Download A new concept of mandibular dental arch forms with normal occlusion

ONLINE ONLY
A new concept of mandibular dental arch
forms with normal occlusion
Tarcila Triviño,a Danilo Furquim Siqueira,b and Marco Antonio Scanavinic
São Paulo and Niterói, Brazil
Introduction: Because it is important to maintain dental arch dimensions during orthodontic therapy, all
possible dental arch forms must be evaluated. Methods: A mathematical method associated with a
polynomial function was used to evaluate the dental arch forms of 63 mandibular models of Brazilian
adolescents in the permanent dentition with normal occlusion. A bead was glued to each tooth to simulate
an orthodontic accessory and help in the measurement of distances between the center of the bead to the
x- and y-axes. The dental casts were digitized, and images were plotted on a computer program to obtain
the sixth-degree polynomial and the graph of this function. These segments were organized into 8 groups
according to the form of the anterior curve of the dental arch; these were named forms A through H. Each
group was subdivided into 3 subgroups: small, medium, and large sizes. Results: Form A was the most
frequently observed at 22%, whereas form G was observed in only 2% of the total sample. Forms A, B, C,
D, E, and F had more curve segments in medium size, and forms G and H had more curves in small size. A
mean dental arch curve was calculated; however, this form coincided with form C, which had an incidence
of 10%. Conclusions: The mandibular dental arch is represented by 23 forms; thus, a normal dental arch
cannot be represented by only 1 simple arch form. (Am J Orthod Dentofacial Orthop 2008;133:10.e15-10.e22)
T
he dental arch, an important element in orthodontics, is a fundamental principle in orthodontic planning and therapy.1,2
A dental arch form is initially established by the
configuration of the bony ridge and then by tooth eruption,
perioral muscles, and intraoral functional forces.
Even though most patients with a malocclusion
have an altered dental arch form, the alterations
achieved with mechanics during orthodontic treatment
should not affect the balance between bone and dental and
muscular structures; the arrangement of these structures
adjacent to teeth and jaws should be considered the limit
for orthodontic movement.1,3-5 To minimize some of
these factors, specialists have investigated the most effective approach for the correct repositioning of teeth to
provide esthetics, function, and stability, and to define the
size and configuration of the dental arch.
Initially, some authors advocated the use of dental
casts in which the alveolar ridge form would be the
From Methodist University of São Paulo, São Bernardo do Campo, São Paulo,
Brazil.
a
Master degree in orthodontics, Methodist University of São Paulo; specialist in
orthodontics, Federal Fluminense University, Niterói, Rio de Janeiro, Brazil.
b
Professor, postgraduate program in orthodontics.
c
Professor and coordinator, postgraduate program in orthodontics.
Reprint requests to: Tarcila Triviño, Av. Nove de Julho, 5483, conj. 111,
Jardim Paulista, São Paulo, SP, Brazil, CEP 01407-200; e-mail, tarcilatrivino@
uol.com.br.
Submitted, April 2006; revised and accepted, July 2007.
0889-5406/$34.00
Copyright © 2008 by the American Association of Orthodontists.
doi:10.1016/j.ajodo.2007.07.014
reference for the fabrication of archwires, thus avoiding
changes in the transverse dental arch dimensions.6,7 Because handling the dental casts might not be practical and
fractures often occurred in these diagnostic elements,
many authors attempted to find a representation of the
dental arch that would allow immediate success, durability, and precision, suggesting the use of prototypes or
references to help the professional during orthodontic
therapy and provide the parameters for fabricating archwires or selecting preformed ones.2,6,7-11
Basically, the standards established comprised description of the dental arch form by geometric figures
such as catenary curve,12,13 parabolic curve,14,15 ellipse,14-17 hyperbola,14 or even a semicircle joined to
straight segments.9,18,19 From these representations,
diagrams were developed on the basis of measurements
of dental arch components that would act as a guide
during orthodontic treatment, because the use of a
customized diagram would provide archwires with
standardized forms and dimensions.8-10,16-19
However, the use of diagrams describing an average or ideal dental arch form was counterindicated
when some authors observed that the dental arch curve
was represented or defined not only by a geometric
shape, but also by several configurations.15,20-26
The various descriptions of dental arch forms in
several studies might be related to the application of
algebraic or geometric functions associated with computations that increased the accuracy of the dental arch
10.e15
10.e16 Triviño, Siqueira, and Scanavini
representation.15,21,22,25-31 Some authors who observed
that polynomial functions could describe the dental
arch form in a simple and symmetric manner accepted
these mathematical equations as an accurate method for
the description of dental arch configurations.26,30,32-38
Because the original mandibular dental arch form
and dimensions should be respected during orthodontic
therapy and because of controversy about dental arch
configuration among authors using various methodologies, in this study, we attempted to establish mandibular
dental arch forms with a precise method applied to an
adequate sample; this would enhance the construction
and use of standardized archwires and, consequently,
allow the orthodontist to obtain and maintain ideal
results after orthodontic treatment.1,3
MATERIAL AND METHODS
Our study sample included 63 subjects (35 female,
28 male) carefully selected from 6118 white Brazilian
adolescents between 12 and 21 years old at Methodist
University of São Paulo who were in permanent dentition, with all teeth in occlusion except for the third
molars, and normal occlusion with at least 4 of the 6
keys to normal occlusion as defined by Andrews.39
Interarch relationship (Andrews’ first key39) should be
present in all cases.
