Monday, 24 May 2010
Sunday, 23 May 2010
http://www.storage.to/get/7w9X7BVP/King.Of.Movie.MTV.Splitsvilla.3.EP3.2.1.10.avi.001
http://www.storage.to/get/s6C2eWyo/King.Of.Movie.MTV.Splitsvilla.3.EP3.2.1.10.avi.002
http://www.storage.to/get/WjUel0Am/King.Of.Movie.MTV.Splitsvilla.3.EP3.2.1.10.avi.003
http://www.storage.to/get/MDJiX2ce/King.Of.Movie.MTV.Splitsvilla.3.EP3.2.1.10.avi.004
http://www.storage.to/get/nxNdXlPj/King.Of.Movie.MTV.Splitsvilla.3.EP3.2.1.10.avi.005
http://www.storage.to/get/aByjGee9/King.Of.Movie.MTV.Splitsvilla.3.EP3.2.1.10.avi.006
Monday, 17 May 2010
Wednesday, 12 May 2010
Tuesday, 11 May 2010
Monday, 10 May 2010
Sunday, 9 May 2010
Angle Orthodontist, Vol 71, No 5, 2001 386
Original Article
The Dental Arch Form Revisited
Hassan Noroozi, DDS, MSca; Tahereh Hosseinzadeh Nik, DDS, MScb; Reza Saeeda, BS, MSc
Abstract: Recently, the beta function has been shown to be an accurate mathematical model of the
human dental arch. In this research, we tried to find the equation of a curve that would be similar to the
generalized beta function curve and at the same time could represent tapered, ovoid, and square dental
arches. A total of 23 sets of naturally well-aligned Class I casts were selected, and the depths and widths
of the dental arches were measured at the canine and second molar regions. Using the mean depths and
widths, functions in the form of Y 5 AXm 1 BXn were calculated that would pass through the central
incisors, canines, and second molars. Each function was compared with the generalized beta function with
the use of root mean square values. It was shown that the polynomial function Y 5 AX6 1 BX2 was the
nearest to the generalized beta function. Then the coordinates of the midincisal edges and buccal cusp tips
of each dental arch were measured, and the correlation coefficient of each dental arch with its corresponding
sixth order polynomial function was calculated. The results showed that the function Y 5 AX6 1 BX2
could be an accurate substitute for the beta function in less common forms of the human dental arch.
(Angle Orthod 2001;71:386–389.)
Key Words: Arch form; Beta function; Equation; Formula; Polynomial; Correlation coefficient
INTRODUCTION
Many geometric forms and mathematical functions have
been proposed as models of the human dental arch.1–25
However, it has become clear that the models defined by 1
parameter cannot describe the dental arch form accurately.26
Recently, it has been shown that the human dental arch
form is accurately represented mathematically by the beta
function.27 Two parameters, the depth and the width of the
dental arch at the second molar region, define this model.
When using the beta function model, if the measured value
for width is increased 1 mm and the measured value of
depth increased 1.5 mm, the resulting equation will be an
excellent representation of the dental arch shape, including
the second molars. In addition, it will be an excellent generalized
equation of the maxillary and mandibular arch
shapes for each of the Angle classifications of occlusions.27
We see naturally well-aligned human dental arches with
different shapes. They are roughly categorized as square,
ovoid, and tapered in prosthodontics. Although these arch
a Researcher, Department of Orthodontics, Faculty of Dentistry,
University of Tehran, Tehran, Iran.
b Professor, Department of Orthodontics, Faculty of Dentistry, University
of Tehran, Tehran, Iran.
c Researcher, Department of Mechanical Engineering, Faculty of
Engineering, University of Tehran, Tehran, Iran.
Corresponding author: Hassan Noroozi, DDS, MSc, 3.15 Bazgeer
Alley, Karoon Street, Azadi Avenue, Tehran, Iran l354865611
(e-mail: Noroozih@yahoo.com).
