Individualised arch form vs modified arch form / /certified fixed orthodontic courses by Indian dental academy

INDIAN DENTAL ACADEMY
Leader in continuing dental education
www.indiandentalacademy.com


Shape of the dental arch is determined by:
Configuration of the supporting Bone.
Circumoral musculature.
Intraoral functional forces.

An analytical equation of dental arch shape is necessary to
describe the relationships between Arch Width, Depth and
Perimeter, which influence the Archform.

With the advent of Nickel Titanium highly elastic preformed
arch wires, the clinician is often able to introduce larger cross-section
wire in the early stages of “leveling and alignment”. The Nickeltitanium archwires exhibit exceptional springiness but, wire bending
in the classical sense (or the formability of the wire) is poor.
Multistrand 0.015 or round 0.014-0.016 Nitinol wires are
used initially in the treatment as the initial leveling and aligning arch
wires, as these exert light forces.
As the teeth align, and the treatment progress into heavier
rectangular Nitinol or Heat activated NiTi and then stainless steel
wires, archwires have greater effect on arch form.

Aims and Objectives
•To compare the Natural human arch form with preformed
Rectangular Nickel titanium archwires by transforming both the
archforms into curves derived through Beta Equation.
To compare the ratio of Intercanine And Intermolar width of
Natural human archform with that of preformed Nickel Titanium
Archwires.
To evaluate the form and symmetry of preformed Rectangular
Nickel Titanium Archwires.
To evaluate the arch co-ordination of Maxillary and Mandibular
preformed Rectangular Nickel Titanium Archwires.

Growth in the Transverse Dimension of Mandible and Maxilla
Mandibular growth in the width, is accomplished relatively early
in the child, shows less total change than the vertical and
anteroposterior dimensions.
Symphysial cartilage is replaced by bone by the end of first year.
Measurements between the right and left mental foramina, show that
this dimension changes relatively little after the sixth year of life.
Increase in width involves alveolar process growth almost totally
since there is little skeletal width increase (none in the mandible) and it
contributes little to dental arch change. Moyers & Vander Linden
(1970).
In a girl the mandibular intercanine dimension is completes by 910 years, at the eruption of permanent canines, in a boy by 10-11
years.
In the maxillary arch, intercanine dimension is completed by 12
in girls whereas in boys www.indiandentalacademy.com
by 18 years of age.

Review of Literature
One of the earliest methods of measuring arch length and width
was that of Bonwill (1905). The Bonwill-Hawley arch formula
produces a geometric design, based upon the combined mesiodistal
widths of the incisors and cuspids.
McConaill and Scher felt that, from biological and engineering
points of view, the Catenary is the simplest curve possible, and it is
easily explained mathematically.
Scott (1957) stated that the use of Catenary chain of standard
length enables one to express in a simple manner the basic form of any
normal human dental arch.
Remson (1964) studied various arch predetermination methods. He
cited shortcomings with all methods and concluded that an arch
which fits a precise pattern is an exception than a rule.

Currier (1969) used the Computer as a tool to evaluate human
dental arches by making mathematical comparisons. between a
selected population sample and the geometric forms of the ellipse and
the parabola.
Brader (1972) in his classic article “Dental arch form related to
intraoral forces gave the formula; PR=C. Brader gave credence to
mathematical relations with the theory of the trifocal ellipse,
particularly for the upper arch.
Robnett J.H. (1980) gave the segment concept in arch design.
The approach to the problem of designing dental arch forms
was conceived because there appears to be no normal shape but,
rather various combinations of width, length and arcs.
Begole E.A. (1981) used the application of cubic spline function
in description of the dental arch form.

Retention and Stability
Dallas McCauley (1944) stated that the two mandibular
dimensions, Molar Width And Cuspid Width are of
uncompromising nature that one should establish them as fixed
quantities. This type of thinking was also emphasized by Strang,
Tweed, Nance and Riedle.
Strang (1952) believed that mandibular intercanine and intermolar
widths are accurate indices of the muscular balance.
Riedal postulated that treatment should be aimed at maintaining, the
arch form presented by the original malocclusion.
Little, Wallen, and Riedel stated that arch width and length
decreased after retention. They concluded that "molar width and
canine width are of an uncompromising nature. This thinking is also
recently emphasised by De la Cruz et al (1995).