Mandibular dental casts for the subjects were obtained, and, in each tooth, from the left second molar to
the right second molar, a glass bead was glued to
simulate the ideal position of an orthodontic brace. All
beads were initially measured with a pachymeter
(model Zurich; Dentaurum, Ispringen, Germany) to
ensure that the diameter was 1.5 mm (⫾ 0.1 mm).
Each glass bead was positioned in the center of the
clinical crown of the incisors, canines, and premolars,
and in the middle third of the mesiobuccal cusps in the
first and second molars.
After bonding the glass beads, which were red to
enhance observation in the grayscale images, dental
casts were digitized on a scanner (Scanjet 6100C;
Hewlett-Packard, Palo Alto, Calif), and images with
300 dpi resolution in TIFF format were obtained. The
position of the dental casts on the scanner was established with millimeter acetate paper, especially designed for this methodology; it was made by photocopying a sheet of millimeter paper on ordinary acetate
paper. After making the photocopies, the prepared
acetate and millimeter papers were superimposed to
verify the lack of distortion in the acetate copy.
The customized acetate paper was placed between
the scanner glass surface and the occlusal plane of the
dental cast, so that the posterior edge of the dental cast
would coincide with the abscissa axis (x) and the dental
American Journal of Orthodontics and Dentofacial Orthopedics
January 2008
Fig 1. Representation of the Cartesian system and the
x and y measurements corresponding to the points
used to establish dental arch form: 7 and 14, distance
between points of the second molars to the x- and
y-axes; 6 and 13, distance between points of the first
molars to the x- and y-axes; 5 and 12, distance between
points of the second premolars to the x- and y-axes; 4
and 11, distance between points of the first premolars
to the x- and y-axes; 3 and 10, distance between points
of the canines to the x- and y-axes; 2 and 9, distance
between points of the lateral incisors to the x- and
y-axes; 1 and 8, distance between points of the central
incisors to the x- and y-axes.
midline with the ordinate axis (y), creating a Cartesian
system.
The arch images of the 63 mandibular dental casts
were divided into right and left sides, and the mirror
method was applied to these hemiarches; this resulted in
symmetric dental arches, for a total of 126 curve segments.26 The mirror method was used because the
geometric figures that would represent the dental arch
form, such as parabolic curve, ellipse, hyperbola, and
others, are symmetric mathematical representations,
and, even though dental casts were obtained from
subjects with normal occlusion, there can be asymmetry between the right and left sides of the dental arch.
With projection of the cast images on a flat computer screen with the software Corel Photo Paint 10
(Corel Corp, Ottawa, Ontario, Canada) with 100%
magnification, the origin of the Cartesian system
adapted to the image of the dental cast (point of contact
between abscissa x and ordinate y, whose value is zero)
was established in the line corresponding to the projection of the interincisal point (dental midline) on axis x.