Accepted: February 2001. Submitted: August 2000.
q 2001 by The EH Angle Education and Research Foundation, Inc.
forms have not yet been accurately defined, they do exist
in nature.28
We tried to present a model that is defined by 4 parameters,
ie, by the depths and widths of the dental arch at the
canine and second molar regions. Such a model will be
flexible at the anterior as well as posterior regions of a
dental arch. Many mathematical models can be found that
are defined by these 4 parameters, but we tried to find the
one that is more compatible with the beta function and,
consequently, with the dental arch. Therefore, this model,
while representing the dental arch with high accuracy, will
represent the square and tapered dental arches as well as
ovoid ones.
MATERIALS AND METHODS
Twenty-three sets of pretreatment orthodontic models of
fully developed Class I dentitions were selected. Casts exhibiting
attrition, fracture, ectopic eruption, crowding, or
midline deviations were not included. The depths and
widths of the dental arches at the canine and second molar
regions were measured using an electronic gauge with an
accuracy of 0.1 mm. The depths and widths were defined
as follows:
1. intersecond molar width (Wm): distance between the
distobuccal cusp tips of the second molars,
2. intercanine width (Wc): distance between the canine
cusp tips,
3. second molar depth (Dm): distance between the contact
DENTAL ARCH FORM REVISITED 387
Angle Orthodontist, Vol 71, No 5, 2001
TABLE 1. Root Mean Square (RMS) Values of the Calculated Functions;
for Odd Powers, the Absolute Value of x Was Used
Function Maxillary RMS Mandibular RMS Mean
FIGURE 1. (A) Maxillary and (B) mandibular curves of the generalized
beta function and the equation y 5 ax6 1 bx2 for the mean
measured data.
of the central incisors and a line that connects the distobuccal
cusp tips of the second molars,
4. canine depth (Dc): distance between the contact of the
central incisors and a line that connects the canine cusp
tips.
Two operators measured each distance and, when there
was a difference between the measurements of the 2 operators,
the mean value was used. The mean depths and
widths were calculated for the maxillary and mandibular
casts, respectively. The values of A and B in the formula
Y(m, n) 5 AXm 1 BXn were calculated so that the curve of
this formula would pass exactly through the contact of the
central incisors, canine cusp tips, and the distobuccal cusp
tips of the second molars. The values were calculated using
the mean depths and widths of the dental arches.
Then the corresponding maxillary and mandibular generalized
beta functions were calculated using the mean
depths and widths of the dental arches. Using this method,
different formulas of the form Y(m, n) 5 AXm 1 BXn were
calculated. All of the resulting formulas represented the
curves that would exactly pass through the contact of the
central incisors, canine cusp tips, and the distobuccal cusp
tips of the second molars.
To find the formula that is most similar to the beta function—
and consequently to the dental arch—we calculated
the root mean square values (RMS). RMS is the standard
mathematical tool by which the similarity of 2 curves is
evaluated (the more the similarity of 2 curves, the lower
the value of the RMS).
A computer program was written to calculate the values
of A, B, and RMS for each of the Y(m, n) functions. The
calculations showed that Y(6, 2) was the nearest to the beta
function (Table 1). As the next step, the occlusal surfaces
of all the casts were photocopied (Xerox 1050, Rank Xerox
Ltd) with a 100-mm ruler in the field to allow for calculation
of enlargement.
Measurement of the 100-mm ruler image in each photocopy
revealed that the copier resulted in an average enlargement
of the image of 4%, which was not statistically
significant.29 The reliability of the use of photocopies of the
occlusal surfaces of dental models has been demonstrated
previously.29 The photocopies were scanned using a flatbed
transparency scanner (Genius Vivid III, Rank Xerox Ltd),
and a digital image of the occlusal surface of each cast was
prepared.
These digital images were transferred to AutoCAD environment
(1982–1999 AutoDesk, Inc), and the coordinates
of the midincisal edges and buccal cusp tips of all the teeth
were determined. Then the polynomial function (in the
form of Y 5 AX6 1 BX2) corresponding to each dental arch
was determined, and the correlation coefficient between
each dental arch and its corresponding sixth order polyno388
NOROOZI, NIK, SAEEDA
Angle Orthodontist, Vol 71, No 5, 2001
mial function was calculated. The coordinates of 18 points
on each dental arch (ie, midincisal edges and buccal cusp
tips of the teeth) were used to calculate the correlation coefficient.
