Dental arch forms /certified fixed orthodontic courses by Indian dental academy

DENTAL ARCH FORMS

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

INTRODUCTION
The basic pattern of tooth position is the arch. The
arch has long been known architecturally (as the word
architecture itself implies) as a strong, stable
arrangement. The maxillary and the mendibular teeth
are positioned on the maxilla and the mandible
respectively to produce a curve “arch” when viewed
from the occlusal surface. This form is determined gy
the underlying basel bone. Malpositioning
of
individual teeth does not alter the arch form.
However, when multiple teeth are misplaced,
irregularities and asymmetries may develop in the
arch form. Proper arch form in addition to improving
the occlusion, also contributes significantly to the
esthetic value of face.

DEFINITION OF DENTAL ARCH FORM
“Dental arch form is the arch, formed by the buccal and
facial surfaces of the teeth when viewed from their
occlusal surfaces.”


IMPORTANCE OF ARCH FORM

The arch form is important mainly from three points of
view :
•

Stability

•

Occlusion

•

Esthetics


STABILITY
From the area of Angle till date, researcher and clinicians have
unarguably accepted the relationship between dental arch form and
the stability of the orthodontic result. Donald Joondeph and Richard
Reidel in one of their nine theorems for stability have stressed on
the need to maintain the existing arch form for stability, particularly
in the mandibular arch.


OCCLUSION
Unless the teeth are aligned in a proper arch form in both the
maxillary and mandibular arches, the occlusion will not be normal.
Angle described his lines of occlusion in 1907, as one of the criteria
for normal occlusion. He described the line of occlusion as “the line
with which in form and position, according to type, the teeth must be
in harmony if in normal occlusion”.


ESTHETICS
Esthetics is the driving force for the patients to seek orthodontic
treatment. A good smile, among other things depends on how the
teeth are arranged. Teeth arranged in a proper arch no doubt
increases the smile value.


BASIC TYPES OF DENTAL ARCH FORM
Many kinds of arch forms have been described in the literature.
Majority of them fall into one of the following types :
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(1).Parabolic :

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(2).Hyperbolic :

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(3).Ellipsoidal :

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converging
(4).Square :

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(5).Omega :

It is shaped like a parabola, with an anterior
curve and slightly diverging posterior legs.
It is shaped like a hyperbola, with a flatter
anterior curve and markedly diverging
posterior legs.
It is shaped like an ellipse with a curved
anterior segment and slightly
posterior legs.
It has a flat anterior segment and relatively
parallel posterior legs.
It has a curved anterior segment and
posterior legs that converge then diverge.


DIFFERENT CONCEPTS OF ARCH FORMS
Many researchers have described a variety of arch forms. The
following six concepts may be considered as milestones in the
development of so called ideal arch forms.
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(1).
(2).
(3).
(4).
(5).
(6).
(7).

Bonwill’s concept of the arch form
Bonwill – Hawley arch form
Angel’s line of occlusion
Catenary curve of Schulhof
Brader’s arch form
Rocky Mountain Data System computer derived arch design
Individualized Ideal Arches by Larry White


BONWILL’S CONCEPT OF ARCH FORM

The question, “What is the normal arch form?”, has interested
dentists since 1885, when Bonwill attempted to establish certain
postulates for constructing artificial dentures. He noted that the
tripod shape of the mandible formes an equilateral triangle, with
the base between the condyles and the apex between the central
incisors. The average length of the sides was 4 inches, with a
variation of not maore that ¼ inch.
Bonwill emphasized the principle that “human anatomy is in
perfect consonance with geometry, physics and mechanism…. If
nature is given a fair chance to right herself, she will return to
normal standard of mathematical and mechanical precision. To do
otherwise would annihilate creation”.


BONWILL – HOWLEY ARCH FORM

Hawley in 1904, modifies the Bonwill approach an recommended that
the combined widths of the six anteriors teeth should serve as the
radius of a circle, and the teeth should be placed on that circle. From
this circle, he constructed an equilateral triangle with the base
representing the intercondylar width. The radius of the circle varied
depending on the size of the anterior teeth, so that the dimensions
differed as a function of tooth size, but arch form was constant for all
individuals. This construction was to serve as a guide for establishing
arch form, though not an absolute orthodontic treatment objective.


ANGLE’S LINE FOR OCCLUSION


Angle in 1906, described the line of occlusion as “the line of
greatest normal occlusal contact”. But in 1907, he redescribed it
as “the line with which in form and position, according to type, the
teeth must be in harmony if in normal occlusion”



The interpretation of Angle’s above statement and his intended
use became confusing. Some believed that Angle was thinking of
a line through the contact points as used for calculating arch
lengths. Others imagined a line through the centers of the clowns,
while still others used a line through a line at the middle of the
buccal surface as the circumference of each arch, such as would
be necessary for the arch wire attached to brackets.


