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INDIAN DENTAL ACADEMY Leader in continuing dental education www.indiandentalacademy.com
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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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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). www.indiandentalacademy.com
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. www.indiandentalacademy.com
Bracket height gauze was used to suitably mark the labial and buccal surfaces of the teeth from second molar to second molar.
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Points were marked on the facial surfaces at the bracket placement points for measurement of the co-ordinate points.
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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.
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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.
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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. www.indiandentalacademy.com
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.
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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
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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
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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.
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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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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). www.indiandentalacademy.com
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. www.indiandentalacademy.com
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
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5. Lancer Orthodontics
TABLE CURVE 2D Automated curve fitting software and equation discovery Version 5.01
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Importing basic data, X and Y co-ordinate values of selected points
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Linear graph joining co-ordinate points
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Selecting Beta function from the list of equations
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Curve fitted using Beta function
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Comparing two curves overlapping them one over enother
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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 www.indiandentalacademy.com
Archform Co-ordination observed between different preformed Rectangular Nickel titanium arch wires SIA Orthodontics Natural Shape Good Coordination of Maxillary and mandibular archform
Ortho Organizers Nitanium Archwires Good Coordination of Maxillary and mandibular archform www.indiandentalacademy.com
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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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 www.indiandentalacademy.com
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. www.indiandentalacademy.com
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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
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