For each image cast, 14 points (x, y) on the dental
arch were measured by the distance between the center
of glass-bead images to the abscissa axis and ordinate
axis, respectively (Fig 1). The centers of the 1.5-mm
Triviño, Siqueira, and Scanavini 10.e17
American Journal of Orthodontics and Dentofacial Orthopedics
Volume 133, Number 1
Table I.
x7, values, class amplitude (CA), and mathematical intervals
Form
Highest x7
Lowest x7
Difference
CA
Interval 1
Interval 2
Interval 3
A
B
C
D
E
F
G
H
3.10
3.15
3.15
3.15
3.10
3.00
2.90
3.15
2.60
2.50
2.60
2.40
2.60
2.50
2.70
2.45
0.50
0.65
0.55
0.75
0.50
0.50
0.20
0.70
0.15
0.20
0.15
0.25
0.15
0.15
0.05
0.20
2.60-2.75
2.50-2.70
2.60-2.75
2.40-2.65
2.60-2.75
2.50-2.65
2.70-2.75
2.45-2.65
2.80-2.95
2.75-2.95
2.80-2.95
2.70-2.95
2.80-2.95
2.70-2.85
2.80-2.85
2.70-2.90
3.00-3.15
3.00-3.20
3.00-3.15
3.00-3.25
3.00-3.15
2.90-3.05
2.90-2.95
2.95-3.15
diameter beads were used to simulate the distance from
the bracket slot base to the buccal aspect of the teeth,
which is about 0.75 mm.
The computer software Curve Expert (version1.3;
http://curveexpert.webhop.biz) was used to choose the
polynomial function that would best describe the curve
corresponding to the dental arch form. By visual
evaluation of graphic representations of various mathematic functions provided by the computer software,
the sixth-degree polynomial was selected to establish
the dental arch form, because this polynomial function,
represented by the equation y ⫽ ax6 ⫹ bx5 ⫹ cx4 ⫹ dx3
⫹ ex2 ⫹ fx ⫹ g, provided the best description of the
curve representing the form of these dental arches.
Measurements of coordinates (x, y) of the 14
Cartesian points of the 126 curved segments were then
plotted on the software Curve Expert to obtain the
sixth-degree polynomial function for each curve segment, ie, the values of ratios a, b, c, d, e, f, and g, as
well as the graphic representations. After this, data of
the curve segments from the software were printed on
white paper (75 g per square millimeter), illustrating
the real size of the dental arches in the casts. The papers
with the graphic representations of the curve segments
were placed on a light box to allow better observation
of the characteristics of the intercanine region of each
dental arch, enhancing observation of the coincidence
of the anterior curve between curve segments.
According to the characteristics and similarities of
the anterior curves, the 126 curve segments were
divided into 8 groups to establish the various dental
arch types and configurations. Division into groups
allowed observation of the most prevalent dental arch
form in the sample; the arithmetic mean applied to the
x and y values of the curve segments of each group
allowed achievement of mean x and y values for the 14
points of the average curve representing each dental
arch form (8 forms, called A through H).
Then, small, medium, and large sizes were determined for each group of dental arch forms by division
of the curve segments of each group into 3 mathemat-
ical intervals, established according to the class amplitude value (used in a distribution of frequencies, it is
the difference between upper and lower limits in the
same class), which was calculated as the distance from
the second molar to the y-axis, because this value—
x7—represents the width of the most posterior region in
the dental arch. These values were organized in ascending order, and the class amplitude value was obtained
by subtraction between the highest and lowest x7 values
of each group and divided by 3 for the 3 dental arch
sizes, represented by the 3 subgroups (Table I, Fig 2).
The minimum value of the first subgroup corresponded to the lowest x7 value of the respective dental
arch form group, and the maximum value of this
interval was obtained by adding the class amplitude
value of the respective group to the minimum or lowest
x7 value. In the second interval, the minimum value
was established by adding 0.05 mm to the maximum
value of the previous interval or subgroup 1, and the
maximum value of the second interval was established
by adding the class amplitude value to its minimum
value. The third interval was obtained with the same
procedures to establish the second interval or subgroup
(Table I).
After establishing the subgroups, the curves of each
dental arch form group were divided into 3 established
sizes according to their x7 values, and, by applying the
arithmetic mean to the x and y values of curve segments
of each interval, the average curves representing the 3
subgroups (small, medium, and large) were obtained
for each group of dental arch forms.
To establish the average curve of a normal dental
arch, 14 mean x values and 14 mean y values were
calculated based on the arithmetic mean of all x and y
values of the 126 curve segments organized in a table;
this provided the positions of the Cartesian points to
establish the possible form of a dental arch with normal
occlusion.
For the graphic representations of average curves
calculated for the groups, subgroups, and normal occlusion, the mean x and y values of each group and the
10.e18 Triviño, Siqueira, and Scanavini
American Journal of Orthodontics and Dentofacial Orthopedics
January 2008
Figure 2 is a graphic representation of the dental
arches in our sample, in small, medium, and large sizes.