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.
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Ricketts in 1977, studied the writings of Dr. angle and made use
of cephalometrics and computerized occlusograms. He redefined
the Angle’s line of occlusion and gave contemporary definition
as :“A distinctively individual line at the incisobuccal contact, with a
location, position and form to which the teeth must to be in its
normal occlusion”
In other words, the line of occlusion is an imaginary line through
the labioinsical and bucco occlusal contact points of the teeth.


CATENARY ARCH FORM OF SCHULHOF


The concept of catenary arch was first used by David Musich and
James Ackerman in 1973 for determining the arch perimeter. The
instrument they used to measure the arch perimeter was a modified
Boley gauge with chain incorporated in it. They named the instrument
a Catenometer.



In the year 1977, Schulhof used the same concept to explain the arch
form for the lower arch. Catenary curve is the shape that the loop of
chain would take if it were suspended by two hooks the length of the
chain and the width between the supports determines the precise
shape of the curve. When the width across the first molars is used to
establish the posterior attachments, a catenary curve fits the dental
arch form of the premolar canine incisor segment of the arch very
nicely for most individuals.


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.

Exceptions includes, patients whose arches would fall into the
prosthodontists classification of square of tapering arch forms. For
all individuals, the fit is not as the catenary curve is extended
posteriorly, because the dental arch normally curves lingually in
the 2nd and 3rd molar region

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Most of the performed archwires offered by contemporary
manufacturers are based on a catenary curve, with average
intermolar dimensions.

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Although these archwires are good starting point, it is apparent
that even if one accepts the catenary curve as ideal, their shape
should be modified if the first molar widths are unusually wide or
narrow. Modification to accommodate for a generally more
tapering or more square morphology are also appropriate, and the
second molar must be “tucked in” slightly.


BRADRER ARCH FORM


Brader in the year 1971, presented a mathematical model of dental
arch form at the annual session of the American Association of
orthodontists for which he won the prestigious Milo Hellman Research
Award of special merit. It was a great leap forward in understanding
the arch form and revolutionized the thinking about the dental arch
forms related with intra oral forces.

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It is interesting to note that he gave that mathematical model not by
his own clinical research but based on findings reported by other
researchers, like Proffit, Norton, Winders.


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Traditional belief in orthodontics was that the tongue pressure at the lip
and the cheek pressure are equal in magnitude and opposite in direction,
this Hypothesis was disproved by Lear and Moorees in the year 1969. They
stated that lingual/tongue pressure is more than lip and cheek pressure.
They even verified the time-pressure equilibrium hypothesis. This
hypothesis states that it is not just the pressure of tongue, cheek and lip
that should be considered for equilibrium but also the duration (or time) of
pressure, mathematically it can be illustrated as follows :



{E (+Pat) + (+Pbt) + (+Pct)……….} + {E (-Pxt) + (-Pyt) + (-Pzt)
………} = 0
Where P is the pressure
t is the time
a, b, c…… represents positive forces, and
x, y, z…… represents negative forces.

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Lear and Moorees also found that 24-hour muscle forces on the
dental arches is more on lingual side than on the buccal side and
said that “ ……… enigma of the relationship between dental arch
form and muscle function remains”.

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To solve this puzzle/enigma Brader hypothesized the arch form as
a trifocal ellipse and PR=C; where P is pressure in Gm/Cm2, R is
the radius of curvature of the elliptical curve at the pressure site
in mm and C is a mathematical constant.

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The trifocal ellipse, which more or less resembles a hen-egg in
longitudinal section, fitted well with many ideal untreated arches
in patients (the samples were taken from Down’s study of
variations in facial relationships, AJO, 1948).

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Secondly, he took the data from the electrodynamics study done
by Winders, which is as follows :

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-------------------------------------------------------------------------------------------------------------------------------SITE PRESSURE (gm/cm2)
-------------------------------------------------------------------------------------------------------------------------------Bucco labial
At lower 6 region
4.0
At lower 4 region
4.9
At lower 3 region
6.9
At lower 1 region
11.3

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Lingual
At lower 6 region
9.2
At lower 1 region
15.2
-------------------------------------------------------------------------------------------------------------------------------In the above sample Brader found out the radius of
curvature at given site and applied the formula, PR=C, to calculate
the mathematical constant.


