Correlation of the arch forms of male and female subjects with those of preformed rectangular nickel-titanium archwires

Introduction

This investigation was carried out to correlate the normal arch forms of male and female subjects derived mathematically by the beta function with commercially available preformed rectangular nickel-titanium archwires.

Methods

The mathematical beta function was used to derive planar projections of natural archforms by using the spatial coordinates of the labial bracket interfacing surfaces in the maxillary and mandibular arches of both sexes. Graphic planar representations of corresponding bracket base spatial coordinates of archforms of 30 popular rectangular nickel-titanium archwire-bracket assemblies (derived through the same mathematical function) were superimposed on relevant maxillary and mandibular arches.

Results

The rectangular nickel-titanium archwire-bracket assemblies exceeded the intercanine width by averages of 7.159 mm in the maxillary arches of females, 6.289 mm in the maxillary arches of males, 6.667 mm in the mandibular arches of females, and 5.337 mm in the mandibular arches of males. The average intermolar width exceeded the natural width by 2.893 mm in the maxillary arches and 1.861 mm in the mandibular arches. The average intermolar-intercanine width ratios for natural arches (2.11 for mandibular and 1.75 for maxillary) were greater than the ratios for the wire-bracket assemblies (1.78 for mandibular and 1.53 for maxillary).

Conclusions

The prefomed rectangular nickel-titanium archwires might result in wider arch forms. The intercanine width difference is greater than the intermolar width. The differences were more pronounced for arches in female subjects compared with those in males. These findings influence posttreatment retention, stability, and facial esthetics. A subsequent change to stainless steel wires to restore a more natural form and size can lead to round tripping and increased treatment duration.

Archwires are the vital and instrumental components of fixed orthodontic treatment. They store and deliver power through the brackets and bands to the teeth and surrounding tissues. Improperly shaped archwires create and contribute to many posttreatment problems. Unplanned contraction or expansion, especially in the canine or molar regions, produces instability.

With the advent of highly elastic nickel-titanium preformed archwires, the clinician can often introduce larger cross-section rectangular wires in the early stages of leveling and alignment. Nickel-titanium archwires exhibit exceptional springiness, but wire bending in the classical sense (or the formability of the wire) is poor because they do not undergo plastic deformation until high forces are applied.

The initial nickel-titanium archwires (0.014 or 0.016 in) used for leveling and alignment exert light forces and are usually tied for short periods. They can be expected to have little influence on the arch form, since their forms are often temporarily distorted from tying on malaligned teeth. As the teeth align and the treatment progresses, heavier rectangular nickel-titanium or heat-activated nickel-titanium followed by stainless steel archwires are used. They have greater tensile strength and are used for longer times, resulting in more influence on the arch form.

The rectangular nickel-titanium archwires of 0.017 × 0.025 in and 0.019 × 0.025 in can permanently alter the arch form if tied for longer periods. This could be a significant factor in determining posttreatment retention and stability. The mandibular intercanine and intermolar widths are accurate indexes of the muscular balance inherent in each patient and dictate the limits of arch expansion during treatment. They are important to establish and maintain proper functional balance as an aid in treating and retaining orthodontic patients.

The dental arch form is initially shaped by the configuration of the supporting bone. After the eruption of teeth, the circumoral musculature and intraoral functional forces have significant influences over the arch form. The principal clinical factors that affect a patient’s arch form and dimensions are dental perimeter, cross-arch width, and arch depth ( Fig 1 ). An analytical equation of dental arch shape is necessary to describe the relationship between arch width, depth, and perimeter, which influence the arch form.

Fig 1
Dental arch shape with variables of arch width, depth, and perimeter that determine the arch form.

The occlusal views of dental arches in an Angle Class I occlusion have been described by the mathematical beta function with average correlation coefficients of 0.98 for the mandible and 0.97 for maxilla. The beta function is shown to be an accurate representation of planar projections of natural arch forms defined by spatial coordinates of labial bracket interfacing surfaces in maxillary and mandibular arches.

This study was undertaken to correlate the arch forms of Angle Class I normal occlusion and various archwire-bracket assemblies derived by the beta function in their form and dimension. The intercanine and intermolar widths of natural arch forms were compared with those of rectangular nickel-titanium archwire-bracket assemblies in the maxillary and mandibular arches of both sexes.

Material and methods

Orthodontic models of maxillary and mandibular arches of 20 male and 20 female subjects with normal occlusions were selected as the control groups from approximately 2500 students in Sawangi, Wardha, India. The control groups belonged to different ethnic groups of the Indian population, with various arch forms and sizes. The inclusion criteria were Angle Class I molar and canine relationships, normal overbite and overjet, and well-aligned arches with the second molars in occlusion. Models with attrition, fractured teeth, ectopically erupted teeth, deciduous teeth, and arch length deficiency greater than 3 mm were excluded. The control groups were female maxillary, female mandibular, male maxillary, and male mandibular arches.