The medium size of form G is shown as a dotted line
because it is a superimposed curve, since in the study
sample there was not a curve segment corresponding to
subgroup 2.
The results of the evaluation of error of the visual
classification of the 126 curve segments showed a high
index of agreement of our methodology, with a P value
of 95.24%; only 6 curve segments were not equally
scored in the 2 evaluations by the examiner (T.T.).
With regard to the error of measurement of the x and y
values, the results of evaluations of systematic error
with a paired t test and the casual error measured with
the Dahlberg formula40 are given in Table IV, in which
no P values were less than .05 and the casual errors
were near zero, showing the accuracy of this method.
DISCUSSION
Fig 2. Graphic representations of the 8 dental arch
forms for natural normal occlusion, in small, medium,
and large sizes.
corresponding subgroup, as well as the possible form
representing the dental arch with normal occlusion,
were plotted in the software Curve Expert to obtain the
corresponding polynomial function and its graphic
representation, and to illustrate their forms.
RESULTS
Table II gives the mean values and corresponding
standard deviations of the x and y values of points in
curve segments representing dental arch forms A to H
and also the mean x and y values of the 14 points
representing the teeth and corresponding standard deviations. These values allowed establishment of a
possible “ideal” form for a dental arch with natural
normal occlusion, illustrated in Figure 3, A.
Table III shows the quantitative and percent incidence of thecurve segments according to sex and the
quantitative incidence of these curve segments and
corresponding percentages in the 3 subgroups of the 8
groups of dental arch forms.
In the literature, there is much diversity among authors
in the choice of reference points to evaluate dental arch
forms and dimensions: cusp tips,2,14,22,27-29,31,33,36,37 contact points,10,20 alveolar bone ridges,6,7 mesiodistal widths
of anterior teeth,9,10,18,19 and cranial structures.16,18 However, as in other studies, we selected labial and buccal
dental surfaces to determine representations or drawings of curve segments that would simulate the
archwires to be inserted into bracket slots or used as
a template for archwire fabrication during orthodontic treatment.10-12,17,21,26,30
Some studies have demonstrated the quality of the
fourth-degree polynomial to establish the dental arch
form,30,32,33,36,37 whereas Hechter35 advocated the use
of a simpler second-degree polynomial. Nevertheless,
Ferrario et al36 and Wakabayashi et al37 observed that
the higher the degree of the polynomial, the most
precise the graphic description of the dental arch.
The sixth-degree polynomial equation was the
function that best described dental arch configuration,
since polynomial functions with lower degrees compromised the descriptions of some important dental arch
regions, such as anterior curvature of the mandibular
arch, which is determined by intercanine distance, and
posterior tooth alignment,8,20,24 whereas polynomials
higher than the sixth degree had graphic representations
of the curve of the dental arch form with a wavy, rather
than smooth, tendency.
In our sample of 126 curve segments from 63 dental
casts, we identified more than the 3 dental arch forms
for Brazilians with natural normal occlusion found by
Telles23 and McLaughlin et al.24 Interpretation of the
curves provided by the Curve Expert showed that curve
morphology in the anterior region has 8 forms, which
Triviño, Siqueira, and Scanavini 10.e19
American Journal of Orthodontics and Dentofacial Orthopedics
Volume 133, Number 1
Table II.