RESULTS
The values of RMS are shown in Table 1 and the correlation
coefficients are presented in Table 2. It is seen that
the RMS of Y(6, 2) is the smallest value and Y(5, 2) and
Y(4, 2) take the next positions (Figure 1). As is seen in
Table 2, the mean correlation coefficient is 0.98 with a standard
deviation of 0.02.
DISCUSSION
The reader might reasonably ask why this research did
not deal with equations of greater degrees. One might assume
that, if y 5 ax6 1 bx2 is a good approximation, equations
of greater degrees should be even better. In theory,
this is quite true. Theoretically, there exists a unique polynomial
equation of degree n 1 1 or less (where n is the
number of data points) that will fit the data exactly. Such
curves accurately fit the data points, but they tend to be
wavy rather than smooth. As n increases, the likelihood of
obtaining a completely accurate curve fit without this wavelike
property is reduced to nearly zero. Even if a smooth
curve of high degree could be obtained, measurement errors
and round-off error make such computations unwieldy, if
not altogether impossible.21 In fact, we examined all polynomial
functions (in the form of y 5 axm 1 bxn) of degree
less than or equal to 10, but for this reason and for the sake
of brevity, they are not included in the results. Here, these
5 points (ie, the contact of the central incisors, canine cusp
tips, and the distobuccal cusp tips of the second molars)
are similar to the knots of a cubic spline function23 and we
chose the form of y 5 axm 1 bxn because it could be accurately
adjusted to pass through these 5 points.
The high correlation coefficient shows that this function
can be an accurate mathematical model of the dental arch.
However, it should be noticed that this study has been performed
on Class I cases and further studies are needed to
determine the fitness of this function for Class II and Class
III occlusions.
The square, ovoid, and tapered arch forms have not yet
been mathematically defined. One solution may be to define
them based on the relative ratios of the canine and the second
molar cross-arch widths along with their relative arch
depths.
When the Wc/Wm ratio increases or the Dc/Dm ratio
decreases, the arch becomes squarer. On the contrary, when
Wc/Wm ratio decreases or Dc/Dm ratio increases, the arch
gets a more tapered form. Therefore, the (Wc/Wm) 3 (Dc/
DENTAL ARCH FORM REVISITED 389
Angle Orthodontist, Vol 71, No 5, 2001
Dm)21 ratio may be able to describe the arch form. When
this ratio of a dental arch is within the range of mean 6 1
SD, we can assume the arch form is ovoid. However, when
this ratio for an arch form is more than mean 1 1 SD (eg,
casts 18, 21, 23), we can consider the arch form as square.
Finally, when the ratio is less than mean 1 1 SD (eg, casts
4, 14), we can consider the arch form as tapered.
It has been shown that the beta function alone is insufficient
to accurately describe an expanded dental arch approximating
the square arch form. Consequently, the arch
form is described by 2 equations, ie, the hyperbolic cosine
function for the 6 anterior teeth and the beta function for
the posterior teeth.30 By the sixth power function presented
here, such an arch form may be defined by only 1 equation.
CONCLUSION
By measuring the 4 parameters of a dental arch (ie, Dc,
Wc, Dm, and Wm), one can simply calculate the y 5 ax6
1 bx2 corresponding to the dental arch. The curve of this
equation can be wide or narrow in the anterior as well as
posterior regions of a dental arch and so can be an accurate
substitute for the beta function in less common, ie, square
or tapered, forms of the human dental arch.
REFERENCES
1. Angle EH. Classification of malocclusion. Dent Cosmos. 1899;
41:264–284.
2. Broomell IN. Anatomy and Histology of the Mouth and Teeth.
2nd ed. Philadelphia, Pa: Blakiston; 1902:99.
3. Hawley CA. Determination of the normal arch and its applications
to orthodontia. Dent cosmos. 1905;47:541–552.
4. Stanton ER. Arch predetermination and a method of relating the
predetermined arch to the malocclusion to show the minimum
tooth movement. Int J Orthod. 1922;8:757–778.