A bracket height gauge was used to mark the bracket placement points on the labial surfaces of the teeth. Points were marked at the center of the tooth incisogingivally and mesiodistally along the long axis ( Fig 2 ). Each cast was oriented in a Microval Co-ordinate Measuring Microscope (Nikon, Tokyo, Japan ) for determining the coordinates of bracket placement points ( Fig 3 ). This device is used in the machine tool industry to measure the precision of parts with an accuracy of 0.001 mm. The linear accuracy of the machine is 0.006 mm, and reproducibility is 0.004 mm.

Fig 2
Marking of bracket placement points.

Fig 3
Oriented model in the measuring microscope.

The casts were secured to a fixed plane, and an optical beam was used to identify the 14 points. The corresponding x, y, and z coordinates were stored automatically in a computer data file. Coordinates of a point in space in 3 orthogonal axes were measured up to 1 μm. The curve fitting program (table curve 2-dimensional version 5.1; Systat Software, Chicago, Ill) was used to apply mathematical beta function (with the least squares method) to process the measured x and y coordinates. The z coordinates were reduced to zero to obtain planar projections of each point. The values were fed into the software, and the beta function was selected from the equation list for data processing and to derive uniform bilaterally symmetrical arch forms representing natural arch forms.

The average correlation coefficient between the dimensions measured on the models and the mathematical arch forms expressed by the beta function was 0.97 (SD 0.03) ( Tables I and II ). By using the average correlation coefficient as a measure of fit, the natural dental arch form is accurately represented mathematically by the beta function as also seen in previous studies. Therefore, the beta function was used to derive accurate planar projections of dental arch forms by using the coordinates of the bracket placement points. These arch forms were used for correlation with arch forms of 0.019 × 0.025-in rectangular nickel-titanium wire-bracket assemblies derived by the beta function.

Table I
Correlation of intercanine and intermolar widths and arch depth of bracket coordinates in the maxillary and mandibular arches of female subjects with the beta function
Sample Measured values (mm) Curve fit values (mm) Correlation
Intercanine width Intermolar width Depth Intercanine width Intermolar width Depth Coefficient
Maxilla
1 32.007 57.415 42.019 32.319 58.021 42.21 0.97
2 31.216 55.616 41.987 31.645 56.104 42.707 0.96
3 32.412 57.853 41.843 32.716 58.757 42.201 0.99
4 32.179 55.813 40.758 32.948 55.915 41.201 0.98
5 33.769 57.314 42.719 34.143 57.925 43.371 0.96
6 35.016 60.879 39.716 35.216 61.425 40.371 0.97
7 31.142 54.119 42.014 31.416 54.724 42.864 0.96
8 34.207 57.614 38.713 34.916 58.124 39.971 0.98
9 36.715 59.143 40.219 37.103 60.215 41.371 0.98
10 31.204 59.463 39.142 31.716 60.224 39.864 0.96
11 32.312 57.216 43.714 32.977 58.106 44.154 0.96
12 34.109 57.515 41.649 34.716 58.216 42.054 0.97
13 28.757 54.719 41.463 29.157 55.216 42.865 0.98
14 32.216 60.763 39.012 32.849 61.931 39.864 0.98
15 34.191 57.419 41.613 34.716 58.345 42.054 0.97
16 34.012 58.213 41.253 34.571 58.941 42.058 0.96
17 31.012 55.814 40.257 31.679 56.745 40.864 0.96
18 34.107 60.713 40.531 34.519 61.025 41.371 0.98
19 31.218 56.771 42.143 31.847 57.214 42.701 0.97
20 31.129 54.121 41.693 31.519 54.781 42.154 0.96
Average 32.65 57.42 41.12 33.13 58.10 41.81 0.97
SD 1.83 2.05 1.30 1.83 2.14 1.19 0.03
SEM 0.41 0.46 0.29 0.41 0.48 0.27 0.01
Maximum 36.71 60.88 43.71 37.10 61.93 44.15 0.99
Minimum 28.76 54.12 38.71 29.16 54.72 39.86 0.96
Mandible
1 24.213 51.718 38.027 24.816 52.241 38.514 0.98
2 24.131 51.415 36.857 24.619 52.247 37.956 0.98
3 25.017 55.614 36.219 25.413 56.104 36.701 0.96
4 24.867 51.713 39.016 25.013 52.147 39.167 0.96
5 25.105 54.721 36.845 25.419 55.021 37.228 0.97
6 26.213 58.137 39.147 26.701 59.051 39.824 0.98
7 24.315 51.713 37.916 24.859 52.051 38.686 0.97
8 26.191 54.619 38.153 26.512 55.051 38.824 0.96
9 26.314 54.859 34.819 26.814 55.284 35.239 0.97
10 27.131 55.613 36.913 27.456 56.121 37.199 0.95
11 25.814 51.783 33.857 26.219 53.184 34.439 0.96
12 26.138 54.783 35.716 26.598 55.284 36.239 0.96
13 21.949 51.649 36.413 22.017 52.213 37.236 0.97
14 25.513 57.413 38.71 26.014 58.741 39.239 0.97
15 27.716 54.615 36.014 28.151 55.787 37.839 0.97
16 25.312 53.714 37.914 25.819 54.159 38.139 0.98
17 26.413 54.106 37.013 26.713 54.253 37.647 0.98
18 27.013 56.213 38.814 27.431 57.105 38.641 0.97
19 22.813 53.141 37.615 22.859 53.841 38.849 0.98
20 23.817 50.014 32.143 24.314 50.147 33.167 0.98
Average 25.30 53.88 36.91 25.69 54.50 37.54 0.97
SD 1.45 2.19 1.79 1.52 2.32 1.70 0.03
SEM 0.33 0.49 0.40 0.34 0.52 0.38 0.01
Maximum 27.72 58.14 39.15 28.15 59.05 39.82 0.98
Minimum 21.95 50.01 32.14 22.02 50.15 33.17 0.95

SEM , Standard error of the mean.

