biomechanics of tooth movements

The Bio-mechanics of Orthodontic Tooth

MovementD 657

Dr. Shiva ShankerDr. Allen Firestone

LECTURE READINGContemporary Orthodontics, Chapter 10, 3rd Edition: pp. 337-3602nd Edition: pp. 302-315

Recommended: Smith and Burstone, Mechanics of tooth movement. American Journal of Orthodontics, 1984; 85:294-307

LECTURE OBJECTIVES1. Definition of terms

2. Mechanics of tooth movement

3. Anchorage in orthodontic appliances

LECTURE OBJECTIVES1. Review Laboratory Procedures:

Arch Length AnalysisMolar Uprighting: Preparing

typodont

Definitions

Force Center of Resistance (Cres) Types of Tooth Movement

Force

Physical property e.g. distance, weight, temperature, force.

Physical properties are, mathematically, scalars or vectors

Scalars have a magnitude and no direction e.g. weight, temperature

Vectors have a magnitude and a direction e.g. force

Vectors

Line of Action

Point of Application

Sense

Magnitude

Resultant of Forces

Common point of application

Resolving force into components

Different points of application

Common point of application Resultant of Forces

Different points of application Resultant of Forces

Resolving Force Into Components Resultant of Forces

Force

A load applied to an object that will tend to move it in the direction of the applied force

Defined in units of Newtons Orthodontic purposes measured as

grams or ounces

Definitions

Force Center of Resistance (Cres) Types of Tooth Movement

Center of Resistance

Free body: center of mass/gravity = point of balance

Restrained body (tooth): center of resistance (Cres)

By definition, a force acting through Cres moves tooth with no change in orientation = translation

Center of Resistance

A point at which resistance to movement can be concentrated for mathematical analysis (= Cres)

The center of resistance for a tooth is 1/2 - 1/3 (40%) root length apical to alveolar crest

Cres varies with root length and alveolar crest height

Center of Resistance

Cres varies with root length and alveolar crest height

Definitions

Force Center of Resistance (Cres) Types of Tooth Movement

Types of Tooth Movement

Translation Rotation Combination/Tipping

• Moment

• Couple

• Center of Rotation (Crot)

Translation = Bodily Tooth Movement

A force applied in line with the center of resistance; the tooth is translated with no rotation relative to the force

Orthodontically, the point of attachment is irrelevant; the line of action of force determines the effect on the tooth

Translation or Bodily Tooth Movement

Tipping Tooth Movement

A force that doesn’t pass through Cres causes translation +

rotation = tipping

i.e., tends to tip the tooth, movement with a rotational component.

Definitions

Force Center of Resistance (Cres) Types of Tooth Movement

MomentCouple

Center of Rotation (Crot)

Moment

If the line of action of a force is at a distance from the Cres the force will produce some rotation. The potential for rotation is measured as a moment

Moment - Magnitude

Magnitude = perpendicular distance from Cres to the line of action X magnitude of force (unit = gram mm)

Direction: Clockwise or Counter-cw

Couple

No single force can cause pure rotation

Only a couple can Two forces: equal magnitude;

parallel and non-collinear; opposite sense

Couple is a ‘free vector’

Couple

• Two forces; equal magnitude; parallel and non-collinear; opposite sense

• Translational effects cancel each other out

Couple

•The moments are in the same direction and are additive

Couple

• The Sum of the Moments =

50 g X 10 mm 50 g X 10 mm+ = 1000 gm mm

• Only a couple can cause pure rotation

• The moment of a couple is equal to the magnitude of one of the forces X distance between them (50g X 20 mm)

Couple

Definitions

Force Center of Resistance (Cres) Types of Tooth Movement

MomentCouple

Center of Rotation (Crot)

Center of Rotation Crot

The point around which rotation occurs when an object is being moved

This point will vary depending on the force/moment/couple being applied

Bodily movement or translationTipping movement

Determining Crot

Connect the before and after positions of 2 points

The intersection of the perpendicular bisectors of these lines is Crot

Tooth Movement and Crot

Type of Movement

Translation

Uncontrolled tipping

Controlled tipping

Root movement

Center of Rotation

Infinity

Slightly apical to Cres

Apex

Incisal edge

Control of Center of Rotation

Point of application of force:Closer to Cres

Smaller momentLess rotationMore translation

LECTURE OBJECTIVES1. Definition of terms

2. Mechanics of tooth movement

3. Anchorage in orthodontic appliances

Anchorage

Resistance to unwanted tooth movement

Resistance to reaction forces Maximizing tooth movement and

minimizing unwanted “reactionary effects”

Strategy 1

Reciprocal space closure Minimum anchorage requirements

Strategy 2 - Differential Anchorage Values

Differential space closure Intermediate anchorage requirements

1237 706

Strategy 2A - Differential Tooth Movement

Differential space closure Intermediate anchorage requirements

Strategy 3 Dissipate reactionary forces over as

many teeth (or as widely) as possible Reinforced anchorage Maximum anchorage

Frictional Effects on Anchorage

Frictional resistance to sliding archwires against brackets

Factors Affecting Friction

Surface of wires/bracket - 1) Stainless steel slides well on

stainless steel; 2) Nickel titanium alloy wires have

greater frictional resistance 3) Ceramic brackets also exhibit

greater frictional resistance

LECTURE OBJECTIVES1. Definition of terms

2. Types of tooth movement

3. Anchorage in orthodontic appliances

LECTURE OBJECTIVES1. Review Laboratory Procedures:

Arch Length AnalysisMolar Uprighting: Preparing

typodont

Arch Length Analysis = Space Analysis

Permanent Dentition Mixed Dentition

Space AnalysisPermanent Dentition +Arch length available - M/D width of 12 teeth: first

molar to first molar__________________________

= Arch length deficiency or

excess

Arch Length

The arch circumference:measured at the proximal contacts of posterior teeth and the incisal edges of anterior teeth i.e., the widest part of the tooth.

Measuring Arch Length

Space Analysis Measuring Tooth Width

Space Analysis: Mixed Dentition

The same procedure in the mixed dentition but

Need to estimate the size of unerupted permanent teeth (premolars and canines)– Moyers proportionality tables, Tanaka

and Johnston

Space Analysis Measuring ALD

+Arch length available - M/D width of teeth mesial

to first molars_______________________

= Arch length deficiency or

excess

Measuring Arch Length

Moyers: Mixed Dentition Space Analysis

To estimate the width of unerupted canines and premolars in a quadrant:

1. Get sum of the mesial-distal width of the 4 mandibular permanent incisors.

2. Locate value in Table and look up predicted width of maxillary and mandibular teeth.

Tanaka-Johnston: Mixed Dentition Space Analysis

To estimate the width of unerupted canines and premolars in a quadrant:

1. Get sum of the mesial-distal width of the 4 mandibular permanent incisors.

2. Divide by 2 and add11.0 for max. canine + premolars10.5 for mand. canine + premolars.

Tanaka &Johnston, JADA 88:798, 1974

Rule of Thumb: Mixed Dentition Space Analysis

To estimate the width of unerupted canines and premolars in a quadrant:

23mm for maxillary quadrant22mm for mandibular quadrant

Molar Uprighting Typodont

Molar Uprighting Teeth

Molar Uprighting Wax

Molar Uprighting Wax Preparation

Molar UprightingSegment Preparation

Molar UprightingSegment Preparation