5. Izard G. New method for the determination of the normal arch
by the function of the face. Int J Orthod. 1927;13:582–595.
6. McConaill MA, Scher EA. Ideal form of the human dental arcade
with some prosthetic applications. Dent Rec. 1949;69:285–302.
7. Sved A. The application of engineering methods to orthodontics.
Am J Orthod. 1952;38:399–421.
8. Scott JH. The shape of the dental arches. J Dent Res. 1957;36:
966–1003.
9. Sicher H. Oral Anatomy. 3rd ed. St Louis, Mo: Mosby; 1960:
269–270.
10. Hayashi T. A mathematical analysis of the curve of the dental
arch. Bull Tokyo Med Dent Univ. 1962;3:175–218.
11. Diggs DB. The Quantification of Arch Form [master’s thesis].
Seattle, Wash: University of Washington; 1962.
12. Mills LF, Hamilton PM. Epidemiological studies of malalignment,
a method for computing arch circumference. Angle Orthod. 1965;
35:244–248.
13. Lu KH. An orthogonal analysis of the form, symmetry and asymmetry
of the dental arch. Arch Oral Biol. 1966;11:1057–1069.
14. Burdi AR, Lillie JH. Catenary analysis of the maxillary dental
arch during human embryogenesis. Anat Rec. 1966;154:13–20.
15. Burdi AR. Morphogenesis of mandibular dental arch shape in
human embryos. J Dent Res. 1968;47:50–58.
16. Currier JH. A computerized geometric analysis of the human dental
arch form. Am J Orthod. 1969;56:164–179.
17. Sanin C, Savara BS, Thomas DR, Clarkson OD. Arch length of
the dental arch estimated by multiple regression. J Dent Res.
1970;49:885.
18. Biggerstaff RH. Three variations in dental arch form estimated
by a quadratic equation. J Dent Res. 1972;51:1509.
19. Brader AC. Dental arch form related with intraoral forces: PR 5
C. Am J Orthod. 1972;62:541–561.
20. Biggerstaff RH. Computerized dentition analyses and simulations.
In: Cook TJ, ed. Proceedings of the Third Orthodontic Congress.
St Albans, UK: Crosby Lockwood Staples; 1975;27–25.
21. Pepe SH. Polynomial and catenary curve fits to human dental
arches. J Dent Res. 1975;54:1124–1132.
22. Hechter FJ. Symmetry and dental arch form of orthodontically
treated patients. J Can Dent Assn. 1978;44:173–184.
23. Begole EA. Application of the cubic spline function in the description
of dental arch form. J Dent Res. 1980;59:1542–1556.
24. Isaacson KG, Williams JK. An Introduction to Fixed Appliances.
London, UK: John Wright and Sons Ltd; 1984:88–90.
25. Germane N, Lindauer SJ, Rubenstein LK, Revere JH, Isaacson
RJ. Increase in arch perimeter due to orthodontic expansion. Am
J Orthod Dentofacial Orthop. 1991;100:421–427.
26. Felton JM, Sinclair PM, Jones DL, Alexander RG. A computerized
analysis of the shape and stability of mandibular arch form.
Am J Orthod Dentofacial Orthop. 1987;92:478–483.
27. Braun S, Hnat WP, Fender DE, Legan HL. The form of the human
dental arch. Angle Orthod. 1998;68:29–36.
28. Hickey JC, Zarb GA, Bolender CL. Boucher’s Prosthodontic
Treatment for Edentulous Patients. St Louis, Mo: CV Mosby;
1985:397.
29. BeGole EA, Fox DL, Sadowsky C. Analysis of change in arch
form with premolar expansion. Am J Orthod Dentofacial Orthop.
1998;113:307–315.
30. Hnat WP, Braun S, Chinhara A, Legan HL. The relationship of
arch length to alterations in dental arch width. Am J Orthod Dentofacial
Orthop. 2000;118:184–188.
Saturday, 8 May 2010
Friday, 7 May 2010
log in to my blog at http://am1502-europeview.blogspot.com write to me if students from anwhr would like to have information or queries ,as i can do my best to help
Subscribe to:
Comments (Atom)
.jpg)