Burke et al (1997) did a Meta analysis of mandibular intercanine

Material and methods
Forty subjects (Twenty male
and twenty female) of Angle
Class I normal occlusion were
selected
Study models were prepared
with the occlusal plane
parallel to the base.
Casts exhibiting attrition,
fractured teeth, ectopically
erupted teeth or deciduous
teeth were excluded.
Samples having arch length
deficiency greater than 3mm
were excluded.

Bracket height gauze was used
to suitably mark the labial and
buccal surfaces of the teeth
from second molar to second
molar.


Points were marked on the facial surfaces at the bracket
placement points for measurement of the co-ordinate points.


Each cast was oriented in
Nikon Microval Co-ordinate
Measuring microscope.

The casts were placed on the
platform of the measuring
microscope. The base of the
model was placed parallel to the
platform and occlusal plane
parallel to the base.


Optical beam was used to identify each measurement point.
The corresponding X, Y and Z coordinates are stored automatically
to a computer data file. Coordinates of a point in space in each of the
three orthogonal axes were measured to 1 Micron
The coordinate components of dental arch forming three
dimensional spaces were recorded in this manner. A planer projection
of each cast is subsequently obtained.
The Table Curve 2-D Curve Fitting Program (Systat Software)
was used for all curve fits and calculations. Using the least squares
method, a Beta function curve was fitted to each of the casts.


An analytical equation of dental arch shape is necessary to describe
the relationship between arch width, depth and perimeter.

W = Molar width. It is the measured distance between the second
molar bracket placement points mesiodistally in millimeters.
D = Arch depth. It is the perpendicular distance from the most
anterior point between the two central incisors to the molar crossarch dimension in millimeters.

The average correlation coefficient between Measured Arch
Shape Data & Mathematical Arch Shape, expressed by the Beta
function is 0.97 with standard deviation of 0.03.
Using the average Correlation Coefficient as a measure of
fit, the Human Dental Arch Form is shown to be accurately
represented mathematically by the Beta Function.
Thus the Mathematical Beta Function was used to derive
accurate planer projection of co-ordinates of the points corresponding
to the bracket placement points for comparison with Preformed
Rectangular Nickel Titanium archforms at the Important Intercanine
and Intermolar Widths.


Maxillary arch
Intercanine Width 32.012mm Depth 33.632
Intermolar width 58.021mm Depth 42.201

Mandibular arch
Intercanine Width 24.124 mm Depth 32.993
Intermolar width 52.241mm Depth 38.514


The archwires included were Rectangular Nickel
Titanium Archwires:
3 M Unitek
Ovoid Archform
Tapered Archform
Square Archform
American Orthodontics
Natural Arch Form 1
Natural Arch Form 2
SIA Orthodontics
Standard Shape
Natural Shape

Nitanium Archwires Ortho
Organizers
Libral Traders Euroform
Orange Orthodontics
Orthotec Nuform
Modern Orthodontics
Natural Form
Orthoform
Proform Arch Shape
Dentaurum
15.Lancer Orthodontics


To compare the Preformed
Rectangular Nickel titanium
archwires with that of Natural
human archform, teeth were
arranged on a typodont with
Class I occlusion

Brackets were positioned at
the centre of the tooth incisogingivally along the long axis
mesiodistally.


The Preformed Rectangular Nickel
titanium archwires were affixed to the
appropriate brackets using Quick-glue.

The Archwire-bracket assembly was
removed from the typodont & placed on
a square aluminum tray.

The archwires and appropriate bracket
systems were measured in a Nikon
Microval measuring machine, which is
available at the Indian Institute of
Technology (I.I.T.) Mumbai. Linear
accuracy of the machine is 0.006 mm
and reproducibility 0.004 mm.

The planer projection of
resulting archform was obtained
for comparison with natural
human archform.
Graphic planer representations
of the corresponding bracket
base spatial coordinates of 30
preformed
Nickel
titanium
archwires. (15 mandibular and
15 maxillary) were compared
with maxillary and mandibular
natural arch forms.