Mean x and y values and corresponding standard deviations of curve segments of the 8 forms and the
average curve
Form A
Measurements Mean
x7 and x14
x6 and x13
x5 and x12
x4 and x11
x3 and x10
x2 and x9
x1 and x8
y7 and y14
y6 and y13
y5 and y12
y4 and y11
y3 and y10
y2 and y9
y1 and y8
2.81
2.49
2.24
1.96
1.51
0.88
0.29
1.62
2.67
3.38
4.09
4.73
5.12
5.28
Form B
Form C
Form D
Form E
Form F
Form G
Form H
Average
curve
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
0.13
0.10
0.10
0.10
0.07
0.06
0.05
0.28
0.30
0.30
0.32
0.33
0.34
0.35
2.83
2.50
2.26
2.00
1.56
0.88
0.29
1.64
2.71
3.41
4.14
4.80
5.18
5.33
0.17
0.14
0.14
0.13
0.09
0.07
0.05
0.27
0.33
0.31
0.32
0.30
0.32
0.33
2.87
2.58
2.30
2.00
1.53
0.90
0.29
1.59
2.68
3.38
4.08
4.72
5.14
5.30
0.15
0.13
0.10
0.07
0.06
0.03
0.04
0.27
0.28
0.31
0.27
0.25
0.23
0.23
2.83
2.56
2.32
2.05
1.53
0.88
0.28
1.52
2.62
3.28
4.00
4.68
5.05
5.21
0.19
0.14
0.15
0.11
0.08
0.05
0.04
0.21
0.22
0.22
0.22
0.26
0.28
0.28
2.87
2.49
2.16
1.89
1.45
0.86
0.29
1.67
2.75
3.47
4.14
4.76
5.18
5.36
0.11
0.09
0.11
0.08
0.05
0.04
0.03
0.23
0.27
0.25
0.27
0.29
0.29
0.29
2.78
2.51
2.23
1.91
1.48
0.88
0.28
1.56
2.64
3.34
4.02
4.65
5.08
5.26
0.13
0.12
0.12
0.07
0.09
0.06
0.04
0.16
0.19
0.20
0.21
0.23
0.24
0.25
2.77
2.50
2.17
1.83
1.40
0.83
0.32
1.88
2.93
3.58
4.25
4.88
5.27
5.50
0.09
0.07
0.13
0.06
0.11
0.05
0.05
0.27
0.24
0.20
0.18
0.16
0.08
0.07
2.71
2.52
2.28
1.95
1.49
0.87
0.28
1.55
2.65
3.32
4.04
4.67
5.05
5.23
0.17
0.18
0.15
0.11
0.08
0.05
0.03
0.26
0.28
0.27
0.23
0.25
0.26
0.28
2.80
2.52
2.25
1.96
1.50
0.88
0.29
1.60
2.68
3.37
4.08
4.72
5.12
5.29
0.16
0.14
0.14
0.11
0.09
0.06
0.04
0.26
0.28
0.28
0.28
0.28
0.29
0.30
Fig 3. A, Graphic representations of average forms of
natural normal occlusion, obtained by the arithmetic
means of x and y values of the 126 curve segments;
B, superimposition of mean normal form (blue) and
form C (black).
were organized in groups and named forms A, B, C, D,
E, F, G, and H; this agreed with some studies that the
application of the sixth-degree polynomial to establish
the dental arch form showed that the dental arch cannot
be represented by a simple geometric shape such as a
parabolic curve, hyperbola, ellipsis, or catenary curve
(Fig 2).26,30,34
According to the results, form A has similar characteristics to forms observed by Engel13 and Raberin
et al,22 with flattening of the anterior curve region and
the origin of the curvature at the distal region of the
lateral incisors. In agreement with the incidence of
18.4% observed by Raberin et al,22 form A had 28
curve segments, representing 22% of the total sample,
and was the most frequent form in subjects with normal
occlusion.
The curve representing form B showed a similar
configuration as form A—ie, mandibular incisors arranged in a straight line. However, its intercanine
distance was slightly wider than in form A. Form B is
considered esthetically unpleasant by orthodontic specialists because it causes a tight, narrow smile.41 This
form is rarely found in the literature, except for the report
of Triviño and Vilella,26 who observed a frequency of
31.2%, which was the predominant form in that study. In
our study, form B had a medium incidence value—15%
of the sample, or 19 curve segments.
With opposite graphic aspects to the aforementioned forms, in form C, the anterior teeth are
roundly arranged, as in an ellipsis, also described by
other diagrams.10,13,16,21-24 Even though its incidence reached medium values (10% of the total
10.e20 Triviño, Siqueira, and Scanavini
American Journal of Orthodontics and Dentofacial Orthopedics
January 2008
Table III. Quantitative distribution of curve segments and corresponding percentages according to sex in the 3
subgroups of the 8 groups of dental arch forms
Female
Male
Subgroup 1
Subgroup 2
Subgroup 3
Form
n
%
n
%
n
%
n
%
n
%
A
B
C
D
E
F
G
H
12
11
8
7
9
9
2
12
43
58
67
64
64
56
67
52
16
8
4
4
5
7
1
11
57
42
33
36
36
44
33
48
4
5
2
2
2
5
2
11
14.3
26.3
16.7
18.2
14.3
31.3
66.7
47.8
13
10
6
7
10
7
0
10
46.4
52.6
50.0
63.6
71.4
43.8
0.0
43.5
11
4
4
2
2
4
1
2
39.3
21.1
33.3
18.2
14.3
25.0
33.3
8.7
Table IV.