Table II
Correlation of intercanine and intermolar widths and arch depth of bracket coordinates in the maxillary and mandibular arches of male subjects with the beta function
Sample Measured values (mm) Curve fit values (mm) Correlation
Intercanine width Intermolar width Depth Intercanine width Intermolar width Depth Coefficient
Maxilla
1 34.103 59.814 42.919 34.639 60.714 43.169 0.98
2 33.219 57.396 42.349 33.714 58.153 43.614 0.98
3 32.413 56.514 43.215 32.749 57.214 44.674 0.98
4 36.747 60.819 42.267 37.143 61.216 43.674 0.98
5 34.103 61.413 45.213 34.913 61.874 46.716 0.98
6 32.219 58.014 41.945 32.839 58.241 43.064 0.98
7 32.314 57.894 44.394 32.914 58.357 45.641 0.98
8 32.105 58.716 45.218 32.216 59.315 46.314 0.99
9 31.716 58.013 43.129 32.082 58.837 44.214 0.98
10 34.716 58.127 39.142 35.216 59.537 40.674 0.97
11 36.107 59.418 46.746 36.419 60.061 46.917 0.99
12 34.213 58.231 43.149 34.713 58.968 44.215 0.97
13 35.357 59.213 44.314 35.813 60.219 45.016 0.96
14 32.814 58.761 42.371 33.256 59.662 42.914 0.97
15 32.747 56.649 42.764 33.143 57.214 43.641 0.98
16 33.216 55.213 43.214 33.813 56.153 44.215 0.98
17 35.014 59.613 43.974 35.649 60.153 44.687 0.99
18 32.987 58.713 46.461 33.413 59.147 47.214 0.97
19 32.659 57.216 46.741 33.143 58.143 46.971 0.97
20 31.807 57.103 42.641 32.219 57.419 42.914 0.98
Average 33.53 58.34 43.61 34.00 59.03 44.52 0.97
SD 1.45 1.48 1.85 1.48 1.46 1.70 0.03
SEM 0.33 0.33 0.41 0.33 0.33 0.38 0.01
Maximum 36.75 61.41 46.75 37.14 61.87 47.21 0.99
Minimum 31.72 55.21 39.14 32.08 56.15 40.67 0.96
Mandible
1 27.945 56.719 38.103 28.143 57.413 38.413 0.97
2 25.341 55.614 35.917 25.817 56.419 36.416 0.98
3 28.164 57.107 36.914 28.716 57.654 37.814 0.98
4 27.264 54.715 37.213 27.614 55.025 37.819 0.96
5 27.647 55.915 39.214 28.103 56.314 40.215 0.96
6 26.814 53.613 37.814 27.417 53.707 38.814 0.96
7 27.914 53.719 37.614 28.513 54.959 38.271 0.97
8 27.641 53.615 33.716 28.115 54.819 34.291 0.97
9 28.146 57.412 38.416 28.716 58.012 39.145 0.95
10 27.846 57.615 40.215 28.315 58.214 40.697 0.97
11 27.761 54.197 39.614 28.149 54.942 40.215 0.96
12 27.209 55.012 40.716 27.769 55.553 41.678 0.95
13 27.461 53.007 38.214 28.144 53.009 39.845 0.98
14 23.016 55.127 40.159 23.412 55.713 41.023 0.98
15 25.541 57.614 37.2154 26.017 58.149 37.841 0.98
16 22.914 57.293 34.974 23.213 57.913 35.417 0.97
17 24.612 57.614 41.697 25.597 58.916 42.614 0.97
18 27.106 59.615 39.146 27.763 60.521 39.941 0.98
19 25.314 56.549 38.645 25.897 57.743 39.745 0.98
20 24.136 58.715 37.415 24.913 58.917 38.413 0.98
Average 26.54 56.04 38.15 27.02 56.70 38.93 0.97
SD 1.75 1.87 1.93 1.70 1.95 2.04 0.03
SEM 0.39 0.42 0.43 0.38 0.44 0.46 0.01
Maximum 28.16 59.62 41.70 28.72 60.52 42.61 0.98
Minimum 22.91 53.01 33.72 23.21 53.01 34.29 0.94
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Apr 8, 2017 | Posted by in Orthodontics | Comments Off on Correlation of the arch forms of male and female subjects with those of preformed rectangular nickel-titanium archwires
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