Results
Intercanine width:
The range of difference between natural archform and the form of
Archwires:
Natural arch

Difference

Female Maxillary

2.9 mm to 8.8 mm

Female Mandibular

3.1 mm to 8.1 mm

Male Maxillary

2.1 mm to 7.9 mm

Male Mandibular

1.7 mm to 6.8 mm

The maximum Intercanine width difference natural Female
Mandibular archform 8.13 mm (SIA Orthodontics Natural Shape).
The maximum Intercanine width difference was 8.85 mm Female
Maxillary archform (Ortho Organizers Nitanium Archwires).

Intermolar width:
The range of difference in Intermolar width of the natural archform
and the form of Archwires
Natural arch
Female Maxillary
Female Mandibular
Male Maxillary
Male Mandibular

Difference
0.74 mm to 5.1 mm
1.6 to 4.9 mm
-0.18 to 4.1 mm
0.2 mm to 2.7 mm

The 3 M Unitek Tapered Archform was narrowest.
The mean maxillary natural human arch form molar/canine width
ratio is 1.74/1; whereas it is 1.54/1 in the Preformed archwires. The
mean mandibular natural human arch form molar/canine width ratio is
2.11/1; it is 1.78 for Preformed archwires.

Archwires
showing Poor
Coordination

Archwires
showing
Asymmetric
Coordination

Archwires
showing Average
Coordination

Archwires
showing Good
Coordination

1. SIA
Orthodontics
Natural Shape

1. 3 M Unitek
Tapered Archform

1. 3 M Unitek
Ovoid Archform

1. American
Orthodontics
Natural Arch Form
1

2. SIA
Orthodontics
Standard Shape

2. American
Orthodontics
Natural Arch Form
2

2. Modern
Orthodontics
Orthoform

2.Nitanium
Archwires Ortho
Organizers

2. SIA
Orthodontics
Standard Shape

2. American
Orthodontics
Natural Arch Form
2

2. Modern
Orthodontics
Orthoform

2.Nitanium
Archwires Ortho
Organizers

3. 3 M Unitek
Square Archform

3.Proform Arch
Shape Dentaurum

3.Libral Traders
Euroform
4. Modern
Orthodontics
Natural Form


5. Lancer
Orthodontics

TABLE CURVE 2D
Automated curve fitting software and equation discovery
Version 5.01


Importing basic data, X and Y co-ordinate values of selected points


Linear graph joining co-ordinate points


Selecting Beta function from the list of equations


Curve fitted using Beta function


Comparing two curves overlapping them one over enother


Archform Co-ordination observed between different preformed Rectangular
Nickel titanium arch wires
American Orthodontics Natural
Arch Form 2
Asymmetric Coordination of
Maxillary and mandibular
archform

SIA Orthodontics Standard Shape
Poor Coordination of Maxillary
and Mandibular Archform

Archform Co-ordination observed between different preformed Rectangular
Nickel titanium arch wires
SIA Orthodontics Natural
Shape
Good Coordination of
archform

Ortho Organizers Nitanium
Archwires
Good Coordination of
archform

Discussion
Archwires are the vital and motivating parts of an orthodontic
appliance.
With the advent of Nickel titanium highly elastic preformed arch
wires, the clinician is often able to introduce larger cross-section wire in
the early stages of “leveling and alignment”.
An investigation was undertaken to evaluate the dental arch form
and size determined by several popular brands of Preformed
Rectangular Nickel titanium arch wires; and they were compared with
the Angle Class I normal occlusion with normal overbite, overjet and
well aligned arches described mathematically by the Beta Function.
The Beta function has been used as a mathematical model of the
human dental arch by Braun, Hnat, Fender and Legan, another study by
Noroozi (2001) has supported this.

Intercanine Width

Intermolar Width

Significant Insignificant Significant

Insignifican
t

Mandibular
arch (F)

15

0

7

8

Maxillary
Arch (F)

15

0

11

4

Mandibular
arch (M)

13

2

2

13

Maxillary
Arch (M)

14

1

9

6

Student T-test was applied to the difference between Intercanine and
Intermolar Widths between the Archwires and the Natural Archform.
The difference in the Intercanine and Intermolar width is greater for
the Females as compared to the Males.