Arithmetic means and standard deviations of measurements in both evaluations, paired t test, and Dahlberg
error analysis
Evaluation 1
Evaluation 2
Measurements
Mean
SD
Mean
SD
P
Casual error
x7 and x14
x6 and x13
x5 and x12
x4 and x11
x3 and x10
x2 and x9
x1 and x8
y7 and y14
y6 and y13
y5 and y12
y4 and y11
y3 and y10
y2 and y9
y1 and y8
2.76
2.47
2.22
1.93
1.47
0.87
0.28
1.58
2.67
3.36
4.04
4.68
5.08
5.26
0.14
0.12
0.11
0.09
0.08
0.06
0.05
0.23
0.24
0.26
0.26
0.27
0.28
0.29
2.76
2.46
2.22
1.93
1.47
0.86
0.29
1.58
2.67
3.36
4.04
4.68
5.08
5.26
0.14
0.12
0.10
0.09
0.07
0.07
0.06
0.24
0.24
0.26
0.26
0.28
0.28
0.29
.33
.16
1.00
1.00
.33
.33
.33
.33
1.00
.33
1.00
.16
.58
.33
0.007
0.000
0.011
0.000
0.000
0.015
0.007
0.007
0.000
0.007
0.011
0.011
0.011
0.007
sample, or 12 curve segments), form C was the most
often observed by Ricketts21 and Telles,23 representing 37.5% and 63.75% of their samples, respectively.
The anterior region of form D is analogous with
form C, although this form has a greater intercanine
distance, and the incisors are positioned nearly in a
plane, giving a quadrangular configuration for this
form. Some authors observed similar forms in their
studies,13,24,26 whereas others developed diagrams that
established this dental arch form as ideal.10 In our
study, only 9% of the sample, or 11 segments of curve,
had this arch form; this agreed with other findings.26
Similar to the morphology of diagrams suggested
by Bonwill,18 Hawley,9 and Sved,19 form E has a
semicircular arrangement of the anterior teeth; therefore, the posterior region is not strictly straight. This
form was observed in 14 curve segments (11% of our
sample), differing from the incidence values found by
Raberin et al22 (23.7%) and Telles23 (16.25%).
Form F was observed in 16 curve segments, or 13%
of the total sample; this is an example of a catenary
curve described by other authors.10,12,13,20-24,26 The
results of studies by Ricketts,21 Telles,23 Raberin
et al,22 and Triviño and Vilella26 showed that this form
has medium prevalence (15%, 20%, 18.7%, 24.2%,
respectively) in the subjects analyzed.
The curve segments representing form G illustrate a
pointed anterior region like a groin. This was an
infrequent dental arch configuration, observed in only 3
curve segments, accounting for 2% of the total sample
of normal occlusion. This incidence was different from
the results of Raberin et al22 and Triviño and Vilella,26
who found medium values of 19.4% and 12.4%, respectively.
Form H was not commonly observed in previous
studies, but it is similar to the shape of archwires
advocated by Angle,42 Chuck,43 and Boone.44 Form H
has a morphology that describes the projection of the
Triviño, Siqueira, and Scanavini 10.e21
American Journal of Orthodontics and Dentofacial Orthopedics
Volume 133, Number 1
mandibular central incisors and had the second highest
frequency in this study, observed in 23 curve segments,
or 18% of the sample, an incidence similar to the results
of Triviño and Vilella,26 who also observed a significant frequency (23%).
Based on Table III, subgroup 2 (medium size) had
the most curve segments in forms A (46.4%), B
(52.6%), C (50.0%), D (63.6%), E (71.4%), and F
(43.8%), whereas forms G (66.7%) and H (47.8%) had
a higher incidence of subgroup 1 (small size), even
though form G had no segment in subgroup 2 because
of our sample size. These results might be related to the
anterior curve of each dental arch form. Forms G and H
had pointed alignments of the incisors, with a smaller
distance between homologous teeth at the canine region, and reduced sizes and more components with
small size, as also observed for form F, which had a
high incidence in subgroup 1 (31.25%).
As stated by some authors, medium-sized dental
arches are generally predominant in normal occlusion;
according to the results, there were 63 curve segments
in subgroup 2, or 50% of the total sample.8,21,26
With regard to the incidence of forms evaluated
according to sex, all groups of forms included both
sexes. As in the studies of Raberin et al22 and Triviño
and Vilella,26 forms A, B, F, and H had homogeneous
distributions between the sexes.
