eight , stainless steel ligatures and teflon coated stainless
steel when used for arch ligation.
Figure of 8 configuration appeared to create highest
friction.
No significant difference between normal conventional
module and stainless steel ligature.
Teflon coated stainsteel had lowest frictional force.
Even the composition of the ligature is another variable in
determining the co_efficient of friction.


As the elastomeric ligatures are polyurethane based
polymers , studies have shown that when exposed
to oral environment they undergo stress relaxation
and hydrolytic decompensation over time which will
effect the properties of the module.
Frictional forces by ligation can be reduced by pre
streching the module , or by using stainless steel
ligatures or using self ligating brackets.
Backing of one quarter turn after tying steel
ligatures.


Conventional ties such as O-rings and stainless steel ligatures make
using optimal forces impossible due to friction and binding.
Elastomeric O-rings will lose half their elasticity within days of
initial tie in, thus compromising tooth control.
O-rings are extremely plaque retentive and greatly increase the
number of microorganisms attached to appliances during treatment,
increasing the incidence of decalcification during treatment.


Self ligating brackets
The first self ligating bracket was the Russel
lock.
 Self ligating brackets are ligatureless bracket
system that have mechanical device built into the
bracket to close off the edgewise slot .
 These brackets show low frictional resistance.
 They are 2 types –
1) Active-spring clip which presses against
archwire.
2) passive- slides which does not press against wire
and produces less friction.
 { This difference in friction is seen only when the
bigger sized arch wire is used.}



A new low force ligation system (jco 2005)






This article describes an
alternative to self ligating
systems a ligature that
markedly reduces the
friction b/w the arch wire
and bracket.
The slide ligature is made
of special polyurethane ,is
applied in the sameway as a
conventional elastomeric
ligature
.Like a passive self ligating
it forms a fourth wall and
allows the archwires to
slide freely in the slot
while transmitting its full
force to the teeth.

•This ligature also forms the buffer b/w the
bracket and soft tissues considerably improving
patient comfort.


Leveling & Aligning

Wider bracket

Narrower bracket

More Mc

Less Mc

Less contact angle

More contact angle

More the play more is the Mc
It was found that a predictable ratio of the moments produced between two
adjacent brackets remained constant regardless of interbracket distance or the
cross section of the wire used if the angles of the bracket remained constant to
the interbracket axis.
AJO DO 1988 Jan (59 – 67)

We put thinner wires at the beginning of alignment i.e. more play - less applied
couple - less M:F - no root moment only crown moment (tipping)


MC

MC

MC

Am J Orthod
1974;65:270-289

MC

MC

The 2 central incisors are rotated
mesial in creating a symmetric V
geometry. The
desired corrective force system
involves 2 equal
and opposite moments as illustrated


Semin Orthod 2001;7:16-25.

The force system developed by inserting a straight wire into the brackets of
the 4 anterior teeth will create counterclockwise moments on the 2 central
incisors as well as lingual movement of the left central incisor and labial
movement of the right central incisor. The initial geometry is not favorable for
alignment.


shows a lingually placed right lateral incisor. In this case, the geometric
relationship between the right lateral and central incisors is a step geometry
and the placement of a straight wire into the brackets of the 4 anterior teeth will
align the teeth and also shift the midline to the right side


In the maxillary arch shown in Figure 5A, the relationship between the
central incisors is a step geometry and an asymmetric V geometry is observed
between the central and lateral incisors on the right side. Analysis of the force
system shows that, although correction of the 2 central incisors will occur as
a result of straight wire placement, the right lateral incisor will be displaced
labially, which is an undesirable side effect .

The relationship between the right lateral and central incisors is
recognized as an asymmetric V geometry. Analysis of the force system
shows that, although the left lateral incisor will be corrected by rotating mesial
out and moving labially, the right lateral incisor will move further lingually


During extrusion of a high canine
unilaterally. Figure A shows the
force system generated by the
placement of a straight wire through
a high maxillary right canine. The
canine will extrude as desired, but
the lateral incisor and first premolar
on that side will intrude and tip
toward the canine space. An open
bite may result on that side of the
arch, and the anterior occlusal plane
will be canted up on the right side.