Arch widths, measured at the canines and first molars,
determined by the Preformed Nickel Titanium Arch
wire/bracket systems were greater than those of the Natural
Human Arch Form.
The archform of the female samples is in general smaller than
the male samples. Therefore the same wires used for the male
and female samples will give greater expansion in the Female
samples.
If subsequently intercanine widths are corrected with the
stainless steel archwires, round-tripping occurs.
If these increased widths are maintained, post treatment
stability may be compromised.
An increased width will result in a decreased arch depth. This
will subsequently impact on lip support, and facial esthetics
may be affected.

Braun, Hnat, Legan 1999 evaluated the shape of some popular
nickel titanium alloy preformed arch wires. They found that the arch
forms of the preformed nickel titanium arch wires and bracket
assemblies did not emulate the natural human arch form. The average
canine width exceeded the natural canine width by 5.95 mm in the
mandibular arch and 8.23 mm in the maxillary arch.
Dr. Larry White (1978), evaluated the four popular formulae
for arch shape determination and categorized his results as “good fit”,
“moderately good fit’ and “poor fit”. His results showed that only 8% of
the Bonwill-Hawley designs could be considered as good fit, while 52%
were poor fits. The Brader designs had 12.5% good fits. Catenaries had
more 27%; good fits.
The RMDS computer-derived arch designs, impressively, had
no poor fitting designs, but had only two good fitting designs. He
concluded that no generalized, universal arch form seems to be
applicable to all of the cases.

Engel G.A. (1979) carried out a study of reliability of fit of preformed
arch wires.. In approximately 40-50% of patients, these one parameter
curved arches have a poor fit.
Felton et al did a study of computerized analysis of the shape and
stability of mandibular arch form. They concluded that customizing
arch forms appears to be necessary in many cases to obtain optimum
long-term stability because of the great individual variability.
Raberin et al (1993) studied the dimensions and form of dental
arches in subjects with normal occlusions. Five mandibular dental arch
forms were defined. The proposed forms are relatively narrow in
comparison with previous studies. They described 5 arch forms: Narrow,
Wide, Mid, Pointed and Flat.

Wire sequence advocated by McLaughlin, Bennett and Trevisi.
The Systemized Orthodontic Treatment Mechanics prescribes two wire
sequences which they call as Traditional Sequence and Recommended
sequence.
In some cases authors follow sequence B to complete the
treatment with few archwire changes. The development of Copper
nickel titanium wires, referred to as 'heat-activated' wires, provided
wires with significantly greater flexibility. As a result, these wires are
used by the authors as a substitute for three of the traditional stainless
steel wires in certain situations. They believe that the archwire
sequence shown reduceswww.indiandentalacademy.com
chair side time and increased the efficiency.

For the orthodontist, wire bending in the classical sense is all but
impossible with A-NiTi wire because they do not undergo plastic
deformation until remarkably high force is applied.
In recognition of such problems, Individualization of the archform
of some Nickel-titanium archwires has proved possible with the use of
Martensitic active alloys.
Theoretically, a localized increase in temperature should allow
adjustment of suitable preformed nickel titanium archwires. The equipment
is being developed at present, which may provide a simple and quick
method of such individualization of archform in alloy wires.
At the present state of the metallurgical art, it is difficult but
possible to accurately control the Martensitic temperature

Conclusion
The individuality of a patient’s arch form and dimensions must be
recognized and respected if a successful treatment outcome is to be
achieved.
By using Rectangular Preformed Nickel Titanium arch wires, the
clinician fails to recognize the uniqueness of arch form and size
required for a particular patient.
This may be a significant factor in contributing to post treatment
problems.
Arch form is a unique expression of individual development and
probably no universal design will ever be able to account for the
many small but significant, variations in the arch shape of
individuals.

Thank you

Correlation of Maxillary Depth, Intermolar and Intercanine Width
of Natural Archform with Curve Fit Values (Female)
57.42 32.698
Correlation of Mandibular Depth, Intermolar and Intercanine
Width of Natural Archform with Curve Fit Values (Female)
25.30, 53.88
Correlation of Maxillary Depth, Intermolar and Intercanine Width
of Natural Archform with Curve Fit Values (Male)
58.34, 33.50
Correlation of Mandibular Depth, Intermolar and Intercanine
Width of Natural Archform with Curve Fit Values (Male)
26.49, 56.04


Thank you
Leader in continuing dental education


Individualised arch form vs modified arch form / /certified fixed orthodontic courses by Indian dental academy

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