Our extensive literature review and results suggested the need to inform orthodontic specialists about
the representative forms of normal occlusion, in case
they believe that there is an ideal form for this type of
dental arch. Application of arithmetic means of x and y
values of the 126 curve segments showed a possible
average form for normal occlusion (blue) that is similar
to the curve representing form C (black), as shown in
Figure 3, B, which illustrates the superimposition of
these 2 arch configurations. However, form C had a low
incidence (10%) in our sample of normal occlusion; it
was the sixth group of dental arch forms in increasing
order.
Therefore, establishing the “ideal” form for the
normal dental arch no longer needs to be the objective
in future studies, since our results show that a normal
dental arch cannot be represented by a single form but,
rather, by 8 forms with 3 sizes in each. Since form G
had no segments in subgroup 2 because of the small
sample, we established 23 possible mandibular dental
arch forms.
The establishment of 8 configurations for the dental
arch in 3 sizes allows more accurate individualization
of form and dimensions, thus reducing the occurrence
of errors in the selection of the best form for a
patient.2,8,11,17,26 These configurations also permit the
fabrication of preformed archwires with the most common
dental arch forms or templates to help in the manual
contouring of archwires, eliminating the need to use dental
casts during orthodontic treatment and consequently reducing the possibility of fracturing them.
CONCLUSIONS
According to our results, the mandibular dental arch
can be represented by 8 forms. There is not 1 ideal or
representative form of normal occlusion. Most arch
forms were medium size, and the incidence of the 8
groups of forms according to sex was homogeneous.
REFERENCES
1. Strang RHW. Factors of influence in producing a stable result in
the treatment of maloclusion. Am J Orthod Oral Surg 1946;32:
313-32.
2. Ricketts RM. A detailed consideration of line of occlusion.
Angle Orthod 1978;48:274-82.
3. Strang RHW. The fallacy of denture expansion as a treatment
procedure. Angle Orthod 1949;14:12-22.
4. Lear CSC, Moorrees CFA. Bucco-lingual muscle force and
dental arch form. Am J Orthod 1969;56:379-93.
5. Vaden JL, Dale JG, Klontz HA. The Tweed-Merrifield edgewise
appliance: philosophy, diagnosis and treatment. In: Graber MT,
Vanarsdall RLJ. Orthodontics: current principles and techniques.
2nd ed. St. Louis: Mosby; 1994:579-635.
6. Strang RHW. Factors associated with successful orthodontic
treatment. Am J Orthod 1952;38:790-800.
7. Andrews LF, Andrews WA. The syllabus of the Andrews®
orthodontic philosophy. 9th ed. San Diego: L. F. Andrews
Foundation; 2001. p. 7-29.
8. Interlandi S. New method for establishing arch form. J Clin
Orthod 1978;12:843-5.
9. Hawley CA. Determination of the normal arch and its application
to orthodontia. Dent Cosmos 1905;47:541-52.
10. Monti AE. Textbook of orthodontics. 3rd ed. 1958. Editorial “El
Ateneo”; Buenos Aires: p. 221-36.
11. Capelozza L Jr, Capelozza JAZ. OAID: Objective anatomic
individual diagram. A proposal for choosing the form of the
arches in the straight-wire tecnique, based on both the anatomic
individuality and the aims of the treatment. Rev Clin Ortodon
Dental Press 2004;3:84-92.
12. Scott JH. The shape of the dental arches. J Dent Res 1957;36:
996-1003.
13. Engel GA. Preformed arch wires: reliability of fit. Am J Orthod
1979;76:497-504.
14. Currier JH. A computerized geometric analysis of human dental
arch form. Am J Orthod 1969;56:164-79.
15. Biggerstaff RH. Three variations in dental arch form estimated
by a quadratic equation. J Dent Res 1972;51:1509.
16. Izard G. New method for the determination of the normal arch by
the function of the face. Int J Orthod Oral Surg Radiog 1927;13:
582-95.
17. Brader AC. Dental arch form related with intraoral forces: PR ⫽
C. Am J Orthod 1972;61:541-61.
18. Bonwill WGA. The scientific articulation on the human teeth as
founded on geometrical, mathematical and mechanical laws.
Dent Items Interest 1899;21:617-43.