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It is shown in the following table-------------------------------------------------------------------------------------------------------------------SITE P (gm/cm2) R (mm)
C
--------------------------------------------------------------------------------------------------------------------------------Bucco
labial
At lower 6 region
4.0
28.0
112.0
At lower 4 region
4.9
23.0
112.7
At lower 3 region
6.9
16.3
112.5
At lower 1 region
11.3
10.0
113.0
Lingual
At lower 6 region
9.2
12.2
112.2
At lower 1 region
15.2
7.5
112.5
--------------------------------------------------------------------------------------------------------------------


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Thus, the equation PR=C expresses the most fundamental associations
between forces and shape and reveals an inverse relation between
force and curvature; that is to say the tighter the curve the greater
Pr/unit area and the converse would follow.
To find out the tension exerted by the lips and cheeks, he
used Laplace formula for elastic container. He considered the circumora
structures as an elastic envelope and applied Laplace formula:
Pi = Pe + T (1/R + 1/R’),
where
Pi = Internal forces
Pe = External forces
T = Tension of the elastic envelope
R = Radius of curvature in horizontal plane
R’ = Radius of curvature in vertical plane
Value for Pe is 0 since the atmospheric pressure is equal
on both the sides.
R’ is not considered because its contribution is presently unknown and
may be of small magnitude for mathematical reasons.
Therefore substituting Pe = 0, and neglecting R’, we get
Pi = T/R
T = Pi * R
Brader found out that T is always equal to C.
The dental arch remains in a state of equilibrium because
the product of P and R on the lingual side(C) is always equal and
opposite to the product of P and R on the facial side(T).

CLINICAL IMPLICATIONS OF PR=C
(1).Growth of dental arches


The traditional view of growth of dental arches, with the form
considered as an open curve like the catenary where superimposed of
serial events is possible only on the single point they share in
common the medical approximal contacts of the central incisor teeth.
This view point implies little or no dimensional change in the outer
and of the arch curve; form such interpretations, restrictive
conclusions have been drawn about the movement of teeth during
Orthodontic therapy.



Taking advantage of the geometric characteristics of the closed
elliptical curve Brader suggested that the dental arches grow total
curve enlargement about geometric centers. This closed curve
concepts, he says, places the arch into different but more satisfying
architectural context with generally accepted understanding about
the growth of the face and head. But more important, a total
internally centered curve orientation provides a new method for the
reliable comparison of arch forms in both serial and cross-sectional
investigations into the nature of growth of the dental arches.

(2).Lower Incisor Crowding:


Since pressure (P) and radius of curvature (R) are inversely
related, PR=C explains why the mandibular incisor teeth
exhibit many crowded positional variations and of all the
teeth in the mouth, the least stability following positional
changes produced by orthodontic movements. It is
precisely here, in the anterior segment of the madibular
dental arch, where the radius of curvature is smallest, that
the pressure are greatest and therefore exercise the most
critical influence on tooth positions.


LIMITATIONS OF BRADER’S ARCH FORM



The Brader’s arch form explains a typical normal arch form. It
may not be applicable in different maloccusions.

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Although it fits majority of cases, there are exception to this,
they include what the Prosthodontists would call as tapering or
square arch form. In such case the arch form of the wire should
be altered accordingly.



Brader’s PR=C is just a hypothesis and not theory and it is
incompletely verified. Further, long term studies are requires to
verify the stability.

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The main clinical criticism of the Brader’s arches is that when
those forms are followed explicitly, there is often severe
narrowing in cuspid region.


COMPUTER DERIVED ARCH DESIGN
The Rocky Mountain Data System computer derived formula that
relies upon measurements taken from intermolar width, intercuspid
width and arch depth as measured from the facial surface of incisors
to the distal surface of the terminal molar. This allows the computer
to be programmed with Cartesian X and Y co-ordinates that are
necessary for a two-dimensional, computer derived formula. Facial
type is also considered in this arch computation. This arch design is
applicable only for the lower arch.


RELATIONSHIP BETWEEN FACIAL FORM
AND ARCH FORM
Most Prosthodontists believe there is a definite correlation between the
arch form and facial form. They state that dolicofacial individual have
long narrow arches; brachyfacial individuals have broad and squarish
dental arches the mesofacial individuals have arch forms which fit
somewhere in between these two and described as average.




However it must not be assumed that narrow arches inevitably go
with narrow faces and broad arches go with broad faces. In
biology, every rule has exceptions. Despite the general trend in
this direction clinical examination frequently will reveal exception
and gradations in the degree of narrowness and broadness of
dental arches, as correlated with facial type. Some
anthropologists would claim that there are so many, exceptions to
this trend that the correlation between facial form and the arch
form has only limited value.