Molar Rotations- absence of maxillary molar rotation is highly desirable in
obtaining class-I occlusion of the molars, premolars, & canines.
B/L Molar rotations:
Palatal Arch

Mc

Mc


Headgear

F

F
MF


MF

U/L Molar Rotations:

D

M

MF

MF
Mc

Mc


Simultaneous Intrusion & Retraction:


MF

MF
MF

MF

Cross bite elastics

Force vectors in Cl-III elastics

Force Vectors in Cl-II elastics

Favorable in low angle deep bite
Favorable in low angle cases
cases

Space Closure

Group A Anchorage

Group B Anchorage

Group C Anchorage

Force system for Group B space closure
M/F Ratio 10/1in anterior & posterior – Translation of anterior & posterior

Mc


Mc

Force System for Group A space closure
M/F ratio 12/1 or more in posterior & 7/1 or 10/1in anteriors – Root moment of
posteriors & tipping or bodily moment of anteriors

IDEAL


Forces Differ


Moments Differ


Force system for Group C space closure mirrors that of group
A.

The anterior teeth becomes the effective anchor teeth.

The anterior moment is of greater magnitude & the vertical force side
effect is an extrusive force on the anterior teeth.


TORQUING WITH THE MOMENT OF A COUPLE
System equilibrium

Incisor movements

AJO DO1993 May (428 – 438)

TORQUING WITH THE MOMENT OF A FORCE
System equilibrium

Incisor movements

AJO DO1993 May (428 – 438)

CONCLUSION

Various mechanics can often be used to achieve the tooth movements
desired for orthodontic treatments. It is important however to understand
the mechanics involved and to recognize when the appliance will not achieve
adequate results or may result in undesirable side effects. This can help us
to prevent prolonged overall treatment time and/or compromise in the final
orthodontic outcome.
The ultimate result will be a happy patient , with a beautiful smile
leaving your clinic at the end of treatment.


REFFERENCES
1. Smith RJ, Burstone CJ: Mechanics of tooth movement. AJO 85:294307,1984.
2. Burstone CJ, Koenig HA: Creative wire bending- The force system from step
& V bends. AJO DO 93(1):59-67,1988.
3. Burstone CJ, Koenig HA: Force system from the ideal arch. AJO 65(3):270289,1974.
4. Demange C: Equlibrium situations in bend force system. AJO DO98(4):333339,1990.
5. Issacson RJ, Lindauer SJ, Rubenstein LK: Moments with edgewise
appliance e: Incisor torque control. AJO DO 103(5):428-438,1993.
6. Koing HA, Vanderby R, Solonche DJ, Burstone CJ: Force system for
orthodontic appliances: An analytical & experimental comparison. J
Biomechanical Eng102(4):294-300,1980.
7. Kusy RP, Tulloch JFC: Analysis of moment/force ratio in the mechanics of
tooth movement. AJO DO 90; 127-131,1986.
8. Nanda R, Goldin B: Biomechanical approaches to the study of alteration of
facial morphology. AJO 78(2):213-226,1980.

9. Vanden Bulcke MM, Burstone CJ, Sachdeva RC , Dermaut LR: Location of
center of resistance for anterior teeth during retraction using the laser reflection
technique. AJO DO 91(5):375-384,1987.
10. Vanden Bulcke MM, Dermaut LR, Sachdeva RC, Burstone CJ: The center
of resistance of anterior teeth during intrusion using the laser reflection
technique & holographic interferometry. AJO DO 90(3): 211-220,1986.
11. Mulligan TF: Common sense mechanics 2 . Forces & moments. JCO
13:676-683,1979.


Indian Dental Academy - Retraction Mechanics in SWA

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