10.e22 Triviño, Siqueira, and Scanavini
American Journal of Orthodontics and Dentofacial Orthopedics
January 2008
19. Sved A. Mathematics of the normal dental arch. Dent Cosmos
1917;59:1116-24.
20. Savostin-Asling I. The geometric analysis of mandibular dental
arch form. Ann Dent 1980;39:3-11.
21. Ricketts RM. Provocations and perceptions in cranio-facial
orthopedics. Dental science and facial art— book 1 (part 2).
Denver: Rocky Mountain Orthodontics; 1989. p. 686-711.
22. Raberin M, Laumon B, Martin JL, Brunner F. Dimensions and
form of dental arches in subjects with normal occlusions. Am J
Orthod Dentofacial Orthop 1993;104:67-72.
23. Telles FS. Contour diagrams: presentation of a new contour
diagram. Rev Soc Parana Ortodon 1995/96;1:29-36.
24. McLaughlin R, Bennett J, Trevisi H. MBT™ arch form and
archwire sequencing—part 2. Rev Dent Press Ortodon Ortopedi
Facial 1998;3:39-48.
25. Noroozi H, Nik TH, Saeeda RBS. The dental arch form revisited.
Angle Orthod 2001;71:386-9.
26. Triviño T, Vilella OV. Forms and dimensions of the lower dental
arch. Rev Soc Bras Ortodon 2005;5:19-28.
27. BeGole EA. Application of the cubic spline function in the
description of dental arch form. J Dent Res 1980;59:1549-56.
28. Valenzuela PA, Pardo MA, Yezioro S. Description of dental arch
form using the Fourier series. Int J Adult Orthod Orthognath
Surg 2002;17:59-65.
29. Taner T, Ciger S, El H, Germeç D, Es A. Evaluation of dental
arch width and form changes after orthodontic treatment and
retention with a new computerized method. Am J Orthod
Dentofacial Orthop 2004;126:464-76.
30. Kageyama T, Domínguez-Rodríguez GC, Vigorito JW, Deguchi
T. A morphological study of the relationship between arch
dimensions and craniofacial structures in adolescents with Class
II Division 1 malocclusions and various facial types. Am J
Orthod Dentofacial Orthop 2006;129:368-75.
31. Nie Q, Lin J. A comparison of dental arch forms between Class
II Division 1 and normal occlusion assessed by euclidean
distance matrix analysis. Am J Orthod Dentofacial Orthop
2006;129:528-35.
Lu KH. An orthogonal analysis of the form, symmetry, and
asymmetry of the dental arch. Arch Oral Biol 1966;11:1057-69.
Sanin C, Savara BS, Thomas DR, Clarkson QD. Arc length of
the dental arch estimated by multiple regression. J Dent Res
1970;49:885.
Pepe SH. Polynomial and catenary curve fits to human dental
arches. J Dent Res 1975;54:1124-32.
Hechter FJ. Symmetric and dental arch form of orthodontically
treated patients. J Can Dent Assoc 1978;44:173-84.
Ferrario VF, Sforza C, Miani AJ, Tartaglia G. Mathematical
definition of the shape of dental arches in human permanent
healthy dentitions. Eur Orthod Soc 1994;16:287-94.
Wakabayashi K, Sohmura T, Takahashi J, Kojima T, Akao T,
Nakamura T, et al. Development of the computerized dental cast
form analyzing system—three dimensional diagnosis of dental
arch form and the investigation of measuring condition. Dent
Mater J 1997;16:180-90.
Ferrario VF, Sforza C, Dellavia C, Colombo A, Ferrari RP.
Three-dimensional hard tissue palatal size and shape: a 10-year
longitudinal evaluation in healthy adults. Int J Adult Orthod
Orthognath Surg 2002;17:51-8.
Andrews LF. The six keys to normal occlusion. Am J Orthod
1972;62:296-309.
Houston WJB. The analysis of errors in orthodontic measurements. Am J Orthod 1983;83:382-90.
Roden-Johnson D, Gallerano R, English J. The effects of buccal
corridor spaces and arch form on smile esthetics. Am J Orthod
Dentofacial Orthop 2005;127:343-50.
Angle EH. The lastest and best in orthodontic mechanism. Dent
Cosmos 1928;52:1143-58.
Chuck GC. Ideal arch form. Angle Orthod 1934;4:312-27.
Boone GN. Archwires designed for individual patients. Angle
Orthod 1963;33:178-85.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.