INDIVIDUALIZED IDEAL ARCHES
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The technique of individualizing arch form was proposed by Larry
White in the year 1978

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Even though various researchers have arrived at different conclusions
while using similar data, a review of literature shows that most have
labored under at least three common presumption:-



There must be algebraic or geometric formula to determine ideal arch
form.

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Every ideal arch form must adhere to a generalized scheme; that is, a
form that is of some quality differing only in size.

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Every arch is considered to be symmetrical, this last presumption is
directly related to mathematical equation used, which make it
impossible to produce asymmetry. Equations are by definition, equal
values.

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White undertook a study to see how a collection of ideal untreated
arches conformed to the predetermined arch forms of the most
popular formula and to come to conclusions, if possible about how
reasonable, ideal arch forms can be derived for individual
patients.

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Dental casts of 24 orthodontically untreated superior adult
occlusions were collected, tracings of the teeth were made on
acetate papes and overlays were super imposed, the closeness of
fit was evaluated and graded as “good fit”, “moderately good fit”
and “poor fit”. The evaluation was of course, subjective and not
without some degree of error

.
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Yet the results were interesting (shown in the table)


Table 1 – 24 untreated superior adult occlusion evaluated for fit various arch
designs :----------------------------------------------------------------------------------------Good Fit
Moderately Good Fit
Poor Fit
----------------------------------------------------------------------------------------Bonwill-Hawley 4 (8.33%)
19 (39.53%)
25 (52.08%)
Brader

6 (12.50%)

21 (43.75%)

21 (43.75%)

Catenary

3 (27.08%)

22 (45.83%)

13 (27.08%)

RMDS
2 (8.33%)
22 (91.67%)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------


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Only 8% of Bonwill-Hawley designs couls be considered a bood fit,
while 52% were poor fits. The Brader designs has two more good
fits, but the percentage was still low at 12.5%. Catenaries had
more good fits than the previous two combined, but the
percentage was still only 27% and there was an equal percentage
of poor fits. The RDMS computer derived arch designs
impressively, had no poor fitting designs. Since lower arches are
computed by RMDS, the sample number is one half that of the
other designs 92% of the RMDS designs were judged to be
moderately good fits.


Absence of arch symmetry

White also evaluated the symmetry of the arches of the ideal
orthodontically untreated models. The most conspicuous finding was
that total absence of true arch symmetry among his collection of
models. Each occlusal tracing was copied onto graph paper and set
within a rectangle to study arch symmetry. Symmetry displayed by
the arches was scored at ‘symmetrical’, ‘moderately symmetrical’ and
‘asymmetrical’. Tabulation showed only 6.25% were evaluated as
symmetrical.


Table – 2
------------------------------------------------------------------------------Symmetrical
Moderately Symmetrical
Asymmetrical
--------------------------------------------------------------------------------------------------------------------------------------------------Number
3
27
18
Percent
6.25%
56.25%
37.5%
-----------------------------------------------------------------------------------------------------------------------------------------------------------By the above observations he came to two conclusions:
No generalized, universal arch form seems to be applicable.
Majority of normal arches are asymmetrical.


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Because of these two observations, White advocated
individualizing arches to the patients by a simple technique called
“occlusal mapping”. The technique involved drawing an outline of
occlusal surfaces of all the teeth on a piece of acetate paper from
an occlusal x-ray. Photo or the study cast. On this the contact
points are marked.



A dotted line is drawn through the masidosital dimension of each
and connecting the lines across the proximal contacts. This line
will represent the center of the basic arch perimeter that is
available for the support of the teeth. The occlusal shape of each
tooth can then be traced in an ideal position on this basic arch and
a customized ideal arch form can be constructed and used
through out the treatment.


PHYSIOLOGIC ARCH FORMS
Charles Oakes and James Hatcher Dallas, Texas (JCO
1991)
Determining arch form is one of the most misunderstood and
neglected aspects of orthodontic treatment. The arch form,
especially in the mandible cannot be permanently expanded by
appliance therapy. There is a lack of stability in both intercanine
and intermolar width after expansion.
Today, many treatment modalities are aimed at widening the arch
as a means of avoiding extractions. Orthodontists might be well
advised to work within the tested limits.


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With few exceptions, the mandibular model with all permanent
teeth present provide the best basis for construction of a correct
or “physiologic” arch form. The arch form can easily be
determined from an initial model as follows.
Attach small beads, representing the ideal bracket positions to the
mandibular model with toothpaste.
A piece of clear glass, plastic or even acetate paper is placed over
the model.
Viewing the model from directly overhead, transfer the bead
positions to the glass, plastic or acetate paper with a permanent
marker.
Remove the glass / plastic / acetate paper from the model and
connect the dots as symmetrically as possible.
Place the lower arch wire directly over the traced arch form. Bend
the upper wire to lie outside the traced arch form.
Physiologic arch forms are difficult to construct in cases with
severe intercanine construction. If the intercanine width is
maintained in such case, the arch form will be unacceptable. In
these cases, expansion is necessary and retainer is encouraged.


THE FORM OF THE HUMAN DENTAL ARCH
Stanley Braun et al
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The human dental arch form is shown to be accurately represented
mathematically Forts sets of casts – 15 Class I, 16 Class II and 9 Class III
– were examined. A precision machine tool was used to record the x, y
and z coordinates of selected dental landmarks on all casts. The
coordinates were processed through a computer curve-fitting programme.
The were as follows :
The Class III mandibular arches had smaller arch depth and greater arch
width (beginning from the premolar area) than the class I arches.
The Class II mandibular arches exhibited generalized reduced arch width
and depth compared with Class I arches.
Maxillary arch depths were similar in all three groups.
The Class III maxillary arch width were greater from the lateral incisorcanine area distally compared with the Class I maxillary arch.
The Class II maxillary arch form was narrower than the Class I arch form
from the lateral incisor-canine area distally.


ARCH SIZE AND FORM IN UNTREATED
ADULTS


Edward Harris, Memphis (AJO, 1997)



Adulthood - the lengthy phase following attainment of biologic
maturity – often is perceived as a period of “no change”, or one of
slow deterioration. Recent skeletodental studies discount this
stereotype.Teeth consolidate during the adolescent age interval,
apparently by mesial drift, and the arch length decreases. Arch widths
also change with age, but the magnitude of the change is smaller.
Changes in arch size and shape were studied in 60 adults with intact
dentitions. Full mouth models were taken at about 20 years of age
and again 55 years of age.
Some variables – particularly those between arches (incisor overbite
and overjet, molar relationship) and mandibular intercanine measures
of arch width and length changed significantly. Arch widths increased
over time, especially in distal segments, whereas arch lengths
decreased. These changes significantly altered arch shape towards
shorter-broader arches. The data suggests that changes during
adulthood occur most rapidly during the second and third decades of
life, but do not stop thereafter.

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CONCLUSION

A study of any aspect of orthodontics immediately involves the problem of
variations in size of structures, variations in the form of parts, variations
in functions; and the dental arch form is no exception to this.
The form and size of dental arches is influenced at least by four factors.
Firstly, the skeletal parts may not be harmonious or in proportion, and
this will mean that appropriate compromises will be indicated from
otherwise ideal relations. Secondly, functional problems may alter the oral
environment when muscle structure itself may be inadequate. Thirdly,
psychologic factors may be present, causing prolonged habits and
fourthly, discrepancies in tooth size and tooth form may alter an
otherwise harmonious situation.
Because of these complex problems, there is no universally accepted arch
form. The irony is that, the more we know about a particular subject, the
more our ignorance unfolds and the goal seems farther ahead.
Accepting there is no generalized, universal, ideal arch form, the question
remains, “to which arch form should we treat our patients?”. To answer
that, I would like to quote none other than the Father of Modern
Orthodontics, Dr. Edward H. Angle. He made this statement nearly eight
decades ago and it is still relevant today.
“The best Orthodontists can do is to secure normal relations of the teeth
and correct general form of the arch, leaving the finer adjustments to
individual typal form to be worked out by nature through her forces,
which must, in any event, finally triumph”.

REFRENCES
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Begole EA et al. Analysis of change in arch form with premolar
expansion. Am J orthod 1998 ; 113: 307-15.
Brader AC. Dental arch form related to intraoral forces, PR=C.
Am J Orthod 1972 ; 61: 541-562.
Braun S et al. The form of the human dental arch. Angle Orthod
1998 ; 68:29-36.
Musich DR, and Ackerman JL. The catenometer: A reliable
device for estimating arch perimeter. Am J Orthod 1973 ; 63:
366-375
Oakes C, Hatcher JE. Determining physiologic arch forms. J Clin
Orthod 1991 ; 25:79-80
Wheeler RC. A textbook of Dental Anatomy, physiology and
occlusion. 7th ed. W.B. Saunders Co. 1993 ; 418-420.
Valiathan A, Oberoi S. Dental Arch Forms. KDJ 1996 ; 19(2):
39-42

White LW. Individualized ideal arches. J Clin Orthod
1978 ; 12:779-87.


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